Asymmetric magma plumbing system beneath Axial Seamount based on full waveform inversion of seismic data

Domain: earth_science
Published: 2024-06-04
Editorial outcome: major_revision

Abstract
The architecture of magma plumbing systems plays a fundamental role in volcano eruption and evolution. However, the precise configuration of crustal magma reservoirs and conduits responsible for supplying eruptions are difficult to explore across most active volcanic systems. Consequently, our understanding of their correlation with eruption dynamics is limited. Axial Seamount is an active submarine volcano located along the Juan de Fuca Ridge, with known eruptions in 1998, 2011, and 2015. Here we present high-resolution images of P-wave velocity, attenuation, and estimates of temperature and partial melt beneath the summit of Axial Seamount, derived from multi-parameter full waveform inversion of a 2D multi-channel seismic line. Multiple magma reservoirs, including a newly discovered western magma reservoir, are identified in the upper crust, with the maximum melt fraction of ~15–32% in the upper main magma reservoir (MMR) and lower fractions of 10% to 26% in other satellite reservoirs. In addition, a feeding conduit below the MMR with a melt fraction of ~4–11% and a low-velocity throat beneath the eastern caldera wall connecting the MMR roof with eruptive fissures are imaged. These findings delineate an asymmetric shallow plumbing system beneath Axial Seamount, providing insights into the magma pathways that fed recent eruptions.

Introduction
The Juan de Fuca Ridge (JdFR) is an oceanic spreading center in the northeast Pacific Ocean with an intermediate spreading rate ~5.6 cm/year1–3. The most prominent feature on the JdFR is Axial Seamount (Fig. 1a), an active submarine volcano with a summit rising ~1 km above the adjacent seafloor and a narrow 11-km-deep crustal root4,5. Because of enhanced magma supply from the juxtaposition of the Cobb hotspot and the JdFR6, Axial Seamount is volcanically active, with known eruptions in 1998, 2011, and 20157–9. Intensive studies of this submarine volcano since the 1990s have monitored its activity and revealed aspects of its underlying magmatic system. For instance, a refraction tomography study in 2001 using ocean-bottom seismometers (OBSs) imaged a 250-km3 low velocity zone beneath Axial Seamount10. Later, multi-channel seismic (MCS) experiments refined this model and identified two large elongated low-velocity magma reservoirs5,11: a 14-km long, 3-km wide, and up-to-1-km thick main magma reservoir (MMR) with a roof ~1.1–2.3 km beneath the summit caldera, and a secondary magma reservoir (SMR) beneath the eastern shoulder of the volcano (Fig. 1). In addition, below the southern end of the MMR, a vertical stack of melt sills were imaged between 2.5 and 4.5 km below the seafloor (bsf) within a 3–5-km-wide mush feeder conduit, providing new insights into magma accumulation and transport in the lower crust for active submarine volcanoes12,13. Multibeam data collected from autonomous underwater vehicles mapped the eruptive fissures associated with recent eruptions along the eastern caldera rim, as well as the north and south rift zones14,15. Long-term geodetic observations of seafloor deformation demonstrated an inflation-predictable eruptive behavior of Axial Seamount, and were used to successfully forecast the 2015 eruption16,17. Furthermore, earthquake catalogues show that outward-dipping ring faults beneath the eastern and western caldera walls were reactivated to accommodate MMR inflation and deflation18–20. Although previous studies have revealed the location and geometry of the MMR, it remains unclear whether additional finer-scale magma reservoirs exist and how magma conduits are distributed in the subsurface.

Identifying magma storage beneath volcanic edifices is important for understanding volcano dynamics, crustal accretion, and eruption triggering. The OBS refraction tomography study10 estimated a magma volume ranging from 5 to 21 km3, with melt fractions up to 5–25%. Shear wave velocities constrained from continuous seafloor compliance data were used to calculate a melt fraction of 14% in the shallow magma reservoir and at least 4% in the lower crust beneath the central caldera21. These estimates are averages over large magma volumes and therefore suffer from limited resolution and large uncertainties. In addition, they fall below the critical threshold (~32–50%) observed in laboratory experiments for mobilizing magma to erupt from a crystal mush22–24, which is inconsistent with the observed frequent volcanic activity of Axial Seamount14,15. More recent joint tomography using both OBS and MCS data further refines the melt volume as ~27–87 km3 with a maximum melt fraction between 39% and 65%5, which is more than two orders of magnitude greater than the amount of melt emplaced during the 2015 eruption (total magma volume of ~0.29 km3 including ~0.15 km3 of seafloor lava flows and ~0.14 km3 of subsurface dikes5,9,15,17). Limited by the low resolution of seismic tomography study, the melt fractions in the high-melt zone beneath the southeast caldera could not be accurately determined, and it is uncertain whether its volume is comparable to the size of recent magmatic events. Moreover, the reason for the connection between the high-melt zone and the focusing of eruptive fissures near the eastern caldera wall in 1998, 2011, and 2015 remains unclear.

Here, we show high-resolution images of P-wave velocity, attenuation, and estimates of temperature and partial melt beneath the summit of Axial Seamount along JdFR, derived from an advanced multi-parameter full waveform inversion (FWI) method for MCS data. The MMR, SMR, and a small magma reservoir beneath the western caldera wall are imaged at high resolution. A low-velocity throat beneath the eastern wall, connecting the MMR roof with eruptive fissures on the seafloor, is identified. These findings reveal an asymmetric shallow plumbing system beneath Axial Seamount, shedding light on the magma pathways that fed recent eruptions.

Results
P-wave velocity and attenuation models across Axial Seamount
Twelve MCS profiles were collected in 2002 over Axial Seamount with a 49.16-L air gun source array fired every 37.5 m, and each source was recorded by a 480-channel, 6-km-long Syntron streamer with a 12.5-m hydrophone interval2,11,25. Because the sources and receivers of MCS data are located far from the seafloor, oceanic crust refractions are usually masked by strong seafloor scatterings, making it challenging to employ seismic tomographic methods. To enhance the energy of crustal refracted arrivals, MCS data can be downward continued to simulate a synthetic ocean bottom experiment with virtual sources and receivers located on the seafloor, which is easier to handle for tomographic imaging26,27. FWI is an advanced seismic tomography method based on full wavefield numerical simulations, which can accurately constrain complex subsurface anomalies of wave speeds, attenuation, and anisotropy28–31. In this study, we started from a traveltime tomography model (Fig. S1) and performed a viscoacoustic FWI (see Methods)32 for downward continued MCS data to simultaneously constrain both P-wave velocity (Vp) and attenuation along the J48 MCS survey line that crosses Axial Seamount from southwest to northeast (Fig. 1b).

The attenuation, which is commonly parametrized by the quality factor (Qp), is a metric for quantifying energy dissipation and phase dispersion of an elastic seismic wave33. Because of its strong dependence on temperature, partial melt, and water content, mapping anelastic attenuation can provide valuable information on Earth’s internal structure and dynamics, complementing seismic velocity information34. P-wave propagation in an anelastic medium can be described by using a viscoacoustic wave equation35. A multi-scale inversion strategy was implemented by gradually incorporating bands of increasing frequency (3–5 Hz, 3–7 Hz, 3–9 Hz) to produce improved Vp and Qp models (Figs. S2–S5). In each frequency band, Vp and Qp models were first simultaneously updated and later the Qp model was updated alone, which allowed us to minimize tradeoffs between these two model parameters. The total misfits of the frequency bands are reduced by 22.6%, 67.8%, and 41.3%, respectively (Figs. S6–S9). Crustal refraction waveform calculations using the final velocity and attenuation models (Fig. 2) fit better with observed data in terms of both traveltimes and amplitudes than the results from the initial models (Fig. 1c, d; Figs. S3–S5). Extensive synthetic tests demonstrate that the inverted Vp and Q models are reliable by the FWI method (Methods; Figs. S10–S12). For example, the MMR with a −17% velocity anomaly and a Qp value as low as 35 at 2.0–2.5 km bsf, as well as shallower magma pockets ranging from 570 m to 1100 m wide and from 150 m to 400 m thick at 0.9–1.5 km bsf, can be accurately imaged by using the same data acquisition and inversion scheme (Fig. S11).

Compared to previous tomographic results5 (Fig. S1), our models reveal more detailed volcanic structure below Axial Seamount (Fig. 2). For instance, most P-wave velocities are less than 3 km/s in oceanic sediments and the shallow basaltic layer, except for a 1.2-km-wide, 0.2-km-thick, high-velocity anomaly (Vp ~3.2 km/s) at 246 m below the caldera (Label A in Fig. 2a). This may be attributed to the presence of thick, dense, ponded lava flows on the subsiding caldera floor. This high-velocity core is bounded by narrow inward-dipping low-velocity zones, which are co-located with inward-dipping ring fault zones identified from caldera walls and seismicity distribution5,20. The estimated Qp above the base of layer 2A ranges from 15 to 60 (Fig. 2b), which is consistent with tomographic results for the East Pacific Rise36 and basalt samples37–39. The low-Qp in the shallow oceanic crust, which might result from the high porosity of the basaltic extrusive layer8, faulting and deformation associated with volcano inflations and deflations18, cracking induced by hydrothermal circulation36, as well as scattering from velocity heterogeneities40,41. Based on a relationship between Qp and porosity for fractured and altered basalt from ODP site 504B39, we estimate a maximum porosity of ~10–16% in layer 2A (see Method; Fig. S13). This estimation is consistent with the measured porosity of Oman Ophiolite pillow basalt (4–12%)42, but it is less than that of the uppermost oceanic crust at 100–200 m depth estimated from gravity surveys (for instance, 10–23% on the Endeavour segment43, 15–33% for Axial Seamount44). This may be caused by the averaging effect of FWI along wave paths over near-seafloor sediments and deeper parts of layer 2A (~287–925 m).

The Vp anomaly pattern (Fig. 2c) reveals the presence of what we interpret to be multiple magma reservoirs in the shallow crust, indicated by blue and red contours plotted according to the estimated partial melt fractions shown in Figs. 3–4. Beneath the high-wave speed thermal boundary layer13, a ~3-km-wide and ~250-m-thick slow P-wave speed anomaly is resolved in the upper MMR at ~1.7 km bsf (dashed red polygon in Fig. 2c), with an ~18% velocity reduction. This is consistent with strong amplitudes of coincident seismic reflections, indicating relatively high melt fraction in the upper MMR11. A smaller Vp reduction (~12%) is found in the lower MMR (dashed blue contour in Fig. 2c), underlain by a 1.6 to 2-km-wide low-velocity conduit that extends down to the mid- to lower crust. Stacked melt lenses characterized by bright reflections have been identified in the deep conduit12, but with a larger width (3–5 km) than observed in our FWI model. In the lower MMR, a low-Qp anomaly is observed with the lowest value ~60 (Fig. 2b), reflecting strong seismic attenuation and high crystal mush. However, the upper MMR has slightly increased Qp values (70–100, Fig. S9c), which may be caused by the decreased viscosity in a framework of fluid-suspended crystals with a higher melt fraction close to the eruption threshold24. An incomplete correlation between velocity and attenuation structures suggests their different responses to temperature and partial melt34. Furthermore, two separated low-velocity zones are identified at the location of the previously recognized secondary magma reservoir, located 3–10 km east of the caldera5 (Fig. 2a, c): a shallower small one adjacent to the eastern shoulder of the caldera (here named the SSMR), and a deeper larger one (here named the SMR) located ~7 km east of the MMR with a top ~1.2 km bsf. Estimated attenuation in the SMR and SSMR is not as strong as within the MMR, reflecting a lower melt fraction. A narrow (0.7–1.2 km wide) east-dipping high-velocity belt at 1–2 km bsf between the MMR and SMR implies that they are not connected along the J48 survey line (Label B in Fig. 2a, c). However, a low-velocity and low-Qp subhorizontal anomaly at ~2.5 km bsf, connecting the deep magma conduit below the MMR and the western flank of the SMR (Label C in Fig. 2b, c), indicates that the SMR may result from tapping of deep melts in the mushy zone of the deep conduit13,45.

In addition to the MMR and SMR, two previously unrecognized low-velocity features are mapped in our FWI models. The first is a west-dipping oval pocket beneath the western caldera rim, extending from 1.1 km to 2 km bsf, which appears to connect with the upper MMR through a ~220-m-thick channel (Fig. 2a, c). This western magma reservoir (WMR) exhibits ~12% Vp reduction and low-Qp below layer 2A and is co-located with strong reflection events to the west-southwest of the MMR12, indicating that this is a third region with relatively high melt fraction (Fig. S14). The distribution of seismicity in and around the caldera at Axial shows that the west-dipping ring fault beneath the western caldera rim terminates in a notch between the MMR and WMR. This suggests enhanced cooling in the western shoulder and the absence of active magma conduits from the deep high-melt reservoir to the seafloor below the western edge of the caldera. Consistently, few eruptive fissures have been observed in this area for the last several hundred years, as mapped by high-resolution multibeam data14. Second, a low-velocity throat is imaged below the eastern caldera wall that connects the MMR roof to the bottom of layer 2A (Fig. 2a). The presence of this throat aligns with the depth extent of seismicity beneath the eastern caldera wall5,20 and shallow-dipping reflectors between the base of Layer 2A and MMR11, suggesting a magmatic pathway for recent diking events and eruptions18.

Differential partial melts in the magma reservoirs and conduit
Based on the FWI velocity and attenuation models in Fig. 2, we estimate the thermal structure and partial melt fraction beneath Axial Seamount by considering both anharmonic and anelastic effects. The anharmonic thermal model is calculated by adding the temperature anomaly estimated from the Vp anomaly to a one-dimensional oceanic thermal model, while anelasticity is incorporated by iteratively updating the temperature model (see Methods)46,47. We try to explain the low-velocity zones as much as possible by thermal anomalies alone below layer 2A, but partial melt is required for temperatures above 1150 °C48. Assuming a two-phase effective medium consisting of solid and molten basalt (crystal mush with interstitial partial melt)5,49, we estimate the melt fraction in regions with temperatures greater than 1150 °C (Fig. 3; Methods). Our final thermal and melt models across Axial Seamount are shown in Fig. 4 and Figs. S15–19.

Vp perturbations far from the summit caldera can be explained by thermal effects alone, with temperatures ranging from ~4 °C near the seafloor to ~440 °C at 2.5 km bsf. However, the thermal effect alone is not enough to explain the observed prominent Vp reductions for the MMR, SMR, and WMR, where partial melt is required. Strong seismic attenuation of partial melts makes the anelastic effect significant for constraining the structure of the magma reservoirs and the deeper feeding conduit, resulting in a much narrower region enclosed by the 1150 °C isotherm than from the anharmonic model (Fig. 4a, Fig. S15). Spherical and vertically aligned elliptical melt bodies with an aspect ratio of 0.1 are considered as two end members for estimating the melt fractions5,50. The upper MMR has the largest melt fraction, ranging from 15% to 37% (Fig. 4b; Figs. S16–20). We estimate the volume of basaltic melt by first applying an area integral over the melt region based on our melt fraction model and then using the 3D reservoir geometry (Fig. S21) extracted from the traveltime tomography model in ref. 11 to constrain the length. The melt volume in the upper MMR is ~0.27–0.57 km3, which is similar to the volume of lava flows and magma intrusions in the fissures during the most recent three eruptions (19988, ~0.21 km3; 201116, ~0.15 km3; 201517, ~0.29 km3). Considering the eastern seismicity cluster connecting eruption vents to the MMR roof at depth, we infer that the high-melt zone in the upper MMR beneath the southeastern caldera is the direct magmatic source for recent eruption and diking events. In the SMR, WMR, and lower MMR, a slightly smaller melt fraction of ~10–26% is mapped. The feeding conduit in the middle- to lower crust has a melt ratio of ~4–11%, consistent with the estimates from continuous observations of seafloor compliance (requiring at least 4%)21. Based on the melt distribution shown in Fig. 4b and Fig. S18b, we estimate a total magma volume of ~12.38–29.60 km3 in the upper and middle crust. This agrees with those estimated by seismic tomography from OBS and MCS data5,10, which is about two orders of magnitude greater than the volume emplaced during recent eruptions. The spatially variable melt content forms thermally and chemically zoned magma reservoirs in shallow crust48,51, which generated seismic reflections with varying amplitudes11 and was tapped by a dike feeding the 2015 lava flows with a range of MgO content9.

An asymmetric magma plumbing system beneath Axial Seamount
The high-resolution P-wave velocity and attenuation models as well as estimated temperature and melt distributions from this study reveal a complex asymmetric magma plumbing system beneath Axial Seamount (Fig. 5). Below a thermally controlled permeability barrier, the MMR formed through magma accumulation and pooling at the base of the sheeted dike layer (Layer 2B). The top of the MMR has a melt fraction up to 37%, approaching the threshold (~35–50%24) for magma mobilization and eruption. The estimated volume of this high-melt fraction (~0.27–0.57 km3) is slightly greater than the volume of recent eruptions (~0.15–0.29 km3), suggesting that the top of the MMR is the major magma source for them. Beneath the eastern caldera wall, a low-velocity magma throat (yellow in Fig. 5) parallel to the outward-dipping fault plane connects the roof of the underlying high-melt reservoir to a shallow dike zone (magenta belt in Fig. 5) that feeds eruptive fissures.

On the other hand, beneath the western caldera wall, similar conduits are not observed in the pillow basalt and sheeted dike layers, although a small magma pocket (WMR) is imaged to the west of the MMR. A thin, subhorizontal melt band connects this pocket with the MMR, providing a magma delivery conduit. As the MMR is replenished during inflation and depleted during deflation, the stress imposed on the western caldera wall can be relaxed by magma transport into or out of the WMR, and the remaining stress associated with viscous magma movement is accommodated by slip along the west-dipping ring fault. However, the stress of the eastern wall is only accommodated by reactivating the east-dipping ring fault during volcanic inflation and deflation, leading to magma intrusion along the fault plane and forming a low-velocity diking throat. Relaxation of the WMR produces differential stresses on the two ring faults, which might explain the observation that less seismicity occurs beneath the west wall than the east wall18–20 (Fig. 4) and that the eastern caldera fault had the most slip during the 2015 eruption52.

Continuous geodetic monitoring of the caldera identified eight discrete short-term deflation events between August 2016 and May 201953, accompanied with low seismicity rates. During the June 2018 event, the bottom pressure recorder near the western caldera wall experienced slightly greater vertical displacement (subsidence) than those near the eastern wall. This could be consistent with short-distance magma movement from the MMR to the WMR, combined with viscoelastic relaxation around the MMR associated with a temporally interrupted magma supply53. The MMR, the WMR and the narrow diking throat on the eastern wall form an asymmetric magmatic plumbing system in the shallow crust (Fig. 5). In this system, the scarcity of observed diking pathways near the western caldera wall and the connection between the high-melt zone of the MMR and seafloor fissures via the eastern magma throat may explain why the recent eruptions have initiated along the eastern edge of the summit caldera.

Beneath Axial Seamount, a narrow-focused magma supply conduit (1.6–2-km-wide, ~4–11% melt fraction) is mapped at the bottom of the MMR and extends to the mid- to lower crust (Figs. 4, 5). Its location is consistent with the center of the thickened crust root revealed by PmP traveltime tomography4, a series of vertically stacked melt lens on MCS reflection images12, and a modeled pressure source determined from geodetic data by removing fault-induced deformation for the 2015 eruption (Fig. 2c)52. These observations provide new details for previous findings: (1) the Cobb hotspot significantly enhances magma flux in the focused melt delivery pipe5; (2) the MMR is episodically replenished from deep sub-axial magma lens via porous flow and with varying magma supply rates during different eruption cycles13; and (3) although magma transport from the deep conduit to the shallow MMR provides pressure needed for triggering eruptions, our models suggest that the high-melt top layer of the MMR is the direct magmatic source (Figs. 2–5). A recent teleseismic study indicates that strong seismic attenuation below the Axial segment of the JdFR requires ~2% in situ melt in a <50-km-wide and ~150-km-deep subridge region54, which may serve as the melt source in the upper mantle for crustal focused magma delivery and accumulation beneath Axial Seamount.

Origin of the asymmetric magma plumbing system beneath Axial Seamount
High-resolution bathymetry shows that most of the lava flows erupted in the last 800 years were extruded from fissures along the eastern edge of the caldera8,14. This is consistent with the eastward offset of the underlying MMR relative to the caldera and the northwestward dip of the magma chamber roof (Fig. 1b)9. The JdFR migrates westward at ~2 cm/a relative to the stationary and persistent Cobb hotspot plume55; the offset between the MMR and the summit caldera at Axial Seamount reveals continuous westward migration of the spreading center since the caldera formed ~1.1 kyr ago56. Due to ridge migration and trapdoor collapse of the caldera5, the southeastern edge of the summit caldera is near the center of the 11-km crustal root associated with the Cobb hotspot and is located above the shallowest part of the MMR (Fig. 1b). Repeated magma transport to the seafloor helps form the diking pathway beneath the eastern caldera wall, where crustal accretion is mainly through lava eruptions from fissures and dike intrusions in the south and north rift zones. We infer that the WMR is a remnant melt-storage pocket left behind as the MMR moved eastward relative to the overlying caldera, and cooling and crystallization of magma in this pocket contributes to forming crust beneath the west caldera wall. This also agrees with the seafloor morphology of Axial Seamount, where the western shoulder is much wider, shallower, and thicker than the eastern one (Figs. 1b and 5).

One limitation of this study is that it uses one 2D seismic line across the summit of Axial Seamount. Additional insights might be gained by applying the analysis used here to other 2D lines of the 2002 MCS survey. This would test some of our ideas about how magma and partial melt is distributed in the shallow crust and the connections between them. For example, our FWI models suggest that the SMR is not directly connected to the MMR through shallow high-melt channels along the image of the J48 survey line. Rather, a deeper low-velocity anomaly appears to connect the SMR to the deep melt-mush feeder conduit. But we cannot rule out intermittent or permanent connection zones between the MMR and SMR that may be located outside of the image plane. In addition, observations of weaker seismic attenuation and moderate partial melt fraction in the SMR suggest that, unlike the MMR, its magma replenishment is more limited, and it is unlikely to trigger an eruption or intrusion event in the near future. This is consistent with the fact that few earthquakes were recorded around the SMR during recent eruption cycles20,57. With the continued migration of Axial Seamount relative to the underlying Cobb hotspot, the SMR is likely to experience enhanced magma supply in the future. But more 3D seismic surveys are needed over the southeast region of Axial Seamount to investigate 3D structure of the SMR and its connection to the MMR and deep magma supply conduits.

Methods
Data processing
The MCS field data was acquired during a 26-day EW0207 cruise in 2002 with the R/V Maurice Ewing to study the axial structure and crustal evolution of the JdFR58,59. The air-gun source, consisting of 10 elements with a total volume of 3005 cubic inches, was towed at a depth of ~7.5 m and fired every 37.5 m along the track. Each shot was recorded by 480 hydrophones with a 12.5-m interval at the depth of 10 m, and the minimum source-receiver distance is 190 m. A total of 10,265 shots were fired above Axial Seamount, and the data was sampled at 250 Hz for a record duration of 10.24 s. In this study, we used data from the J48 survey line crossing the Axial Seamount from the southwest to the northeast (Fig. 1). Prestack data processing includes bad trace killing and interpolation, random noise removal, bandpass filtering of 3–20 Hz, and 3D to 2D amplitude correction (3D field data records but 2D wave equation simulations and inversion are used in this study)60. A predictive deconvolution filter was used to suppress the bubble effects of the air gun sources. To reduce the mask effects of deep water for refraction arrivals, a true-amplitude redatuming process is applied to the MCS streamer data to simulate on-bottom seismic experiments5,26; the receivers and sources were sequentially downward continued to the seafloor in common-source and common-receiver gathers61. The refractions in the redatuming data appear as the first arrivals, making it easy for fitting in traveltime tomography and FWI (Fig. S2).

Viscoacoustic FWI
FWI is an advanced seismic imaging technology for high-resolution mapping subsurface model parameters, which directly fits observed data with synthetic records computed by solving the wave equation62,63. In exploration seismology, it has been successfully applied to characterize hydrocarbon reservoirs, with a resolution of tens to hundreds of meters64,65. In regional and global seismology, by fitting earthquake recordings28,30,66 or ambient-noise cross correlation data24,67,68, FWI has been used to image heterogeneous geological structures within the crust and mantle, with a resolution of a few to hundreds of kilometers. To account for seismic attenuation, we apply a viscoacoustic FWI scheme in this study to constrain both P-wave velocity and attenuation below the Axial Seamount32. The misfit function can be defined as

J(m) = ||dobs − dsyn(m)||2, (1)

where m = [Vp, Qp]T, and Vp and Qp denote the P-wave velocity and quality factor models, dobs represents the redatuming MCS data, and dsyn(Vp, Qp) denotes the synthetic data with sources and receives deployed on the seafloor. The synthetic data dsyn(Vp, Qp) is computed by solving a time-domain complex-valued viscoacoustic wave equation that explicitly includes Qp35. The misfit gradients are derived based on the adjoint-state method, and a preconditioned limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm69 is used to reduce interparameter crosstalk and update Vp and Qp models as

mk+1 = mk(1 + αδm), (2)

where k and k+1 denote the current and next iterations, δm is the updating direction calculated based on the L-BFGS algorithm, and α is the step length computed using a parabolic search method. The detailed implementation for the multi-parameter inversion can be found in ref. 32. To avoid the cycle skipping issue in FWI, we apply a multi-scale strategy to gradually incorporate high-frequency data70; three frequency bands are used, i.e., 3–5 Hz, 3–7 Hz, and 3–9 Hz (Figs. S2–S9). Numerical experiments show that the velocity perturbations have first-order effects on seismic data, while the attenuation perturbations have second- and even third-order effects. To mitigate large differences in data sensitivity to velocity and attenuation, we first update both Vp and Qp models at the first stage and then update Qp model alone at the second stage. The detailed iteration numbers and data reduction at these two stages are presented in Fig. S6. The source wavelet is estimated for each source using the frequency-domain deconvolution as

F(ω) = (Dobs(ω)G*(ω)) / (G(ω)G*(ω) + ϵ), (3)

where ω denotes the angular frequency, Dobs(ω) is the frequency spectrum of observed data, G(ω) is the frequency spectrum of the Green’s function computed by solving the viscoacoustic wave equation with a zero-phase broadband wavelet, and ϵ is a small value to avoid division by zero. A cosine taper is applied to the estimated wavelet to attenuate oscillations after 2.5 periods. After the inversion in the frequency band of 3–5 Hz, the Vp signatures for MMR, SMR, and hydrothermal boundary layer above the MMR become clearer than those in the initial tomographic model, and the resolution of shallow layer 2A is improved (Fig. S7a). In the Qp model, a shallow strong attenuation layer associated with hydrothermal circulation and deep low-Qp region related to the MMR and magma feeding conduit have been recovered but with a lower resolution than the Vp model (Fig. S7b, c). Increasing the data frequency to 9 Hz, the resolutions of Vp and Qp models have been significantly improved, and small-scale magma reservoir features can be clearly imaged (Figs. S8 and S9).

Calculation of temperature structure
Both anharmonic and anelastic effects have been considered to estimate the subsurface temperature structure beneath Axial Seamount based on FWI velocity and attenuation models. The derivative of P-wave velocity with respect to temperature can be written as46,71

(∂lnVp/∂T)(x) = (∂lnVp/∂T)anhar + (πF(κ)Qp−1(x)R H*)/(T2(x)), (4)

where x denotes the subsurface location, Qp is FWI quality factor model, R = 8.314 J K−1 mol−1 is the universal gas constant, T is the temperature, F(κ) = (πκ/2) cot(πκ/2), and κ is the power law exponent of the frequency-dependent Qp. H* is the activation enthalpy and is set to 276 kJ mol−1 based on the creep activation energy in the crust72. We computed two temperature models: (1) only assuming the anharmonic effect alone and (2) considering both anharmonic and anelastic effects, which approximate the minimum and maximum contributions of temperature to velocity perturbations46. In the first scenario, the first term on the right-hand-side of Eq. (4), i.e., (∂lnVp/∂T)anhar, is set to −8.1e−5 K−173 and the second term is set to zero. The temperature model can be calculated as

T(x) = T0(x) + δlnVp(x) / (∂lnVp/∂T), (5)

where T0 is a reference off-axis temperature model74, δlnVp = (Vp − Vp0)/Vp0 is the relative velocity perturbation (Fig. 2c), Vp is the FWI velocity model, and Vp0 is the background velocity model (Fig. S1c). In the second scenario, F(κ) is set to one to estimate the maximum anelastic effects46. Because the second term on the right-hand-side of Eq. (4) is temperature dependent, calculating the anelastic associated temperature model is a nonlinear problem. Following ref. 46, we iteratively update the temperature profile until the difference between adjacent iterations is less than 10 °C. The iteration scheme can be expressed as

Tk+1(x) = T0(x) + δlnVp(x) / [(∂lnVp/∂T)anhar + (πQp−1(x)R H*)/(Tk2(x))], (6)

where k and k+1 denote the current and next iterations. Estimated temperature models are shown in Fig. 4a and Fig. S15. Compared with the anharmonic model, high-temperature anomalies in the anelastic model are more focused around the deep melt conduit and magma reservoirs.

Melt estimation
The thermal effect is not enough to explain the observed low velocity anomalies with temperature above 1150 °C. Thus, it is necessary to take partial melting into account. As shown in ref. 5, we apply a two-phase differential effective medium method to compute the melt fraction. The background matrix is assumed as solid basalt with P-wave velocity of 6.4 km/s, S-wave velocity of 3.5 km/s, and density of 2.97 g/cm3. The fluid phase is assumed as basaltic melt with P-wave velocity of 2.35 km/s, S-wave velocity of 0 km/s, and density of 2.7 g/cm3. Spherical and vertically aligned elliptical inclusions with aspect ratios of 1, 0.5, 0.1, and 0.002 are used to simulate the effect of partial melt on P-wave velocity (Fig. 3). Based on this relation, we calculate subsurface melt fraction within the 1150 °C isotherm. For the case only considering the anharmonic effect, FWI velocity is directly used to predict the melt ratio. If incorporating the anelastic effect, the P-wave velocity is corrected according to the phase dispersion as

Vp(x, ω) = Vpref(x) [1 + (1/πQp(x)) ln(ω/ω0)], (7)

where ω = 2πf, f0 denotes the reference frequency and is set to 1 Hz in viscoacoustic FWI32, and Vpref is the FWI velocity estimated at the reference frequency. The melt fraction models with different inclusion geometries are shown in Fig. 4a and Figs. 15–18. Spherical inclusions generate the largest melt fraction, as high as 37% in the upper layer of the MMR. The melt fraction decreases significantly for elliptical inclusions with smaller aspect ratios. In addition to melt inclusion geometry, there are many other factors influencing the accuracy of estimated partial melt fractions. For instance, representing magma as an effective medium comprising solid basalt and basaltic melt is merely a two-phase simplification, whereas real magma might contain volatiles. Achieving a more realistic rock-physics representation for magma and an accurate relationship between seismic velocity and partial melt requires further investigation.

Porosity estimation in the uppermost crust
Because of faults, fissures, pillow fragments, lava flows, and hydrothermal alteration, the uppermost oceanic crust has strong seismic attenuation75,76. Regression analysis for in situ log data from the ODP Hole 504B in the eastern equatorial Pacific showed that the crustal attenuation is prominent and related to porosity as39

Q−1 = Q0−1 exp(βϕ) (8)

where Q0 is a reference quality factor of 250 close to the intrinsic attention of deep crustal rocks77, and β = 25 is the regression exponential coefficient. For low porosities, a linear model was also derived as39

Q−1 = Qi−1 + Qp−1ϕ (9)

with Qi−1 = 0.0025 and Qp−1 = 0.29. Based on these two regression relations and the FWI Qp model, we compute the porosity profiles within seabed sediments and layer 2A (Fig. S13). The maximum porosities of ~10–16% are found at depths of 287–925 m, and slightly lower porosities of ~9–12% are present below the caldera. These porosity distributions are consistent with the shallow low-velocity perturbations, which might be caused by hydrothermal circulation in fractured basalt between the off-axis flank and axial caldera.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review by William Chadwick\nGeneral comments on the manuscript:\nThis paper presents the results of re-processing one 2D multi-channel seismic (MCS) line\ncollected at Axial Seamount in 2002 with a new method (full waveform inversion, FWI) that\nyields new 2D cross-sections of P-wave velocity and seismic attenuation with higher\nresolution than previously published. The paper then makes a series of new interpretations\nbased on the new views along this one 2D cross-section. One of the main new\ninterpretations is that there appear to be 4 distinct magma bodies below the summit of\nAxial Seamount, rather than the 2 previously imaged (which were one main magma\nreservoir below the summit caldera and a secondary one 5-10 km to the east below the SE\nflank of the volcano). The authors speculate on magma pathways between the 4 reservoirs,\nand between the main reservoir and the surface, based on narrow linear spatial variations\nof the P-wave velocity and attenuation in the 2D cross-sections. They also calculate melt-\nfraction in the various reservoirs and porosity in the crust.\nOne strength of the manuscript is that the authors thoroughly describe and reference\nrelevant previous studies at Axial Seamount, and they attempt to explain and reconcile all\nrecent data and observations with their proposed models and interpretations. The paper is\nwell-written and the figures are good.\nThe main weakness of the manuscript is that the new results are only based on one single\n2D seismic line from the 2002 survey (that included multiple lines), so it is unclear if what\nthey observe extends into the 3rd dimension. Presumably the method they use could be\napplied to other 2D lines from the 2002 survey to see if the results are consistent with their\npresent conclusions (and allowing the extrapolation of their results from one 2D line into\n3D). The paper would be stronger and more convincing if the interpretations were\nsupported by more than one 2D line. There is much more information that could be gained\nby considering the 3rd dimension (for example, spatial extent of the magma reservoirs,\nspatial variations melt fraction, etc)\nSimilarly, from the little that has been presented so far from a newer high-resolution 3D\nMCS seismic survey at Axial Seamount in 2019 (for example, in a 2020 AGU abstract by\nArnulf et al), the newer MCS results do not seem to support the conclusions in this paper\n(particularly the 2 “extra” magma reservoirs, nor the lateral connections between them).\nCan the FWI method be applied to the data from the 2019 survey? If so, what would it\nshow? Would it support the conclusions presented here?\nSo this raises the fundamental question of how confident we can be that the 2D P-wave\nvelocity and attenuation variations in this paper really show the distribution of partial melt\nin the 3D shallow crust at Axial? And what is the real resolution of these data in terms of\ndiscerning relatively small structures and melt conduits?\nI think if the paper stays as the analysis of just one 2D MCS line, then it should treat the\nresults as provisional, subject to confirmation by future analysis of other 2D lines from the\n2002 survey, or analysis of data from the 2019 3D survey. Also, I think that some of the\ninterpretations should be presented with less certainty and more as interesting possibilities\nthan definite conclusions. For example, I think the existence and significance of the\napparent “shallow LV zone” (=dike conduit?) is highly debatable and not very convincing.\nFor this reason, I do not think it should be the focus of the Abstract (which should be\ncompletely re-written) or highlighted in the title. Instead, I would highlight the increased\nresolution of the seismic imaging method, the provisional interpretation of multiple shallow\nmagma reservoirs compared to earlier interpretations, the possible imaging of connections\nbetween them, and the deeper conduit below them. But it also important that the paper\nclearly state that confirmation of these interpretations must await additional evidence from\nfurther studies.\nI recommend a re-evaluation of the paper after major revisions to address the editorial\nsuggestions and specific comments in the annotated manuscript, some of which are listed\nbelow.\nSpecific comments (keyed to lines in the annotated manuscript):\nLine 13 (Abstract): To me, the Abstract does not do a good job of summarizing the key\nresults. I would not make the eastern offset of recent eruptive fissures an emphasis in (so I\nwould omit the 2nd sentence). I think a more important conclusion to highlight in the\nAbstract, is that you image more magma reservoirs in the shallow crust compared with\nearlier analysis of this same data set. I think the Abstract should be re-written with that\nemphasis. In the 3rd sentence, you need to say you are only re-analyzing one 2D line from\nthe 2002 MCS survey. The 4th sentence about melt fractions makes it sound like the\n\"deeper feeding conduit\" is part of the MMR, but in the rest of the paper it is treated as\nsomething separate. Rephrase to be consistent. I would re-write the last 3 sentences of the\nAbstract to focus on the magma reservoir results rather than the \"LV throat\" and the\neastern offset of recent eruptions.\nLine 21: I think your reference #28 (Carbotte et al., 2008) might be a more appropriate here\nthan your #6 (Canales et al., 2009).\nLine 25: You could add reference #56 here for the 2015 eruption.\nLine 28: Reference #12 is not directly related to the details in this sentence. However, it\ncould be used at the end of the previous sentence if you want.\nLine 30: Again, not sure reference #6 (Canales et al., 2009) is relevant here.\nLine 32: Not sure reference #16 (Dziak et al., 2011) is relevant here.\nLine 36: The end of this sentence doesn't make sense because the eastern wall *is*\nseismically active.\nLine 39: It's important to put this West et al. (2001) study in the right context. It was the first\nto use seismic tomography to attempt to image the magmatic system below Axial, so is\nsignificant. But its results now seem primitive and coarse compared to the much higher\nresolution methods used by Arnulf et al. (2014; 2018) from the 2D MCS survey in 2002 and\nthe 3D MCS survey in 2019 (still unpublished except for AGU abstracts in 2019 and 2020).\nLines 42-44: Yes, but for both of these studies the melt fraction numbers are average values\nover a very large volume.\nLine 47: You should reference where these numbers come from and clarify that they include\nestimates of the volume of lava flows and subsurface dikes.\nLine 48: In Arnulf et al. (2014), which is reference #13, they interpreted a high melt zone at\nthe top of the MMR beneath the southern part of the caldera, so a \"high-melt zone\" has\nbeen mapped before, but they did not assign any quantitative melt fractions (just \"high\" and\n\"low\", or \"melt\" and \"mush\"). Arnulf et al. (2018) placed some constraints on the melt\nfractions. So saying it's \"...unclear whether there is a high-melt zone...\" doesn't seem\naccurate. What are you trying to say here exactly?\nLine 56: Whether it is easy or not is subjective. What are the authors really trying to say\nhere? Should be rephrased. Is there an simple way to explain what \"downward continued to\nthe seafloor\" means for readers who are not seismic experts?\nLine 58: You should note that it was called the \"SMR\" in Arnulf et al. (2018), ref #9 here,\nand that you are calling it something different here (“EMR”).\nLine 64: In the caption for Figure S1, explain what Qp is and how it relates to the figure. Also\ncan you add a plain language explanation of what \"viscoacoustic\" means in this context?\nLine 65: Cross-sections of \"attenuation\" are important in the rest of the paper. I think it\nwould help to take a sentence or two here to explain what \"attenuation\" means in this\ncontext and what these cross-sections show.\nLine 72: What data are fit better? Need to better explain this.\nLine 75: How much of a velocity anomaly or how low a low-Q anomaly? And at what\ndepths? Is this claim substantiated in the figures in the Supplementary materials? If so,\nwhich figures?\nLines 82-84: To me, this sentence is poorly constrained speculation. \"Hydrothermal cooling\nabove the MMR\" is a pretty generic explanation and is unconvincing. I can think of other\ninterpretations (the existence of thick, dense, ponded lava flows in the subsiding caldera\nfloor block, for example), but I don't think there is compelling evidence for any one idea.\nLikewise, the low-velocity boundaries could be just due to the caldera faults. There is\nnothing that convincingly identifies them as \"magma pathways\". In fact, I might expect a\nzone of diking to have higher velocities. Then there is the problem that zones of diking are\nlikely vertical and narrow, so would be hard to image seismically. Also, the references cited\nin this sentence seem generic and do not particularly substantiate the interpretations. For\nall these reasons, I would omit this sentence.\nLine 85: Does attenuation (Qp) have units?\nLines 86-88: How does hydrothermal alteration \"induce\" high-porosity? Not obvious to me.\nCracking itself & deformation make high porosity. Or the extrusive layer itself starts with\nhigh porosity.\nLine 95 (Figure 2): In Fig. 2, I would change the y-axis labels to \"depth below sealevel\" to\nclarify that it is not depth below the seafloor. What is the \"perturbed Vp model\" in Figure\n2c? And what is the difference between Fig. 2a and c? This needs some explanation if this is\nwhat you are referring to as what is showing \"more detail\". Is it just imaging the MMR in\nmore detail? Or is it imaging multiple magma reservoirs in the shallow crust in more detail?\nAlso, I think the blue contours in Figure 2c deserve some explanation in the text. What is\ninterpreted that this contour signifies and what is it based on? I would also add a plain\nlanguage explanation of what Fig. 2b shows and why it makes intuitive sense (if it does).\nWhat is \"seismic attenuation\" exactly, and why isn't there major (and more uniform)\nattenuation inside the MMR?\nLine 96: You need to indicate which panel in Figure 2 the reader should refer to to see this.\nIs this the red/white \"smile\" at 2km depth in Fig. 2c??? Also is the \"P-wave speed anomaly\"\nfast or slow? And is it really \"at the top\" of the MMR, or above it?\nLine 98: Wait a minute ... there is \"high-melt fraction\" in the pink \"smile\" at ~500 m depth\nbelow the caldera??? I thought the magma was in the MMR at ~1 km depth below the\nseafloor. This needs clarification.\nLine 103: What does this mean or imply and how does it make sense?\nLine 108: I would say ~7 km east of the MMR, if you measure from the center of the MMR to\nthe center of the EMR.\nLines 111-112: Depth below sealevel? Or depth below the seafloor?\nLine 117: Can this method *really* identify something of this scale at this depth? How do\nyou know this is actually a fluid conduit?\nLine 118: I can't help but wonder how confident can we be of this interpretation... This is\njust one 2D seismic line. Would these \"extra\" low-V zones interpreted as magma reservoirs\nbe imaged on other lines from the 2002 MCS survey? The evidence would be stronger if you\nsaw the same things on other 2D lines and that made sense in three dimensions.\nLines 118-121: I would say that the distribution of seismicity on the caldera ring fault doesn't\nnecessarily say anything about whether the WMR could feed a dike to the surface in the\nwestern part of the caldera. That said, there aren't many eruptive fissures there from the\nlast several hundred years from the mapping of Clague et al. (2013). In general I think it's\ndubious that MCS methods can image narrow vertical structures like dikes in the shallow\ncrust. I would not expect to see them, even if they do exist.\nLines 121-124: I'm equally dubious of this interpretation. I'm not convinced this \"LV throat\"\nis real or significant. The seismicity shows slip along the caldera faults during inflationary or\ndeflationary deformation. It doesn't necessarily say anything about diking or the existence\nof a magma pathway there. In fact, one might expect a \"diking pathway\" to have a high\nvelocity. I'm not convinced that MCS can image narrow vertical structures like \"dike\npathways\".\nLine 141: I wonder why there isn't a high melt fraction at the very top (roof) of the MMR in\nFigure 4b. Isn't that where the MCS data show the highest seismic reflections indicative of a\nchange from solid to melt?\nLine 143: What you are calling the “upper MMR” in Figure 4, looks like the middle of the\nMMR to me, based on the pink and blue outlines.\nLine 145: Is the volume of melt in the \"upper MMR\" a subset? If so, what percent of the\nMMR is the \"upper MMR\"? How can you constrain the volume of the \"upper MMR\", based\non only one 2D MCS line? How do you know the 3rd dimension for calculating a volume?\nNeeds clarification.\nLine 147: Note reference #11 is duplicated as reference #43.\nLine 150: It’s still unclear what constitutes the \"upper\" vs. \"lower\" MMR.\nLine 162: What is the \"boundary layer\" in Figure 5?\nLine 168-170: I'm not convinced the data show this, especially the \"LV throat\". You could\nhave drawn these features on Figure 5 before this study was done, because it was already\nobvious there is some sort of focusing of magma from the top of the MMR into dikes that\nintrude upward near the eastern caldera fault, but I’d say the reasons for that are still\nunclear. To me, the results in this paper do not illuminate why that is the case.\nLines 173-178: This explanation for the difference between the eastern and western sides of\nthe caldera seems very speculative...\nLine 216: Actually, Clague et al. now think the present caldera only formed about 1100 years\nago (the age reported in Clague et al. (2013) is incorrect). This was presented in an AGU\nabstract:\nClague, D. A., R. A. Portner, J. B. Paduan, M. Le Saout, and B. M. Dreyer (2019), Formation of\nthe summit caldera at Axial Seamount. Abstract presented at 2019 Fall Meeting, AGU, San\nFrancisco, CA, 9-13 Dec.\nLines 223-225: This is an interesting idea, but what would explain the EMR?\nLines 229-232: This is the first acknowledgement that all the results in this paper are based\non only one 2D seismic line and that this could limit what you can conclude! In my opinion,\nthere should be much more of this type of discussion of the limitation of this study, and\nwhat would be needed to better substantiate the tentative results presented.\nAnother important question that should be addressed in the paper is: if they are real, why\nwere the WMR and ESMR (the 2 “extra” magma reservoirs) not previously identified by\nseismic reflection methods in the 2002 (and 2019) MCS surveys? To me, seismic reflection is\na more compelling way to identify where magma bodies exist in the crust, because of the\nstrong reflections produced by the change from solid rock to liquid, whereas mapping\nseismic velocities seems like a less definitive and more indirect way of doing the same thing.\nWhy should readers believe these new results based on only seismic velocities if they are\nnot confirmed by reflection seismology?\nThis is an important and excellent paper and may be accepted with minor revision.\nImportant contributions of the paper include P-velocity imaging with much higher spatial\nresolution than previous work and novel synoptic attenuation imaging. Taken together, these\nadvances allow the authors to address connectivity (or lack thereof) between shallow magma\nsystems and to obtain more accurate estimates of the melt fraction. The former is important to\nunderstanding how the shallow magma plumbing influence eruptive style (eruptions being the\narguably the best monitored of any submarine volcano). The latter is important because of the\nperceived discrepancy between previous estimated of melt fraction and that thought, on\nexperimental grounds, needed to promote robust magma storage.\nMy suggestion for a minor revision concerns the discussion of melt faction. I confess that I have\na hard time wrapping my mind about quantifications like “ranging from 39% to 65%” (line 144).\nFirst, melt fraction is likely a matter of spatial scale. I presume that at the finest scale, the\nmaximum is 100%, meaning that somewhere in the magma system is a little pocket of pure\nmelt. So, a number like 39% is only meaningful in the sense of representing an average with\nrespect to some volume of material (rock+melt). As the imaging is tomographic, I suppose that\nthe relevant averaging volume ought to be based on the volume of the resolving kernel. The\nSupplementary Material mentions resolution in connection with Figs 10-12, but I was unable to\ndiscern how to use them to figure out this volume. After pondering the issue for a while, I\nwould like to make the suggestion that the authors add an “exceedance plot” like this:\nHere, X is informed by some estimate of the resolving power of the tomography. Such a\ncumulative histogram would provide more information than what’s in line 144. It could be\ngenerated very easily from the model underpinning the author’s Fig 4b.\nI also confess that ranges like “39% to 65” (line 144) raise more questions with me than they\nanswer. Is the range estimate a confidence interval, e.g., 52% +/- 13? If so, what is the formal\nconfidence? Is it 95%, or something else? What sources of variation contribute to this\nconfidence, and has “model error” been included. I imagine that model error (including the\nability to map Vp and Qp into melt fraction) is the main source of error. But speaking only for\nmyself, and not for the authors, I have no confidence in my ability to quantify such an error.\nAnyway, I think that the authors ought to explain what they intend a range to mean. Such an\nexplanation could be based on the exceedance plot (as in my figure). I also wonder whether an\nintercomparison of a range with that stated in another paper (as the authors provide, e.g., in\nline 40) is really as straightforward as it seems. This point could be addressed with a few\nadditional lines of text.\nReviewer #3 (Remarks to the Author):\nThis manuscript presents a 2-D full waveform inversion for VP and QP along a profile that\ncrosses the summit caldera in WSW-ENE orientation. The inversion is technically impressive\nand reveals some interesting features, specifically a low velocity pathway in the location\nwhere dikes are emplaced along the eastern side of the caldera to feed eruptions from the\nmain magma chamber, a western magma reservoir that has not been previously reported, a\nshallow high velocity region infilling the caldera and a narrow region of low velocities\nunderlying the main magma chamber. The presentation of the results is somewhat jumbled,\nand the interpretation does an inadequate job of identifying what has been learned that is\nnew and what is just confirming previous ideas. In discussing the connection between\nmagma bodies, the authors seem to be inferring 3-D geometry from a 2-D inversion – a 2-D\ninversion can show bodies are connected but not demonstrate that they are not. It is\nimpressive that the inversions can image the magma pathway on the eastern wall, but we\nknow from previous studies that is where eruptions occur because that is where the plate\nboundary is, so what is new in the interpretation? The paper does develop some ideas\nabout the asymmetry of the magma chamber relative to the caldera and its influence on the\nlocation of eruptions. There is also speculation that the connectivity to the western magma\nbody may play a role in supporting asymmetric on the caldera fault and several short\ndeflation events observed from 2016 to 2019, but the manuscript does not make any\nattempt to test this idea with the geodetic data. With some thought and more reference to\nthe prior literature, I think this manuscript could be revised into an inciteful publication.\nDetailed comments:\n14-51. It is not clear what questions are motivating this study?\n34-36 “Although previous studies revealed the location of the subcaldera magma chamber,\nit remains unclear why all recent eruptions were only from the eastern wall rather than the\ntwo seismically active walls” – I disagree, it is very clear why recent eruptions are on the\neast wall. This is where the plate boundary is and where the summit connects to the north\nand south rifts, one of which also spreads in each eruption and takes most of the melt\nvolume. Given the location of the plate boundary (e.g., Chadwick et al., 2013), how can a\nspreading event be supported by an eruption on the west wall? It is interesting that the\nasymmetric offset of the main magma chamber relative to the caldera which was first\nreported by Arnulf et al. (2014) centers it beneath the plate boundary.\n48-50. “it is unclear whether there is a high-melt zone beneath the caldera with a melt\nfraction close to the eruption threshold and a volume comparable to the size of recent\nmagmatic events” – If it is unclear what is the alternative? This is the only mechanism that I\nam aware of to explain eruptions on mid-ocean ridges and the presence of a shallow high-\nmelt zone supporting eruptions has been demonstrated along the East Pacific Rise (e.g.,\nSingh et al., 1998; Xu et al., 2022) and the Juan de Fuca Ridge (Canales et al., 2006)\n79-80. What is the significance of the shallow high velocity body in the caldera? At least in\nsome other calderas, the caldera infill has a very low velocity (e.g., Hooft et al., 2019; ). I\nthink a review of prior observations in calderas would be useful to interpret this result which\nis presently not interpreted\n80. “246 m” - To this level of precision?\n81-82. The inward dipping normal faults are mainly identified by the caldera walls. Most of\nthe seismicity is on the buried outward dipping ring fault. While both Arnulf et al. (2018) and\nWaldhauser et al. (2020) associate some earthquakes with the inward dipping fault on the\neastern side of the caldera, the catalogs are inconsistent.\n82-84. The first half of this sentence seems to be referring to structure right above the\nmagma body which doesn’t seem to be mentioned anywhere else. The second half seem to\nbe referring to the feature that is presented in more detail in line 121-124. The whole\nsentence is orphaned in a section on shallow structure and thus quite misplaced.\n110-114. Since the center of the EMR is well to the south of the MMR (Arnulf et al., 2014)\nand this profile, there is no justification for concluding it lacks connectivity to the MMR from\na 2-D model. I think this is a major flaw in the interpretation.\n117. Is the WMR seen in the reflection data? If not, why not given the sharp velocity\ngradients near its top?\n119-121. I do not follow. Geometrically, the fault must terminate in a mushy zone that can\ndeform viscously so this could be a magma conduit. From the plots in Figure 4b and S15-18,\nit looks suspiciously like the earthquakes do root in the combined melt body producing a\nnotch in it, potentially because of enhanced cooling.\n121. “In addition”. Should this be “Second” based on lines 114-115.\n122-124. How does this pathway compare with those inferred by Arnulf et al. (2014) from a\n3-D inversion?\n145. How do the authors get this estimate? In Figures 4b/S15 the 32% region looks to be 0.2\nkm thick and 3 km wide so for the upper limit of 0.57 km3, this requires a 3rd dimension of\n0.57 / (3 x 0.2 x 0.32) = 3 km but the magma chamber extends 15 km along axis. If the 26%\ncontour was used, there would be much more melt, so why select the 32% contour other\nthan to get the answer that is desired? Some clarification in supplementary docs would be\nhelpful.\n156-159. How does this interpretation relate to previous interpretations of magma\nchambers on mid-ocean ridges? Isn’t this the long-standing interpretation of crustal magma\nchambers at mid ocean ridges (Sinton and Detrick, 1992; Singh et al., 1998)?\n173-176. If magma transport in and out of the WMR relaxes stresses why are there\nremaining stresses? Hefner et al. (2020) have modeled caldera inflation with asymmetric\nfault motions and show the remaining caldera inflation is quite symmetric, so I am not sure\nwhat need to be explained by transport of magma in and out of the WMR? The fault\nmotions are asymmetric because the center of inflating magma body is offset to the east of\nthe caldera.\n178-180. This is one reasonable explanation and that adopted by Hefner et al. (2020), but an\nalternative explanation is that the west wall is less coupled.\n180.-182. The short-term deflation events from 2016-2019 are intriguing and loss of magma\nto the WMR is a feasible explanation, but such short-term deflation events were not seen\nbetween the 1998 and 2011 eruptions and the 2011 and 2015 eruptions so they are not\nrelated to a process that is inherent to the eruptive cycle as the model presented here\nseems to suggest. If these events are related to loss of magma into the WMR, then they\nshould be geodetically observable by comparing the pressure gauge and tilt meter from\nthe cabled instruments at the ASHES vent field on the western side of the caldera with those\nelsewhere. Have the authors looked?\n186-188. The lack of a magma pathway is consistent with magma not erupting along the\nwestern wall, but it is not an explanation of why there is no pathway.\n189-191. This is an odd choice of citations and prior work does not predict a broad magma\nbody – indeed quite the opposite. At the EPR Dunn et al. (2000) report a width that “is\nnarrow in the {lower} crust (5–7 km)” at 2-6 km depth and given the limits of travel time\ntomographic resolution, it presumably could be even narrower. Indeed, in a more recent\npaper Dunn (2022) estimates a width of 4.5 km at shallower depths broadening somewhat\nin the lower crust. Arnoux et al. (2019) also conclude the magma chamber is narrow in the\nlower crust along the Endeavour segment of the Juan de Fuca Ridge.\nThe model in this manuscript only extends to 2.5 km bsf so it not at all clear how wide the\nlow velocity zone is at greater depth. The inversions in this manuscript have higher\nresolution and thus resolve structure beneath the MMR that not been resolved previously\nbut it is not clear that if the image extended to greater depth, it wouldn’t be anything\nother than very consistent with the prior travel time tomography studies.\n201-204. Where else other than the upper mantle can the melt come from? What is\npurpose of this sentence.\n221-227. This is interesting.\n228-229. As noted above a 2-D image cannot show this.\nWilliam Wilcock", "reviewer_2": "My suggestion for a minor revision concerns the discussion of melt faction. I confess that I have a hard time wrapping my mind about quantifications like “ranging from 39% to 65%” (line 144). First, melt fraction is likely a matter of spatial scale. I presume that at the finest scale, the maximum is 100%, meaning that somewhere in the magma system is a little pocket of pure melt. So, a number like 39% is only meaningful in the sense of representing an average with respect to some volume of material (rock+melt). As the imaging is tomographic, I suppose that the relevant averaging volume ought to be based on the volume of the resolving kernel. The Supplementary Material mentions resolution in connection with Figs 10-12, but I was unable to discern how to use them to figure out this volume. After pondering the issue for a while, I would like to make the suggestion that the authors add an “exceedance plot” like this:\nHere, X is informed by some estimate of the resolving power of the tomography. Such a cumulative histogram would provide more information than what’s in line 144. It could be generated very easily from the model underpinning the author’s Fig 4b.\nI also confess that ranges like “39% to 65” (line 144) raise more questions with me than they answer. Is the range estimate a confidence interval, e.g., 52% +/- 13? If so, what is the formal confidence? Is it 95%, or something else? What sources of variation contribute to this confidence, and has “model error” been included. I imagine that model error (including the ability to map Vp and Qp into melt fraction) is the main source of error. But speaking only for myself, and not for the authors, I have no confidence in my ability to quantify such an error. Anyway, I think that the authors ought to explain what they intend a range to mean. Such an explanation could be based on the exceedance plot (as in my figure). I also wonder whether an intercomparison of a range with that stated in another paper (as the authors provide, e.g., in line 40) is really as straightforward as it seems. This point could be addressed with a few additional lines of text."}, "author_response": "Dear reviewers:\nThis is our response to the reviews of manuscript, entitled “Asymmetric magma plumbing beneath Axial\nSeamount,JuandeFucaRidge”. Commentsfromeditorsandreviewersareinreditalicsandourresponseis\ninblacknormaltype. Pagenumbersofthemodificationcorrespondedtothecommentsareatthebeginning\nof each response. A revised version with tracked changes is uploaded for supporting review, in which each\nresponse is marked at the margin. All figure numbers refer to the resubmitted manuscript, unless noted\notherwise. Bibliographic references can be found in the manuscript.\nI. Responses for Reviewer-1\n1.1: The paper is well-written and the figures are good. The main weakness of the manuscript is that\nthe new results are only based on one single 2D seismic line from the 2002 survey (that included multiple\nlines), so it is unclear if what they observe extends into the 3rd dimension. Presumably the method they use\ncould be applied to other 2D lines from the 2002 survey to see if the results are consistent with their present\nconclusions (and allowing the extrapolation of their results from one 2D line into 3D). The paper would be\nstronger and more convincing if the interpretations were supported by more than one 2D line. There is much\nmore information that could be gained by considering the 3rd dimension (for example, spatial extent of the\nmagma reservoirs, spatial variations melt fraction, etc).\nResponse: Weagreewiththereviewerthat3DimagingforAxialSeamountcangiveamorecomprehessive\nviewthan2Dseismicanalysis. Limitedbytheavailabledataandtheexpensivecomputationalrequirements\nof3Dwaveforminversion,2Dseismicvelocityinversionandreflectionimagingarecommonlyusedforstudy-\ning the structure of mid-ocean ridges. Representative publications include:\n(1) Wilcock, W.S., Solomon, S.C., Purdy, G.M. and Toomey, D.R., 1992. The seismic attenuation structure\nof a fast-spreading mid-ocean ridge. Science, 258(5087), pp.1470-1474.\n(2) Team, T.M.S., 1998. Imaging the deep seismic structure beneath a mid-ocean ridge: The MELT experi-\nment. Science, 280(5367), pp.1215-1218.\n(3) Guo, P., Singh, S.C., Vaddineni, V.A., Grevemeyer, I. and Saygin, E., 2022. Lower oceanic crust formed\nby in situ melt crystallization revealed by seismic layering. Nature geoscience, 15(7), pp.591-596.\n(3) Vaddineni, V.A., Singh, S.C., Grevemeyer, I., Audhkhasi, P. and Papenberg, C., 2021. Evolution of the\ncrustal and upper mantle seismic structure from 027 Ma in the equatorial Atlantic Ocean at 2 43 S. Journal\nof Geophysical Research: Solid Earth, 126(6), p.e2020JB021390.\n(4) Holmes, R.C., Tolstoy, M., Cochran, J.R. and Floyd, J.S., 2008. Crustal thickness variations along the\nSoutheastIndianRidge(100116E)from2Dbodywavetomography. Geochemistry,Geophysics,Geosystems,\n9(12).\n(5) White, D.J. and Clowes, R.M., 1990. Shallow crustal structure beneath the Juan de Fuca Ridge from\n2-D seismic refraction tomography. Geophysical Journal International, 100(3), pp.349-367.\n(6) Dannowski, A., Grevemeyer, I., Ranero, C.R., Ceuleneer, G., Maia, M., Morgan, J.P. and Gente, P.,\n2010. Seismic structure of an oceanic core complex at the MidAtlantic Ridge, 22 19 N. Journal of Geophys-\nical Research: Solid Earth, 115(B7).\nAccording to the reviewer’s suggestion, we have incorporated more analysis into the updated manuscript.\nThe 3D geometries for the main magma reservoir (MMR) and the high-melt upper MMR are shown in\nFig.S21, extractedfromthetomographymodelproposedbyArnulfetal. (2018). Thedescriptionregarding\ntheconnectionbetweentheMMRandothermagmareservoirsmaybeinaccurateintheoriginalmanuscript.\nWe have rewritten and revised them in the updated version. Furthermore, to validate our models, we have\ncarefully analyzed the reflection images of Arnulf et al. (2014) and Carbotte et al. (2020), the geodetic\ndata in Chadwick et al. (2022), the 3D tomography velocity model by Arnulf et al. (2018), and slip along\noutward-dipping fault planes from Hefner et al. (2020). Detailed discussions can be found in the responses\nto questions 1.33, 1.47, 3.2, 3.11, 3.14, 3.18, and 3.19.\n1.2: Similarly, from the little that has been presented so far from a newer high-resolution 3D MCS seismic\nsurvey at Axial Seamount in 2019 (for example, in a 2020 AGU abstract by Arnulf et al), the newer MCS\nresults do not seem to support the conclusions in this paper (particularly the 2 “extra” magma reservoirs, nor\nthe lateral connections between them). Can the FWI method be applied to the data from the 2019 survey? If\nso, what would it show? Would it support the conclusions presented here?\nResponse: At the current stage, we do not have access to the 3D MCS seismic dataset. Upon reviewing\nthe reflection images in Carbotte et al. (2020), we observed some coherent reflection events at the locations\nof the newly identified magma reservoirs in the shallow crust. But previous studies did not interpret these\nreflections in detail. In addition, we examined the tomography velocity model and geodetic data from\npublished papers (Arnulf et al., 2018, Chadwick et al., 2022), which support our proposed model with\nmultiple magma reservoirs in the shallow crust. Regarding the 2019 3D dataset, we will discuss the data\nsharing process with Dr. Adrien Arnulf. If we gain access to this data in the future, we will try our best\nto conduct high-resolution 3D FWI to image the detailed velocity and attenuation structures beneath Axial\nSeamount.\n2\n1.3: So this raises the fundamental question of how confident we can be that the 2D P-wave velocity and\nattenuation variations in this paper really show the distribution of partial melt in the 3D shallow crust at\nAxial? And what is the real resolution of these data in terms of discerning relatively small structures and\nmelt conduits?\nResponse: The Rayleigh criterion, which states that the resolution of seismic imaging is approximately\none fourth of the seismic wavelength, is commonly used as a measure of resolution. Based on the velocity\ndistribution, the resolution is approximately 83 m in the shallow layer with a Vp of 3 km/s and around\n167 m in a deeper layer with a Vp of 6 km/s along the 2D plane. But because of using 2D inversion,\nthe uncertainty out of the plane is relatively large, with a resolution limit up to ten wavelengths (∼3-6\nkm). Regarding the reliability of 2D inversion results, we conducted tests using different parameters and\noptimizationmethods. Thepresenceofmultiplereservoirsintheshallowcrustandalow-velocitythroatare\nstable features. Therefore, the results along the J48 survey line are considered reliable. In seismology and\nmid-ocean ridge studies as shown in the response to question 1.1, 2D imaging is commonly employed and\nthe results can provide important insights into subsurface structure and geological information. Based on\nour high-resolution 2D models and previous 3D tomography model, we can extrapolate the 2D structures to\n3D to give give a general view of melt distribution.\n1.4: I think that some of the interpretations should be presented with less certainty and more as interesting\npossibilities than definite conclusions. For example, I think the existence and significance of the apparent\n“shallow LV zone” (dike conduit?) is highly debatable and not very convincing. For this reason, I do not\nthink it should be the focus of the Abstract (which should be completely re-written) or highlighted in the title.\nResponse:[Abstract] On reflection images, the nearly vertical dike conduits are very difficult to resolve,\nbecause useful signals cannot be recorded at surface (see the black line in the following figure). However,\nFWI is a high-resolution quantitative inversion method for estimating the subsurface physical property\n(velocity), which utilizes all kind of wave types, including refractions (yellow line), diving waves (red line)\nand scatterings (purple lines), thus having the potential to constrain vertical and fine-scale structures.\nIn seismology, therearemanysuccessfulapplicationsofFWItomapthemudstoneandsaltdiapirs(Xiaoetal,\n2016, Interpretation, An offshore Gabon full-waveform inversion case study; Wang et al, 2019, The Leading\nEdge, Full-waveform inversion for salt: A coming of age). According to the reviewer’s suggestion, we have\nrewritten the abstract, without highlighting the shallow low-velocity zone.\n3\n1.5: Instead, I would highlight the increased resolution of the seismic imaging method, the provisional\ninterpretation of multiple shallow magma reservoirs compared to earlier interpretations, the possible imaging\nof connections between them, and the deeper conduit below them. But it also important that the paper clearly\nstate that confirmation of these interpretations must await additional evidence from further studies.\nResponse:[Abstract, p. 6, 11] According to the reviewer’s suggestion, we have rewritten the abstract and\nemphasize the multiple magma reservoirs in the shallow crust in the update manuscript. We also added\nmore descriptions about the necessity to do more 3D investigation in the future.\n1.6: Line 13 (Abstract): To me, the Abstract does not do a good job of summarizing the key results. I would\nnot make the eastern offset of recent eruptive fissures an emphasis in (so I would omit the 2nd sentence).\nI think a more important conclusion to highlight in the Abstract, is that you image more magma reservoirs\nin the shallow crust compared with earlier analysis of this same data set. I think the Abstract should be\nre-written with that emphasis. In the 3rd sentence, you need to say you are only re-analyzing one 2D line\nfrom the 2002 MCS survey. The 4th sentence about melt fractions makes it sound like the “deeper feeding\nconduit” is part of the MMR, but in the rest of the paper it is treated as something separate. Rephrase to\nbe consistent. I would re-write the last 3 sentences of the Abstract to focus on the magma reservoir results\nrather than the “LV throat” and the eastern offset of recent eruptions.\nResponse:[Abstract] Following this suggestion, we rewrote the abstract in the updated manuscript, remov-\ning the second sentence and emphasizing the magma reservoir results.\n1.7: Line 21: I think your reference 28 (Carbotte et al., 2008) might be a more appropriate here than your\nreference 6 (Canales et al., 2009).\nResponse:[p. 2] We have changed the reference of Canales et al. (2009) to a more appropriate reference of\nCarbotte et al. (2008) in the revised manuscript.\n1.8: Line 25: You could add reference 56 here for the 2015 eruption.\nResponse:[p. 2] We have added the reference of Chadwick et al. (2016) here in the updated manuscript.\n1.9: Line 28: Reference 12 is not directly related to the details in this sentence. However, it could be used\nat the end of the previous sentence if you want.\nResponse:[p. 2] We have adjusted the references of West et al. (2001), Arnulf et al. (2014) and Arnulf et\nal. (2018) in these two sentences.\n1.10: Line 30: Again, not sure reference #6 (Canales et al., 2009) is relevant here.\n1.11: Line 32: Not sure reference #16 (Dziak et al., 2011) is relevant here.\nResponse:[p. 2] We have removed the reference of Dziak et al. (2012) here in the revised manuscript.\n1.12: Line 36: The end of this sentence doesn’t make sense because the eastern wall is seismically active.\nResponse:[p. 2] We have revised this sentence based on the reviewer’s suggestion to make it clear and\nreasonable.\n1.13: Line 39: It’s important to put this West et al. (2001) study in the right context. It was the first to use\nseismic tomography to attempt to image the magmatic system below Axial, so is significant. But its results\nnow seem primitive and coarse compared to the much higher resolution methods used by Arnulf et al. (2014;\n2018) from the 2D MCS survey in 2002 and the 3D MCS survey in 2019 (still unpublished except for AGU\nabstracts in 2019 and 2020).\nResponse:[p. 2] We have rewritten this sentence according to the reviewer’s annotation and adjusted the\nlocation in the text to describe the significance and limitation of West et al. (2001)’s work.\n1.14: Lines 42-44: Yes, but for both of these studies the melt fraction numbers are average values over a\nvery large volume.\nResponse:[p. 3] We agree with the reviewer about this point. The melt fractions estimated in these two\nstudies are average values over a large volume, which might have large uncertainty. We have revised this\nsentence to make it more reasonable in the updated manuscript.\n1.15: Line 47: You should reference where these numbers come from and clarify that they include\nestimates of the volume of lava flows and subsurface dikes.\nResponse:[p. 3] We have clarified the magma volume of seafloor lava flow and subsurface dikes, and cited\nrelated references in the updated manuscript.\n5\n1.16: Line 48: In Arnulf et al. (2014), which is reference #13, they interpreted a high melt zone at the top\nof the MMR beneath the southern part of the caldera, so a “high-melt zone” has been mapped before, but they\ndid not assign any quantitative melt fractions (just “high” and “low”, or “melt” and “mush”). Arnulf et al.\n(2018) placed some constraints on the melt fractions. So saying it’s “...unclear whether there is a high-melt\nzone ...” doesn’t seem accurate. What are you trying to say here exactly?\nResponse:[p. 3] We carefully checked the papers of Arnulf et al. (2014) and Arnulf et al. (2018) and agree\nwith the reviewer’s statement. Dr. Adrien Arnulf is also our co-author. The description in the original\nmanuscript might be not accurate. Here we would like to say that previous studies did not provide accurate\nand quantitative estimations of the melt fractions and magma volume in the high-melt zone due to limited\nresolution of seismic tomography and sparse distribution of geodetic stations. We have rewritten this part\nin the revised manuscript.\n1.17: Line 56: Whether it is easy or not is subjective. What are the authors really trying to say here?\nShould be rephrased. Is there an simple way to explain what “downward continued to the seafloor” means for\nreaders who are not seismic experts?\nResponse:[p. 3] As noted by Arnulf et al. (2018), the sources and receivers for multichannel seismic\ndata are located on the sea surface, far from the seafloor. The refractions, which carry critical velocity\ninformation, are typically masked behind strong scatterings from the seafloor, preventing a tomographic\napproach. Downward continuing multichannel data simulates a seismic acquisition right above the seafloor\nand produces a new dataset with virtual sources and receivers near the seafloor. In the new data, crustal\nrefracted arrivals become first arrivals that can be easily used for tomographic imaging. We have added\nmoredescriptionaboutdownwardcontinueddatatomakeiteasilytofollowforreaderswhoarenotfamiliar\nwith seismic acquisition.\n1.18: Line 58: You should note that it was called the “SMR” in Arnulf et al. (2018), ref #9 here, and that\nyou are calling it something different here (“EMR”).\nResponse:[p. 2]Wehaverephrasedtheabbreviationofthesecondarymagmareservoiras“SMR”hereand\nin Fig. 1.\n1.19: Line 64: In the caption for Figure S1, explain what Qp is and how it relates to the figure. Also\ncan you add a plain language explanation of what “viscoacoustic” means in this context?\np\nis defined as Q =2π E , where E is the elastic energy in a wave cycle and ∆E is the dissipated energy in\np ∆E\na cycle. Small Qp values indicate strong attenuation, while large Qp values reflect weak attenuation. We\nhave added more explanation in the caption of Fig. S1. In perfectly elastic solids, the stress is proportional\nto the strain but independent of the rate of strain, and the mechanical energy is stored without dissipation.\nOn the other hand, for perfectly viscous liquids, the stress is directly proportional to the rate of strain and\nindependent of the strain itself, but in this case the energy is completely dissipated (Toks¨oz et al., 1988;\nCarcione, 1993). A realistic representation of the Earth can combine the mechanical properties of elastic\nsolids and viscous liquids. In the resulting material, the stress depends upon both the strain and the rate\nof strain. Such a medium that has the characteristics of solids and liquids is named viscoelastic. A similar\nanelastic medium but only allowing P-wave propagation is called viscoacoustic, and the corresponding wave\nequation is viscoacoustic wave equation. In the main text, we have added a plain language explanation for\nattenuation and viscoacoustic.\n1.20: Line65: Cross-sectionsof“attenuation”areimportantintherestofthepaper. Ithinkitwouldhelpto\ntakeasentenceortwoheretoexplainwhat“attenuation”meansinthiscontextandwhatthesecross-sections\nshow.\nResponse:[p. 4] Seismic attenuation is a metric of elastic wave energy dissipation (Toks¨oz et al., 1988;\nCarcione, 1993). It strongly depends on temperature, partial melting and water content, and can provide\nvaluableinformationonEarth’sinternalstructureanddynamics,incomplementtothatlearnedfromseismic\nvelocity (Karato and Jung, 1998; Takei, 2017; Debayle et al. 2020). We have added more explanation in the\nupdated manuscript.\n1.21: Line 72: What data are fit better? Need to better explain this.\nResponse:[p. 4]Comparisonsofsyntheticandobserveddatashowthattheestimatedvelocityandattenua-\ntionmodelsfromtheFWIcanproducemuchmoreaccuratetraveltimesandwaveformsthanthosecalculated\nusing the initial tomographic models. In addition, the incorporation of attenuation in the FWI enables us\nto match the weak large-offset amplitudes.\n1.22: Line 75: How much of a velocity anomaly or how low a low-Q anomaly? And at what depths? Is this\nclaim substantiated in the figures in the Supplementary materials? If so, which figures?\nResponse:[p. 4] The descriptions in the original manuscript are not clear. We have revised this sentence\nto make it easier to understand in the updated manuscript.\n7\n1.23: Lines 82-84: To me, this sentence is poorly constrained speculation. “Hydrothermal cooling above the\nMMR”isaprettygenericexplanationandisunconvincing. Icanthinkofotherinterpretations(theexistence\nof thick, dense, ponded lava flows in the subsiding caldera floor block, for example), but I don’t think there is\ncompelling evidence for any one idea. Likewise, the low-velocity boundaries could be just due to the caldera\nfaults. There is nothing that convincingly identifies them as “magma pathways”. In fact, I might expect a\nzone of diking to have higher velocities. Then there is the problem that zones of diking are likely vertical and\nnarrow, so would be hard to image seismically. Also, the references cited in this sentence seem generic and\ndo not particularly substantiate the interpretations. For all these reasons, I would omit this sentence.\nResponse:[p. 4] We agree with the reviewer’s interpretation. The high-velocity core could be formed by\nthick, dense, ponded lava flows on the subsiding caldera floor, and its low-velocity rims are more like to be\nthe inward-dipping fault zones formed by the subsidence of the caldera floor. If the diking zones are vertical\nstripes, it is very difficult to image using reflection data because we cannot record relative reflection signals\nat the surface (see the figure in the response to question 1.4). We have rewritten these two sentences in the\nupdated manuscript.\n1.24: Line 85: Does attenuation (Qp) have units?\nResponse: The quality factor (Q ) is defined as Q = 2π E , where E denotes the total energy in one\np p ∆E\nwave cycle and ∆E denotes the dissipated energy in one cycle. Therefore, Q is dimensionless, i.e., having\np\nno physical units.\n1.25: Lines 86-88: How does hydrothermal alteration “induce” high-porosity? Not obvious to me. Cracking\nitself and deformation make high porosity. Or the extrusive layer itself starts with high porosity.\nResponse:[p. 4] We agree with the reviewer on this point. After reviewing additional references, we have\nidentified that off-axis, cool, downflowing fluids can induce cracking in the host rock, thereby increasing\nporosity. However, near the axis, ascending hot fluids are likely to heat the surrounding rocks and poten-\ntially reduce preexisting porosity through thermal expansion or rapid deposition of hydrothermal minerals.\nTherefore,theobservedhighporositymaybeassociatedwiththeextrusivebasalticlayer,aswellascracking\nanddeformationcausedbyAxialvolcanoinflationanddeflation, andvelocityheterogeneities. Thissentence\nhas been revised in the updated manuscript to reflect these considerations.\n1.26: Line 95 (Figure 2): In Fig. 2, I would change the y-axis labels to “depth below sealevel” to clarify that\nit is not depth below the seafloor. What is the “perturbed Vp model” in Figure 2c? And what is the difference\nbetween Fig. 2a and c? This needs some explanation if this is what you are referring to as what is showing\n“more detail”. Is it just imaging the MMR in more detail? Or is it imaging multiple magma reservoirs in\nthe shallow crust in more detail? Also, I think the blue contours in Figure 2c deserve some explanation in\nthe text. What is interpreted that this contour signifies and what is it based on? I would also add a plain\nlanguage explanation of what Fig. 2b shows and why it makes intuitive sense (if it does). What is “seismic\nattenuation” exactly, and why isn’t there major (and more uniform) attenuation inside the MMR?\nperturbed Vp (δlnV ) model is the relative P-wave velocity anomaly, and it is calculated as δlnV =\np p\n(V −V )/V (detailed calculation is shown in the Methods), where V is the estimated velocity model\np p0 p0 p\n(Fig.2b)fromFWIandV isthebackgroundvelocitymodel(SupplementaryFig. S1c). Therelativevelocity\np0\nanomaly model (δlnV ) shows more details for multiple magma reservoirs than the absolute velocity model\np\n(V ). The blue contours are plotted according to the different melt fractions estimated in Fig. 4b. It shows\np\nthat the melt fractions are zoned in the MMR and underlying conduit. We have added more explanations\nin the figure caption and main text. Seismic attenuation reflects the energy dissipation during seismic wave\npropagations, which can be caused by viscous friction across grains and dislocations, fluid motions in pores\nand fractures, as well as wave scattering due to velocity heterogeneities. From our FWI model, we see that\nthe melt fraction in the upper MMR is greater than 32%, which is a framework of fluid-suspended crystals\nand has significantly reduced viscosity. However, in the lower MMR, the melt fraction decreases, leading\nto increased viscosity and low Q values. To enhance the understanding of Fig. 2b, we have added more\nplain-language explanations in the updated manuscript.\n1.27: Line 96: You need to indicate which panel in Figure 2 the reader should refer to to see this. Is this\nthe red/white “smile” at 2km depth in Fig. 2c? Also is the “P-wave speed anomaly” fast or slow? And is it\nreally “at the top” of the MMR, or above it?\nResponse:[Fig 2, p. 5] The thermal boundary layer is the “smile” at ∼ 1.5 km below the seafloor as shown\nin Fig 2c. We have added a marker in Fig 2c to show its location. The P-wave speed anomaly is slow. We\nhave revise this sentence in the update manuscript. In Arnulf et al. (2018)’s tomography study, the MMR\nis identified at the location shown by the red polygons in Figs. 2a and 2b. Our FWI produces a higher\nresolution result for the MMR (Fig. 2c), with its roof is slightly deeper than Arnulf et al. (2018)’s result.\nIn our FWI models, the slowest P-wave anomaly is observed in the upper MMR, as depicted in the newly\nplotted Fig. 2c.\n1.28: Line 98: Wait a minute ... there is “high-melt fraction” in the pink “smile” at 500 m depth below the\ncaldera? I thought the magma was in the MMR at ∼1 km depth below the seafloor. This needs clarification.\nResponse:[p. 5]WeagreewiththerevieweronthatthemagmaisintheMMRatdepth∼1.6kmbelowthe\nseafloor. The pink “smile” at 500 m depth below the caldera in the original manuscript is not the magma\nreservoir. We have added more labels on Fig. 2c to show the MMR and clarified in the text that the partial\nmelt is in the upper MMR.\n1.29: Line 103: What does this mean or imply and how does it make sense?\n1.27, we observed that the lower MMR has a smaller Q value than the upper MMR. This difference may\nbe attributed to variations in melt fractions. In the upper MMR, the melt fraction is near the eruption\nthreshold (∼30-50%), resulting in a framework of fluid-suspended crystals. This leads to decreased viscosity\nand relatively higher Q values. In contrast, the lower MMR has a smaller melt fraction and is in a crystal-\nsupported framework, resulting in increased viscosity and smaller Q values. We have revised this sentence\nin the updated manuscript to provide a clearer explanation.\n1.30: Line 108: I would say ∼7 km east of the MMR, if you measure from the center of the MMR to the\ncenter of the EMR.\nResponse:[p. 5] We have revised this sentence according to the reviewer’s suggestion using the distance\nfrom the center of the MMR to the center of the EMR.\n1.31: Lines 111-112: Depth below sealevel? Or depth below the seafloor?\nResponse:[p. 6]Intheoriginalmanuscript, themeasureofthedepthisbelowthesealevel. Intheupdated\nmanuscript, we use a depth measure below the seafloor (bsf) according to the reviewer’s suggestion.\n1.32: Line 117: Can this method really identify something of this scale at this depth? How do\nyou know this is actually a fluid conduit?\nResponse:[p. 6]Inseismology,theRayleighcriterioniscommonlyusedtomeasuretheresolutionofseismic\nimaging, which states the resolution is approximate one fourth wavelength. Inversion-based methods, such\nas least-squares migration and full-waveform inversion, offer higher resolution than one fourth wavelength\nbecause they reduce the Hessian blurring effect. The P-wave velocity in the magma reservoir is around 4.6\nkm/s, and the highest frequency used in the full-waveform inversion is 9Hz. Therefore, the resolution is 127\nm or less. From our FWI model, we observed the channel between MMR and WMR is greater than 200 m.\nTheoretically, it can be resolved using the FWI method. Based on the velocity, temperature, and partial\nmeltmodels, weobservedthatthischannelexhibitslowvelocity, hightemperatureand∼20%meltfraction.\nTherefore, it may be a magma conduit connecting the MMR and WMR.\n1.33: Line 118: I can’t help but wonder how confident can we be of this interpretation... This is just one\n2D seismic line. Would these “extra” low-V zones interpreted as magma reservoirs be imaged on other lines\nfrom the 2002 MCS survey? The evidence would be stronger if you saw the same things on other 2D lines\nand that made sense in three dimensions.\n3D structure of the MMR and WMR. For the data of the J48 survey line, we have done many tests of FWI\nby adjusting different parameters, including frequency bands, gradient smoothing size and optimization\nmethods. Alltestsshowedthatthelow-velocityanomalyofWMRisastablefeature. Wehavealsocarefully\nchecked the 3D tomography model from Arnulf et al. (2018). The velocity profiles of the J54 and J63\nsurveylines,whichrunparalleltotheJ48line,showthecontinuityofthelow-velocityanomalyintheMMR\ntowards the west-southwest direction (see the white arrows on the following J54 and J63 velocity profiles).\nIn addition, the velocity profile of the J45 line, which is perpendicular to the J48 line, reveals a low-velocity\nanomalyatadepthof2.5kmbelowthesealevel(seethedashedcircleontheJ45velocityprofiles). Although\nthetomographyresolutionislimited,theselow-velocityfeaturesareco-locatedwiththeWMRimagedinour\nFWImodel,providingevidencesupportingouridentificationoftheWMR.Inaddition,wealsoexaminedthe\nreflection images from Carbotte et al. (2020). We observed strong reflection events at the top of the WMR,\nMMR,SSMR,andSMRasshowninthefollowingfigure. Previousstudiesdidnotinterpretthesereflections\nin detail, but they are co-located with our newly identified multiple magma reservoirs in the shallow crust\n(see the red arrows and labels in the following reflection image).\n11\n1.34: Lines 118-121: I would say that the distribution of seismicity on the caldera ring fault doesn’t neces-\nsarilysayanythingaboutwhethertheWMRcouldfeedadiketothesurfaceinthewesternpartofthecaldera.\nThat said, there aren’t many eruptive fissures there from the last several hundred years from the mapping of\nClague et al. (2013). In general I think it’s dubious that MCS methods can image narrow vertical structures\nlike dikes in the shallow crust. I would not expect to see them, even if they do exist.\nResponse:[p. 6] We agree with the reviewer that there aren’t many eruptive fissures on the seafloor in the\nwestern part of the caldera. If the stresses on the western and eastern caldera shoulders are similar during\nvolcano inflations and deflations, and if there are magma pathways from deep high-melt reservoirs to their\nseafloor, eruptions can occur on both sides of the caldera. However, actual eruptions only occur from the\neastern side. In this study, we aim to reveal the subsurface volcano structure and try to explain why the\nmagma does not transport from subsurface magma reservoir to western caldera. From our FWI models, we\nobserved that there is no low-velocity zone beneath the western caldera, but there is a small WMR, which\nhelps in understanding volcano structures beneath Axial Seamount. Regarding seismic imaging for vertical\ndikes, the reflection method may not work because effective signals reflected from the vertical dikes cannot\nbe received on the surface (see the response to question 1.4). However, the FWI method uses not only the\nreflections but also refractions, diving waves and scatterings, thus having the potential to image the vertical\ndikes. Of course, the resolution depends on the frequency and optimized strategies used in the FWI, and\nthe imaging accuracy for thin vertical dikes using FWI needs further systematic investigation.\n1.35: Lines 121-124: I’m equally dubious of this interpretation. I’m not convinced this “LV throat” is\nreal or significant. The seismicity shows slip along the caldera faults during inflationary or deflationary\ndeformation. It doesn’t necessarily say anything about diking or the existence of a magma pathway there. In\nfact, one might expect a “diking pathway” to have a high velocity. I’m not convinced that MCS can image\nnarrow vertical structures like “dike pathways”.\nResponse:[p. 6]Seismicvelocityisdeterminedbybulkmodulus(K),shearmodulus(G)anddensity(ρ). If\nmagma intrudes into sedimentary rock, the dike should exhibit a higher P-wave velocity than the host rock\nbecause the igneous rock commonly has greater bulk modulus and density. But beneath Axial Seamount,\nthecalderawasformedbyhistoricalintrusionanderuptionevents. Thehostrockisoldanddenser,whereas\nthe dike is new and lighter. The diking pathway may have a slower velocity than surrounding rock. As\nfor the accuracy of imaging the LV-throat, as discussed in response to question 1.34, it is difficult for\nreflection imaging methods to image narrow vertical dike pathway. However, FWI uses all kinds of wave\narrivals,includingreflections,refractions,divingwavesandscatterings,andhaspotentialtoimagefine-scale\nfeatures. The feasibility of FWI has been demonstrated, such as imaging detailed gas reservoir structures in\nthe North Sea (Operto et al., 2015, Geophysical Journal International) and complex salt structures in the\nGulf of Mexico (Wang et al. 2019, The Leading Edge).\n1.36: Line 141: I wonder why there isn’t a high melt fraction at the very top (roof) of the MMR in Figure\n4b. Isn’t that where the MCS data show the highest seismic reflections indicative of a change from solid to\nmelt?\net al. (2018). They defined the location according to reflection images. Because the migration velocity is\nbuilt using tomography, the image uncertainty is relatively large. Based on our FWI models, the roof of\nthe MMR is slightly deeper than Arnulf et al. (2018)’s model. Furthermore, our model shows that the top\nof the MMR (named the upper MMR in the text) has the largest partial melt, approximately reaching the\neruption threshold.\n1.37: Line 143: What you are calling the “upper MMR” in Figure 4, looks like the middle of the MMR to\nme, based on the pink and blue outlines.\nResponse:[Figs. 2and4]Inoriginalmanuscript,thepinkandbluepolygonsinFig. 4aretheMMRlocation\nidentified by Arnulf et al. (2018). In our new FWI model, the roof of the MMR is slight deeper. We have\nreplotted Figures 2 and 4 to show the locations of upper and lower MMR based on our FWI models.\n1.38: Line 145: Is the volume of melt in the “upper MMR” a subset? If so, what percent of the MMR is the\n“upper MMR”? How can you constrain the volume of the “upper MMR”, based on only one 2D MCS line?\nHow do you know the 3rd dimension for calculating a volume? Needs clarification.\nResponse:[p. 7, Fig. S21] We estimate the melt volume by combining our partial melt model and the\n3D MMR geometry extracted from the tomography model of Arnulf et al. (2018). The 3D geometries of\nthe whole MMR and high-melt upper MMR are shown in Fig. S21. The melt volume in the high-melt\nupper MMR is a subset of the whole MMR, and it is about 4-6% of the whole MMR melt according to our\nestimation.\n1.39: Line 147: Note reference #11 is duplicated as reference #43.\nResponse: We have removed the original reference of #43.\n1.40: Line 150: It’s still unclear what constitutes the “upper” vs. “lower” MMR.\nResponse:[Figs 2c, 4b, p. 7] We have added labels on Figs. 2c and 4b to show the locations of the upper\nand lower MMR. They are identified according to the estimated partial melt fractions.\n1.41: Line 162: What is the “boundary layer” in Figure 5?\natthebaseoftheuppercrustaldike,belowwhichrisingmeltpondandaccumulate,formingtheaxialmagma\nreservoir (Suzanne et al., 2021). We have modified the label of original Fig. 5 and added more explanation\nin the caption.\n1.42: Line 168-170: I’m not convinced the data show this, especially the “LV throat”. You could\nhave drawn these features on Figure 5 before this study was done, because it was already\nobvious there is some sort of focusing of magma from the top of the MMR into dikes that\nintrude upward near the eastern caldera fault, but I’d say the reasons for that are still\nunclear. To me, the results in this paper do not illuminate why that is the case.\nResponse:[p. 8] Previous studies, including seismicity, active- and passive-source tomography, seismic\nreflection imaging, and multibeam mapping, have revealed the geometry of the MMR and seafloor fissures,\nbut they do not provide high-resolution subsurface structure beneath Axial Seamount. In this study, we\nutilized the advanced full-waveform inversion method to constrain P-wave velocity and attenuation models\noftheJ48surveyline,followedbycalculatingtemperaturesandpartialmeltfractions. Thesemodelsrevealed\nmultiple magma reservoirs in the shallow crust and a magma pathway beneath the eastern caldera, which\nimproves our understanding of the subsurface structure of this marine volcano and provides geophysical\nevidence for previous geological hypotheses.\n1.43: Lines173-178: Thisexplanationforthedifferencebetweentheeasternandwesternsidesofthecaldera\nseems very speculative.\nResponse:[p. 8] Previous seismicity studies show that more earthquakes occurred on the eastern outward-\ndipping fault than on the western fault, and the earthquake sources terminate deeper on the eastern wall\nthan on the western wall. In addition, using vertical deformation data, Hefner et al. (2020) demonstrated\nthat the 2015 eruption can be approximated by a nearly vertical prolate-spheroid pressure source, but the\neastern caldera fault has the most slip during the eruption. This suggests that the pressure in the magma\nconduit of the middle-to-low crust is relatively equal for both sides, but the stresses exerted on the caldera\nwalls in the shallow crust are different. Here, combined with our FWI models, we attempt to provide an\nexplanation for the differential stresses in the shallow structure of Axial volcano.\n1.44: Line 216: Actually, Clague et al. now think the present caldera only formed about 1100 years\nago (the age reported in Clague et al. (2013) is incorrect). This was presented in an AGU abstract: Clague,\nD. A., R. A. Portner, J. B. Paduan, M. Le Saout, and B. M. Dreyer (2019), Formation of the summit\ncaldera at Axial Seamount. Abstract presented at 2019 Fall Meeting, AGU, San Francisco, CA, 9-13 Dec.\nResponse:[p. 10] We have noted this AGU report and updated the formation time of the caldera in the\nmanuscript according to Clague et al. (2019).\n1.45: Lines 223-225: This is an interesting idea, but what would explain the SMR?\nsurveylinedoesnotcrossthecenteroftheSMR.Therefore,basedonthisstudyalone,wecannotaccurately\ninfer the formation of SMR. Arnulf et al. (2014, 2018) have suggested possible magma conduits linking the\nMMRandSMRbasedonseismicmigrationsections. Togainabetterunderstandingofmagmaaccumulation\nprocesses within the SMR and magma movement between these two reservoirs, more geophysical data are\nneeded to be acquired over the SMR.\n1.46: Lines 229-232: This is the first acknowledgement that all the results in this paper are based\non only one 2D seismic line and that this could limit what you can conclude! In my opinion, there should be\nmuch more of this type of discussion of the limitation of this study, and what would be needed to better\nsubstantiate the tentative results presented.\nResponse:[p. 6, 10] We have added more descriptions in the revised manuscript about the limitations of\nthe 2D seismic investigation.\n1.47: Another important question that should be addressed in the paper is: if they are real, why\nwere the WMR and ESMR (the 2 “extra” magma reservoirs) not previously identified by seismic reflection\nmethods in the 2002 (and 2019) MCS surveys? To me, seismic reflection is a more compelling way to\nidentify where magma bodies exist in the crust, because of the strong reflections produced by the change\nfrom solid rock to liquid, whereas mapping seismic velocities seems like a less definitive and more indirect\nway of doing the same thing. Why should readers believe these new results based on only seismic velocities\nif they are not confirmed by reflection seismology?\nResponse: We have carefully checked the reflection images calculated using reverse-time migration from\nCarbotte et al. (2020). As shown in the following figure, there are actually some coherent reflection events\nat the top of WMR, SSMR and SMR identified in this study. But previous studies did not interpret these\nreflection energies in detail. The co-locations of these coherent reflections provide evidence for our newly\nidentified magma reservoirs.\n2.1: My suggestion for a minor revision concerns the discussion of melt faction. I confess that I have\na hard time wrapping my mind about quantifications like “ranging from 39% to 65%” (line 144). First,\nmelt fraction is likely a matter of spatial scale. I presume that at the finest scale, the maximum is 100%,\nmeaning that somewhere in the magma system is a little pocket of pure melt. So, a number like 39% is only\nmeaningful in the sense of representing an average with respect to some volume of material (rock+melt).\nAs the imaging is tomographic, I suppose that the relevant averaging volume ought to be based on the\nvolume of the resolving kernel. The Supplementary Material mentions resolution in connection with Figs\n10-12, but I was unable to discern how to use them to figure out this volume. After pondering the is-\nsue for a while, I would like to make the suggestion that the authors add an “exceedance plot” like this:\nHere, X is informed by some estimate of the resolving power of the tomography. Such a cumulative histogram\nwould provide more information than whats in line 144. It could be generated very easily from the model\nunderpinning the authors Fig 4b.\nwith respect to the inclusions of solid basalt and basaltic melt. According to the Rayleigh criterion, the\nresolutionofseismicimagingisapproximatelyonefourthoftheseismicwavelength. Therefore,theresolving\nkernel is about 83 m at a shallow layer with V ∼ 3 km/s and is around 167 m at a deep layer with V ∼ 6\np p\nkm/s. Following the reviewer’s suggestion, we have added an exceedance figure in the support information\n(Fig. S20) to show the relation between the melt volume and partial melt fractions (refer to the following\nfigure).\n30\n25\n20\n15\n10\n5\n0\n0 10 20 30 40 50\nMelt fraction, f (%)\n)3mk(\nf\n>\nnoitcarf\ntlem\nhtiw\nemuloV\nRange of maximum f\nTheerrorbarsarebasedontwoend-memberpartialmodels: onewithsphericalinclusionandtheotherwith\na vertically aligned elliptical body with an aspect ratio of 0.1. The fractions falling between the two dashed\nred lines represent the potential maximum partial melt range.\n2.2: I also confess that ranges like “39% to 65” (line 144) raise more questions with me than they answer.\nIs the range estimate a confidence interval, e.g., 52% +/- 13? If so, what is the formal confidence? Is it\n95%, or something else? What sources of variation contribute to this confidence, and has “model error been\nincluded. I imagine that model error (including the ability to map Vp and Qp into melt fraction) is the main\nsource of error. But speaking only for myself, and not for the authors, I have no confidence in my ability\nto quantify such an error. Anyway, I think that the authors ought to explain what they intend a range to\nmean. Such an explanation could be based on the exceedance plot (as in my figure). I also wonder whether\nan intercomparison of a range with that stated in another paper (as the authors provide, e.g., in line 40) is\nreally as straightforward as it seems. This point could be addressed with a few additional lines of text.\nResponse:[p. 21]Weagreewiththereviewerthatthereisarangeofconfidenceintervalandtheconfidence\ndepends on many factors. In this study, we first explained the low-velocity anomaly as much as possible\nusing temperature variations, and then estimated the partial melt fractions with temperature above 1,150\n◦C. Different inclusions have been tested to calculate melt models, and the models with spherical inclusion\nand vertically aligned elliptical body with an aspect ratio of 0.1 are used as the two end members. The\nabove exceedance plot has shown the error bars constrained from the two end-member models. We have\naddedmoreexplanationabouttheinfluencefactorsontheaccuracyofestimatedpartialmeltsintheupdated\nmanuscript.\n3.1: In discussing the connection between magma bodies, the authors seem to be inferring 3-D geometry\nfrom a 2-D inversion. A 2-D inversion can show bodies are connected but not demonstrate that they are not.\nIt is impressive that the inversions can image the magma pathway on the eastern wall, but we know from\nprevious studies that is where eruptions occur because that is where the plate boundary is, so what is new in\nthe interpretation?\nResponse: In this study, we utilized the advanced full-waveform inversion method to constrain P-wave\nvelocity and attenuation models along the J48 survey line, followed by detailed analysis of temperature and\npartial melt structures. Because full-waveform inversion can utilize not only reflections but also refractions,\ndiving waves, and scattering, it can resolve very fine-scale features. Its feasibility has been verified by many\nsuccessfulapplicationsinseismology,suchasprovidinghigh-resolutionimagesforgasreservoirsintheNorth\nSea and revealing complex salt structures in the Gulf of Mexico. Some descriptions about the connection\nbetween magma bodies in the original manuscript may be inaccurate. We have rewritten and revised them\nin the updated manuscript. Previous studies, including multi-beam mapping, seismic tomography, and\nearthquakelocation,haveshownthegeometryofthemainmagmareservoir(MMR)beneathAxialSeamount\nandthelocationofplateboundaryalongtheeasternwall. However,theydonotrevealthedetailedstructure\nbelow the surface fissures or how these fissures connect with the high-melt magma reservoirs at depth.\nThis study presents high-resolution P-wave velocity models, attenuation models, temperature profiles, and\npartialmeltdistributions, whichclearlymaptheconnectionbetweentheMMRandsurfaceeruptivefissures\n(plate boundary). Therefore, the innovation of this paper includes: (1) high-resolution P-wave velocity and\nattenuationmodelsalongtheJ48surveyline, (2)temperatureandpartialmeltprofiles, (3)multiplemagma\nreservoirs in the shallow crust beneath Axial Seamount, and (4) connections between subsurface magma\nreservoirs and between these magma reservoirs and surface fissures. Some additional details can also be\nfound in the response to question 1.1.\n3.2: The paper does develop some ideas about the asymmetry of the magma chamber relative to the caldera\nand its influence on the location of eruptions. There is also speculation that the connectivity to the western\nmagma body may play a role in supporting asymmetric on the caldera fault and several short deflation events\nobserved from 2016 to 2019, but the manuscript does not make any attempt to test this idea with the geodetic\ndata. With some thought and more reference to the prior literature, I think this manuscript could be revised\ninto an inciteful publication.\nResponse:[p. 9]Weagreewiththereviewerthatgeodeticanalysiswillhelptoverifythemodelproposedin\nthis study. We carefully reviewed the work of Chadwick et al. (2022) and found that during the June 2018\nshort-term deflation event, the bottom pressure recorder on the western caldera wall experienced greater\nvertical displacement than those on the eastern wall (see the following figure). This may indicate that it is\nmorepossiblethatmagmamagmamovementbeneaththewesternwall,suchasfromtheMMRtoWMR,ledtothis\ndeflation event. We also provide a detailed explanation in response to question 3.19.\n18\n3.3: 14-51. It is not clear what questions are motivating this study?\nResponse: According to three reviewers’ comments and suggestion, we have carefully revised our\nmanuscript, rewriting many places. Previous studies have revealed the location and geometries of the main\nmagma reservoir, as well as the surface eruptive fissures. However, few studies have explored whether addi-\ntional fine-scale magma reservoirs exist beneath the caldera, and there are no high-resolution velocity and\nattenuation images of Axial Seamount directly showing the conduit from the MMR to surface fissures. Our\nstudy, based on advanced full waveform inversion, identified multiple magma reservoirs in the shallow crust,\nin addition to the MMR, and revealed a possible magma pathway beneath the eastern wall. This provides\nimportant geophysical evidence to reveal the magma plumbing system of Axial Seamount. In addition, we\nconstrained the temperature and partial melt profiles based on the velocity and attenuation models, which\nare more accurate than those using only velocity models. A high-melt zone in the top layer of the MMR\nis observed, with a melt fraction near the eruption threshold and a comparable volume to recent magmatic\nevents. This indicates it may be the magma source of recent eruptions.\n3.4: 34-36 “Although previous studies revealed the location of the subcaldera magma chamber,\nit remains unclearwhyallrecenteruptionswereonlyfromtheeasternwallratherthanthetwoseismicallyactivewalls.”\nI disagree, it is very clear why recent eruptions are on the east wall. This is where the plate boundary is and\nwhere the summit connects to the north and south rifts, one of which also spreads in each eruption and takes\nmost of the melt volume. Given the location of the plate boundary (e.g., Chadwick et al., 2013), how can a\nspreading event be supported by an eruption on the west wall? It is interesting that the asymmetric offset of\nthe main magma chamber relative to the caldera which was first reported by Arnulf et al. (2014) centers it\nbeneath the plate boundary.\nChadwicketal. (2013,2017)havereportedtheeruptivefissuresassociatedwithrecenteruptions. According\ntothefirstreviewer’ssuggestion,wehaverewrittenthissentenceintheupdatedmanuscript. Thisworkiden-\ntifiesmultiplemagmareservoirsintheshallowcrust,inadditiontothemainmagmareservoirdocumentedin\npreviousresearch. Furthermore,thehigh-resolutionimagesgeneratedthroughfullwaveforminversionreveal\na low-velocity throat beneath the eastern caldera wall, potentially serving as a magma pathway from the\nhigh-melt reservoir to surface fissures. These findings augment our understanding of the subsurface magma\nplumbing structure beneath Axial Seamount and provide geophysical evidence supporting the eastern offset\nof recent eruptions.\n3.5: 48-50. “It is unclear whether there is a high-melt zone beneath the caldera with a melt fraction close\nto the eruption threshold and a volume comparable to the size of recent magmatic events.” If it is unclear\nwhat is the alternative? This is the only mechanism that I am aware of to explain eruptions on mid-ocean\nridges and the presence of a shallow high-melt zone supporting eruptions has been demonstrated along the\nEast Pacific Rise (e.g., Singh et al., 1998; Xu et al., 2022) and the Juan de Fuca Ridge (Canales et al.,\n2006).\nResponse:[p. 3]Accordingtothefirstreviewer’ssuggestion,wehaverewrittenthissentenceintheupdated\nmanuscript. In the revision, we emphasize the partial melt distribution in magma reservoirs and the con-\nnection between the high-melt zone in the MMR to the focusing of eruptive fissures near the eastern caldera\nwall in 1998, 2011 and 2015.\n3.6: 79-80. What is the significance of the shallow high velocity body in the caldera? At least in\nsome other calderas, the caldera infill has a very low velocity (e.g., Hooft et al., 2019). I think a review of prior\nobservations in calderas would be useful to interpret this result which is presently not interpreted.\nResponse:[p. 4] We have carefully reviewed the reference of Hooft et al. (2019). A 3-km-wide, cylindrical\nlow-velocity anomaly in the upper 3 km was revealed beneath the north-central portion of the Santorini\ncaldera. Hooft et al. (2019) interpret this anomaly as a low-density volume caused by excess porosities up\nto 28%, with pore spaces filled with hot seawater. As suggested by the first reviewer, the high-velocity core\nin the caldera may be formed by thick, dense, ponded lava flows on the subsiding caldera floor. We have\nrewritten this sentence in the updated manuscript.\n3.7: 80. “246 m” - To this level of precision?\nResponse: In seismology, the Rayleigh criterion (one fourth wavelength of the seismic wave) is commonly\nusedtomeasuretheresolutionofseismicimaging. FWIcanproduceabetterresolutionbecauseititeratively\nreduces the blurring effect of the Hessian matrix. Assuming a P-wave velocity of 3 km/s at the caldera and\nthe maximum frequency of 9 Hz used in FWI, the wavelength is ∼333 m and the scale that FWI can resolve\nis at least 83 m. Therefore, for a 200-m thick anomaly, FWI can provide a good constraint.\n20\n3.8: 81-82. The inward dipping normal faults are mainly identified by the caldera walls. Most of\nthe seismicity is on the buried outward dipping ring fault. While both Arnulf et al. (2018) and Waldhauser et\nal. (2020) associate some earthquakes with the inward dipping fault on the eastern side of the caldera,\nthe catalogs are inconsistent.\nResponse:[p. 4]Weagreewiththereviewerthattheinward-dippingfaultsaremainlyconstrainedbycaldera\nwalls. While some seismicity studies can detect these faults, there may be variations in their catalogs. We\nhave revised this sentence in the updated manuscript.\n3.9: 82-84. The first half of this sentence seems to be referring to structure right above the\nmagma body which doesn’t seem to be mentioned anywhere else. The second half seem to be referring to the\nfeature that is presented in more detail in line 121-124. The whole sentence is orphaned in a section on\nshallow structure and thus quite misplaced.\nResponse:[p. 4] According to the suggestion of the first reviewer, we have rewritten these two sentences to\nexplain the formation of the high-velocity caldera floor.\n3.10: 110-114. Since the center of the SMR is well to the south of the MMR (Arnulf et al., 2014)\nand this profile, there is no justification for concluding it lacks connectivity to the MMR from a 2-D model.\nI think this is a major flaw in the interpretation.\nResponse:[p. 6, 10] We agree with the review about this point. The SMR is to the south of the MMR and\nthe J48 survey line does not cross the center of the SMR. It is difficult to infer the connection of the MMR\nand SMR in real 3D structure. We have revised this sentence to clarify that the SMR may not connect to\nthe MMR along the image of the J48 line. In addition, we cannot rule out intermittent connection zones\nbetween the MMR and SMR that locate out of the image plane of the J48 survey line.\n3.11: 117. Is the WMR seen in the reflection data? If not, why not given the sharp velocity\ngradients near its top?\nResponse: The following figure is the reflection image calculated by Carbotte et al. (2020). As in the\nresponse to question 1.47, there are actually some coherent reflection events around the newly identified\nWMR and SSMR. But previous studies did not interpret these reflection energy in detail.\n21\n3.12: 119-121. I do not follow. Geometrically, the fault must terminate in a mushy zone that can\ndeform viscously, sothiscouldbeamagmaconduit. FromtheplotsinFigure4bandS15-18, itlookssuspiciouslylike\nthe earthquakes do root in the combined melt body, producing a notch in it, potentially because of enhanced\ncooling.\nResponse:[p. 6]Weagreewiththereviewerthatthefaultshouldterminateinaductile/viscouszone. Based\non seismicity distribution, there are some earthquakes in the magma conduit between the MMR and WMR,\nbut their number is not as large as that beneath the eastern caldera wall. As suggested by the reviewer, we\nhave revised this sentence in the update manuscript to ensure accuracy.\n3.13: 121. “In addition”. Should this be “Second” based on lines 114-115.\nResponse:[p. 6] We have changed “In addition” to “Second” in the updated manuscript.\n3.14: 122-124. How does this pathway compare with those inferred by Arnulf et al. (2014) from a\n3-D inversion?\nused to image the structures of MMR. We have carefully analyzed the pathways proposed by Arnulf et al.\n(2014). Asshownbytheredarrowsinthefollowingfigure,thereareacoupleofdippingpathwaysintheshal-\nlowcrustthatlinktheMMRandseafloorfissuresalongthereflectionprofileoftheJ48line. Thelow-velocity\nthroatidentifiedinthisstudymaybetheprojectionofthesepathwaysonthevelocityimageoftheJ48line.\n3.15: 145. How do the authors get this estimate? In Figures 4b/S15 the 32% region looks to be 0.2 km thick\nand 3 km wide so for the upper limit of 0.57 km3, this requires a 3rd dimension of 0.57 / (3 × 0.2 × 0.32) =\n3 km but the magma chamber extends 15 km along axis. If the 26% contour was used, there would be much\nmore melt, so why select the 32% contour other than to get the answer that is desired? Some clarification in\nsupplementary docs would be helpful.\nResponse:[p. 7] We estimate the melt volume by combining our partial melt fraction model with the 3D\ngeometry of the MMR described in Arnulf et al. (2018). As shown by Arnulf et al. (2014) and Chadwick et\nal. (2016) (see the following 2D zoned MMR figure), the MMR is zoned with different melt properties. The\nregionjustbelowthecalderaexhibitsstrongreflectionamplitudes, indicatingahighmeltfraction, whilethe\nnorthern region shows weak reflection energy, suggesting a smaller melt fraction. Therefore, the high-melt\nupper MMR does not extend to the entire MMR; it is only located just below the caldera (see the following\n3D MMR figure). We calculate the volume by first applying an area integral over the upper MMR based\non our melt model and then using the 3D MMR model to constrain the length. The total melt volume is\ncalculated similarly. We have added more description about the volume calculation in the main text.\n23\n24\n3.16: 156-159. How does this interpretation relate to previous interpretations of magma\nchambers on mid-ocean ridges? Isn’t this the long-standing interpretation of crustal magma\nchambers at mid ocean ridges (Sinton and Detrick, 1992; Singh et al., 1998)?\nResponse:[p. 8] We have carefully reviewed the papers by Sinton and Detrick (1992) and Singh et al.\n(1998). The crustal magma chambers at the mid-ocean ridge consist of melt and mush with varying partial\nmelt fractions. Here, our aim is to reveal the detailed melt structure of shallow magma reservoirs below\nAxial Seamount. We have revised this sentence and cited these two references in the updated manuscript.\n3.17: 173-176. IfmagmatransportinandoutoftheWMRrelaxesstresseswhyarethereremainingstresses?\nHefner et al. (2020) have modeled caldera inflation with asymmetric fault motions and show the remaining\ncaldera inflation is quite symmetric, so I am not sure what need to be explained by transport of magma in\nand out of the WMR? The fault motions are asymmetric because the center of inflating magma body is offset\nto the east of the caldera.\nResponse:[p. 8] Hefner et al. (2020) inverted a nearly vertical spheroid source to model caldera inflation\nduring the 2015 eruption, with a depth of 3.01 km, by removing fault-induced deformation. As analyzed by\nHefner et al. (2020), the source pattern indicates that the pressure in the magma conduit below the MMR\nis symmetric. However, the different slips on the western and eastern faults indicate that the stress in the\nshallowcrustisnotsymmetric. OurFWImodelscanprovidesomeinsighttoexplainsuchasymmetricstress\nresults in the shallow crust. The WMR may accommodate a part of the pressure beneath the western wall,\nand the viscous magma infilling and movement in the MMR and WMR may still produce some residual\npressure. This part of the pressure can be accommodated by the slip on the western outward-dipping fault\nplane.”\n3.18: 178-180. This is one reasonable explanation and that adopted by Hefner et al. (2020), but an\nalternative explanation is that the west wall is less coupled.\nResponse: Factors controlling fault coupling include a combination of effective stress and frictional prop-\nerties related to rheological and geometrical changes on the fault interface. Faults with low coupling ac-\ncommodate most of their slip as stable sliding, while the slip on faults with strong coupling is commonly\naccommodated by large earthquakes. If the western wall is less coupled than the eastern wall, the western\noutward-dippingfaultcanbestablyslidingandgeneratefewerearthquakes. Despitelessseismicityrecorded\nat the surface, its slip should be the same as the eastern wall if the pressure is the same on both sides.\nHowever, Hefner et al. (2020) have shown that during the 2015 eruption, the eastern fault had the most\nslip (with a maximum of 3.6 m), while the western fault had a maximum slip of 0.8 m. Therefore, it is\nchallenging to use low coupling of the western fault to explain its different seismic activity compared to the\neastern wall. Of course, accurate fault coupling analysis of the two faults and related factors requires future\ndetailed investigation.\n25\n3.19: 180.-182. The short-term deflation events from 2016-2019 are intriguing and loss of magma\nto the WMR is a feasible explanation, but such short-term deflation events were not seen between the 1998\nand 2011 eruptions and the 2011 and 2015 eruptions so they are not related to a process that is inherent to\nthe eruptive cycle as the model presented here seems to suggest. If these events are related to loss of magma\ninto the WMR, then they should be geodetically observable by comparing the pressure gauge and tilt meter\nfrom the cabled instruments at the ASHES vent field on the western side of the caldera with those\nelsewhere. Have the authors looked?\nResponse:[p. 9] We agree with the reviewer that short-term deflation events are not necessarily related\nto eruptive cycles but may be associated with the rate of magma supply. As shown by Chadwick et al.\n(2021), the supply rate has been waning since the 2015 eruption. The slow inflation may allow for the local\nmovement of magma in the multiple reservoirs in the shallow crust. We have carefully checked the data\nfrom bottom pressure recorders (BPRs) in Chadwick et al. (2021) for the June 2018 short-term deflation\nevent (see the following figure). The BPR on the western caldera wall, i.e., MJ03B (purple line), shows\ngreater vertical displacement than those on the eastern walls, MJ03D (brown line) and MJ03E (green line).\nThis may provide indirect evidence that this deflation event may have been caused by movement of magma\nbeneath the western wall.\n26\n3.20: 186-188. The lack of a magma pathway is consistent with magma not erupting along the\nwestern wall, but it is not an explanation of why there is no pathway.\nResponse:[p. 9] We agree with the review that the absence of a magma pathway and the lack of eruptions\nalong the western wall do not provide an explanation for why there is no pathway. Through analysis of\nourhigh-resolutionFWImodelsandpreviousseismicitystudies, weobservedthattheoutward-dippingfault\nbeneath the western wall terminates at the notch between the MMR and WMR. In addition, there is no\nlow-velocity stripping anomaly below the western volcano shoulder, as observed on the eastern shoulder.\nConsidering these observations, we infer that there may not have magma pathways beneath the western\nwall.\n3.21: 189-191. This is an odd choice of citations and prior work does not predict a broad magma\nbody -indeed quite the opposite. At the EPR Dunn et al. (2000) report a width that “is narrow in the lower\ncrust (5-7 km)” at 2-6 km depth and given the limits of travel time tomographic resolution, it presumably\ncould be even narrower. Indeed, in a more recent paper Dunn (2022) estimates a width of 4.5 km at shallower\ndepths broadening somewhat in the lower crust. Arnoux et al. (2019) also conclude the magma chamber is\nnarrow in the lower crust along the Endeavour segment of the Juan de Fuca Ridge. The model in this\nmanuscript only extends to 2.5 km bsf so it not at all clear how wide the low velocity zone is at greater depth.\nThe inversions in this manuscript have higher resolution and thus resolve structure beneath the MMR that not\nbeen resolved previously but it is not clear that if the image extended to greater depth, it wouldnt be anything\nother than very consistent with the prior travel time tomography studies.\nResponse:[p. 9] We have thoroughly reviewed the references of Dunn et al. (2000), Dunn (2022), and\nArnoux et al. (2019). In the original manuscript, we primarily referenced older papers, which may not have\nbeen the most appropriate. We have cited more recent works in the updated manuscript and revised this\nsentence for accuracy.\n3.22: 201-204. Where else other than the upper mantle can the melt come from? What is\npurpose of this sentence.\nResponse:[p. 9] Eilon and Abers (2017) revealed a region 50 km wide and 150 km deep with a 2% melt\nfraction beneath the Axial segment. Here we cite their work to explain the magma source in the mantle,\nwhich contributes to the formation of a compressive magmatic system below Axial Seamount.\n3.23: 221-227. This is interesting. 228-229. As noted above a 2-D image cannot show this.\nResponse:[p. 10] We agree with the reviewer on this point. The SMR lies to the south of the MMR, and\nthe J48 survey line does not intersect the center of the SMR. Based on the current 2D profile, we cannot\ninfertheconnectionbetweentheMMRandSMRinactual3Dconfiguration. Thedescriptionintheoriginal\nmanuscript may not be accurate. We have revised these sentences to clarify that the SMR may not connect\ntotheMMRatshallowdepthsontheJ48surveylineprofile,andwecannotruleoutintermittentconnection\nzones between them that lie outside of the image plane.\nReviewer #1 (Remarks to the Author):\nReview of revised manuscript by William Chadwick\nThis is my second review of this manuscript, which has been substantially revised. I find that\nthe revisions have addressed most of my concerns about the original manuscript and that\nthe paper is much improved. However, it still needs some minor revision to respond to\nsuggested edits and comments in the accompanying annotated manuscript.\nSpecific comments (keyed to lines in the annotated manuscript):\nLine 2 (Title): Consider making the title more informative by adding something like this to\nthe end: \"..., based on full waveform inversion of seismic data\"\nLine 13 (Abstract): I think it's important to make clear that you are not using data from the\nwhole seismic survey. Just one 2D line. I omitted \"short-term deflation events\" from the end\nof the Abstract, because they are a very limited and specific part of the observations at\nAxial, and this sentence is better as a \"big picture\" statement.\nLine 18: Could add a hotspot reference here, such as:\nChadwick, J., M. Perfit, I. Ridley, I. Jonasson, G. Kamenov, W. W. Chadwick, Jr., R. Embley, P.\nLe Roux, and M. Smith (2005), Magmatic effects of the Cobb Hotspot on the Juan de Fuca\nRidge, Journal of Geophysical Research: Solid Earth, 110, B03101,\ndoi:10.1029/2003JB002767.\nLine 32: Pre- and co-eruption would be 2014-2015 (not 2015-2016), but this statement\nreally applies to all the seismicity, so I omitted that qualifier.\nLines 34-36: Good statement of motivation.\nLines 45-50: I omitted this because geodetic data isn't used to constrain the melt fraction.\nLine 67 (Figure 1): In Figure 1b, it is actually difficult to see all the overlays because of the 3D\ntopography. Consider making this a 2D map instead. I think it would make it much easier to\nsee all the information.\nLines 67-83: This is a much improved description of methods.\nLines 87-88: To me, it would be better to leave out this comparison with Santorini, since it is\na silicic system, and its relevance is questionable.\nLines 111-112: Is a \"than\" missing in this sentence? I think you are trying to say that the\nCarbotte imagery shows a wider conduit than in this study, right? Need to clarify wording\nhere. Don't need phrase at the end of the sentence.\nLine 113: What does \"high melt-related viscosity\" mean here? Does this imply relatively high\ncrystal mush (vs. melt) content? If so, it would be clearer to use that terminology.\nLines 126-128: There already was a 3D MCS survey at Axial in 2019, led by Adrien Arnulf. Is\nthat what you are referring to here? If so, this sentence should be re-written to clarify that.\nOr this sentence could be omitted.\nLine 144: You don't need this first sentence.\nLines 211-213: This sentence seems a bit tangential to me and unnecessary. It isn't integral\nto the rest of the paragraph. Omit?\nLines 228-230: Again, this first sentence is unnecessary and could be omitted.\nLines 230-233: The evidence for the eastern side of the caldera being the source of most\nrecent lava flows is not so much from the distribution of different lava flow types, it's that\nthe eruptive fissures are clearly along the eastern edge of the caldera, and this is reflected in\nthe relatively shallower bathymetry where the south rift zone enters the caldera from the\nsouth.\nLines 243-244: The wording of this sentence is unclear. Omit, since it is not necessary.\nLine 249: I feel strongly that a sentence like this needs to be added here, to acknowledge\nthe limitations of what you can say from just one 2D seismic line: “One limitation of this\nstudy is that it is limited to only one 2D seismic line across the summit of Axial Seamount.\nAdditional insights might be gained by applying the analysis used here to other 2D lines\ncollected during the 2002 MCS survey. This would test some of our ideas about how magma\nand partial melt is distributed in the shallow crust and the connections between them. For\nexample, …”\nReviewer #2 (Remarks to the Author):\nReviewer 2. My original review was that the paper be published after minor revision to\naddress issues related to the quantification of melt fraction, with the strong suggestion that\nthe authors include an \"exceedance plot\" for better quantifying uncertainty. The authors\nhave added such a plot and use it effectively to address the issues that I raise. Additionally,\nafter reading the complete rebuttal document and spot-checking the revised manuscript, I\nfind that the authors to a very-reasonable job addressing the other reviewers' criticisms.\nConsequently, my opinion is that this paper is in excellent shape and may now be published.\nReviewer #3 (Remarks to the Author):\nThe authors have diligently but cautiously revised the manuscript and responded to the\nreviewers’ comments, and it is certainly in a form that is publishable. As noted in my first\nreview, the inversions are technically impressive, but in my view the revised manuscript still\nlacks a clear discernment of what is new and what just repeats previous ideas with a higher\nresolution model. There is nothing very exciting in the abstract which provides melt\nfractions that confirm existing ideas about the magmatic structure of Axial and mid-ocean\nridge volcanos in general and notes a conduit connecting the magma chamber to eruptive\nfissures where we know one must exist. Only the last sentence alludes to something new.\nTo my mind, an exciting new discovery is the western magma reservoir (WMR), which prior\nauthors seems to overlook, and its link to the eruptive cycle and asymmetry of the volcano. I\nsuggested that the reviewers look for geodetic evidence to support their idea that magma\nescaped to the WMR from the main magma reservoir (MMR) during deflation events. The\nauthors found this and presented it in their response to the reviewers, but it has not made\nits way into the manuscript. I am not sure why not.\nOn 3.18 (their numbering) they cite Hefner et all as evidence of less deformation on the\nwest wall in the 2015 eruption. Hefner took the measurements of couple deformation on\nthe faults from a seismic catalog (the figure in the response to the reviewers) as a constraint\nand then inverted them for a deflation model. That is not evidence that this was the actual\nslip on the fault.\nThe statement in the revised manuscript on line 251 “But we cannot rule out intermittent\nconnection between the MMR and SMR that is located outside of the image plane” is still\nmisleading because the authors cannot rule out a “permanent” connection based on a 2-D\nprofile.\nWilliam Wilcock\nDear reviewers:\nThis is our response to the reviews of manuscript, entitled “Asymmetric magma plumbing beneath Axial\nSeamount based on full-waveform inversion of seismic data”. Comments from editors and reviewers are in\nred italics and our response is in black normal type. Page numbers of the modification corresponded to\nthe comments are at the beginning of each response. A revised version with tracked changes is uploaded\nfor supporting review, in which each response is marked at the margin. All figure numbers refer to the\nresubmitted manuscript, unless noted otherwise. Bibliographic references can be found in the manuscript.\nI. Responses for Reviewer-1\n1.1: Line 2 (Title): Consider making the title more informative by adding something like this to the end:\n“..., based on full waveform inversion of seismic data”\nResponse:[Title] We have changed the title to “Asymmetric magma plumbing system beneath Axial\nSeamount based on full-waveform inversion of seismic data”.\n1.2: Line 13 (Abstract): I think it’s important to make clear that you are not using data from the whole\nseismic survey. Just one 2D line. I omitted “short-term deflation events” from the end of the Abstract,\nbecause they are a very limited and specific part of the observations at Axial, and this sentence is better as\na “big picture” statement.\nResponse:[Abstract] We have clarified that the full-waveform inversion is for a seismic 2D line and deleted\nthe description of “short-term deflation events” in the updated abstract.\n1.3: Line 18: Could add a hotspot reference here, such as: Chadwick, J., M. Perfit, I. Ridley, I. Jonasson,\nG. Kamenov, W. W. Chadwick, Jr., R. Embley, P. Le Roux, and M. Smith (2005), Magmatic effects of\nthe Cobb Hotspot on the Juan de Fuca Ridge, Journal of Geophysical Research: Solid Earth, 110, B03101,\ndoi:10.1029/2003JB002767.\nResponse:[p. 2] We have added this reference in the updated manuscript.\n1.4: Line 32: Pre- and co-eruption would be 2014-2015 (not 2015-2016), but this statement really applies\nto all the seismicity, so I omitted that qualifier.\nResponse:[p. 2] We agree with the reviewer about this point and have revised this sentence in the updated\nmanuscript.\n1.5: Lines 45-50: I omitted this because geodetic data isn’t used to constrain the melt fraction.\nResponse:[p. 3] We have deleted the description about geodetic data in this sentence.\n1.6: Line 67 (Figure 1): In Figure 1b, it is actually difficult to see all the overlays because of the 3D\ntopography. Consider making this a 2D map instead. I think it would make it much easier to see all the\ninformation.\nResponse:[Fig. 1b]WehavereplottedFig. 1bbyadjustingtheviewangleandazimuthtomakeallfeatures\nclear.\n1.7: Lines 87-88: To me, it would be better to leave out this comparison with Santorini, since it is a silicic\nsystem, and its relevance is questionable.\nResponse:[p. 4] We have delete the description about the comparison with Santorini volcano.\n1.8: Lines 111-112: Is a “than” missing in this sentence? I think you are trying to say that the\nCarbotte imagery shows a wider conduit than in this study, right? Need to clarify wording here. Don’t need\nphrase at the end of the sentence.\nResponse:[p. 5] Yes. We have added “than” in the this sentence to make it clear.\n1.9: Line 113: What does “high melt-related viscosity” mean here? Does this imply relatively high\ncrystal mush (vs. melt) content? If so, it would be clearer to use that terminology.\nResponse:[p. 5] Yes. High crystal mush produces strong seismic attenuation due to the viscosity. We have\nrevised this sentence according to the reviewer’s suggestion.\n1.10: Lines 126-128: There already was a 3D MCS survey at Axial in 2019, led by Adrien Arnulf. Is that\nwhat you are referring to here? If so, this sentence should be re-written to clarify that. Or this sentence\ncould be omitted.\nResponse: We have deleted this sentence to avoid confusion.\n1.11: Line 144: You don’t need this first sentence.\nResponse: We have deleted this sentence in the updated manuscript.\n2\n1.12: Lines 211-213: This sentence seems a bit tangential to me and unnecessary. It isn’t integral to the\nrest of the paragraph. Omit?\nResponse: We have deleted this sentence according to the reviewers’ comment.\n1.13: Lines 228-230: Again, this first sentence is unnecessary and could be omitted.\nResponse: We have deleted this sentence to make it more compact in the updated manuscript.\n1.14: Lines 230-233: The evidence for the eastern side of the caldera being the source of most recent lava\nflowsisnotsomuchfromthedistributionofdifferentlavaflowtypes, it’sthattheeruptivefissuresareclearly\nalong the eastern edge of the caldera, and this is reflected in the relatively shallower bathymetry where the\nsouth rift zone enters the caldera from the south.\nResponse:[p. 10] We agree with the reviewer’s about this point. These part has been revised according to\nreviewer’s annotation in the updated manuscript.\n1.15: Lines 243-244: The wording of this sentence is unclear. Omit, since it is not necessary.\nResponse: We have deleted this sentence according to the reviewers’ suggestion.\n1.16: Line249: Ifeelstronglythatasentencelikethisneedstobeaddedhere, toacknowledgethelimitations\nof what you can say from just one 2D seismic line: “One limitation of this study is that it is limited to only\none 2D seismic line across the summit of Axial Seamount. Additional insights might be gained by applying\nthe analysis used here to other 2D lines collected during the 2002 MCS survey. This would test some of\nour ideas about how magma and partial melt is distributed in the shallow crust and the connections between\nthem. For example, ”\nResponse:[p. 10, 11] We have added a couple of sentences to clarify the limitation of the 2D line analysis\nin the updated manuscript according to the reviewer’s suggestion.\nII. Responses for Reviewer 2\n3\n2.1: My original review was that the paper be published after minor revision to address issues related to\nthe quantification of melt fraction, with the strong suggestion that the authors include an “exceedance plot”\nfor better quantifying uncertainty. The authors have added such a plot and use it effectively to address\nthe issues that I raise. Additionally, after reading the complete rebuttal document and spot-checking the\nrevisedmanuscript, Ifindthattheauthorstoavery-reasonablejobaddressingtheotherreviewers’criticisms.\nConsequently, my opinion is that this paper is in excellent shape and may now be published.\nResponse: Thanks a lot for your suggestions. We have further revised the manuscript according to the\nother reviewers’ suggestions and comments.\nIII. Responses for Reviewer 3\n3.1: The authors have diligently but cautiously revised the manuscript and responded to the reviewers’\ncomments, and it is certainly in a form that is publishable. As noted in my first review, the inversions are\ntechnically impressive, but in my view the revised manuscript still lacks a clear discernment of what is new\nand what just repeats previous ideas with a higher resolution model. There is nothing very exciting in the\nabstract which provides melt fractions that confirm existing ideas about the magmatic structure of Axial and\nmid-ocean ridge volcano in general and notes a conduit connecting the magma chamber to eruptive fissures\nwhere we know one must exist. Only the last sentence alludes to something new. To my mind, an exciting\nnew discovery is the western magma reservoir (WMR), which prior authors seems to overlook, and its link\nto the eruptive cycle and asymmetry of the volcano. I suggested that the authors look for geodetic evidence to\nsupport their idea that magma escaped to the WMR from the main magma reservoir (MMR) during deflation\nevents. The authors found this and presented it in their response to the reviewers, but it has not made\nits way into the manuscript. I am not sure why not.\nResponse:[p. 1, 3, 9] We have revised the abstract according to the reviewers’ suggestions and emphasized\nthe newly discovered western magma reservoir in the abstract and main text. As for the geodetic evidence,\nwe have added more description in the main text of the updated manuscript.\n3.2: On 3.18 (their numbering) they cite Hefner et all as evidence of less deformation on the west wall in\nthe 2015 eruption. Hefner took the measurements of couple deformation on the faults from a seismic catalog\n(the figure in the response to the reviewers) as a constraint and then inverted them for a deflation model.\nThat is not evidence that this was the actual slip on the fault.\nResponse: WehavecarefullyreviewedHefner’spaper(2020)andfullyagreewiththerevieweronthispoint.\nThe inverted slips from a deflation model might not represent the actual slips on the faults, but rather they\nmay reflect the relative slip relationship of the faults beneath the western and eastern caldera walls.\n3.3: The statement in the revised manuscript on line 251 “But we cannot rule out intermittent connection\nbetween the MMR and SMR that is located outside of the image plane” is still misleading because the authors\ncannot rule out a “permanent” connection based on a 2-D profile.\nResponse:[p. 11] In the updated manuscript, we have added the limitation of the 2D analysis according to\nthe first reviewers’ suggestion, and also revised this sentence to avoid misleading.\n4"}]

Decision letter