Inferring 3-D S- and P-velocity structure of D″
beneath Central America using waveform inversion
東京大学 大学院理学系研究科 地球惑星科学専攻 固体地球科学講座 修士2年 佐藤嶺Points•

We extend the waveform inversion method to infer Vs & Vp structure
simultaneously.

•Our models are consistent with previous studies but have higher
resolution than them.

•We image the paleo-Farallon slabs reaching the D″ region.

Introduction•••

The D″ region, the lowermost several hundred km of the Earth’s
mantle just above the core-mantle boundary (CMB), is thought tohave 3-D chemical heterogeneities (Garnero+ 2008; Tackley 2011)
and important to understanding the Earth’s chemical evolution.

Conceptual figure in D″ based on Garnero+ (2008) &Tackley (2011)
VsVp

It is required to infer both S- & P-wave velocity (Vs and Vp)
anomalous structures in order to distinguish thermal and chemicaleffects on the seismic velocities (Masters+ 2000).
Different resolution!!
Previous studies inferring Vs & Vp structure uses different kinds of The results of synthetic resolution test of Houser+ (2008). The regions
data or has a different resolution between Vs & Vp (e.g., Houser+ where checkerboard patterns are recovered well have good resolution2008).

Reference••••Garnero, E. J., & McNamara, A. K. (2008). Structure and dynamics of earth’s lower mantle. Science, 320(5876), 626-628. https://doi.org/10.1126/science.1148028
Houser, C., Masters, G., Shearer, P., & Laske, G. (2008). Shear and compressional velocity models of the mantle from cluster analysis of long-period waveforms. Geophysical Journal International, 174(1),195-212. https://doi.org/10.1111/j.1365-246X.2008.03763.x
Masters, G., Laske, G., Bolton, H., & Dziewonski, A. (2000). The relative behavior of shear velocity, bulk sound speed, and compressional velocity in the mantle: implications for chemical and thermalstructure. Geophysical Monograph Series, 117, 63-87. https://doi.org/10.1029/GM117p0063
Tackley, P. J. (2011). Living dead slabs in 3-D: The dynamics of compositionallystratified slabs entering a ‘‘slab graveyard’’ above the core-mantle boundary. Physics of the Earth and Planetary Interiors,
188(3-4), 150-162. https://doi.org/10.1016/j.pepi.2011.04.013

Dataset•

We use the waveforms from 105 deep- and intermediatefocus South American, Caribbean, and Alaskan
earthquakes in the period 2001-2019 with moment
magnitude 5.6 ≤ Mw ≤ 7.2 recorded at 2818 stations of thefull USArray & other networks.

•For transverse (T) components, we use 14,116 waveforms
cut from 20s before S to 60s after ScS with a period range
10s~200s.
For vertical (Z) components, we use 3077 waveforms cut
from 20s before P to 60s after PcP with a period range
5s~200s.

•Z component

T component

Event-station geometry. Red lines; The raypaths sampling the D″region, black crosses; the turning points at the CMB, orange stars;
seismic stations, and blue triangles; earthquakes※ Vs =𝜇 ⁄𝜌, Vp =••(𝜆 + 2𝜇)⁄𝜌 (𝜌: density)

The independence between 𝝏𝒖𝒁 ⁄𝝏𝝁 & 𝝏𝒖𝒁 ⁄𝝏𝝀•The vectors of 𝜕𝑢! ⁄𝜕𝜇 & 𝜕𝑢! ⁄𝜕𝜆 in each voxel are not orthogonal toeach other, which means 𝜕𝑢! ⁄𝜕𝜇 & 𝜕𝑢! ⁄𝜕𝜆 are NOT independent ofeach other•

It may be not easy to distinguish the effect of 𝜇 & 𝜆 from P wave

The absolute values of cosine of the angle between the vectors of 𝜕𝑢! ⁄𝜕𝜇& 𝜕𝑢! ⁄𝜕𝜆 in each voxel.

We divide target regions into 1528 voxels of dimensions
5°×5°×50km
Two isotropic elastic parameters (𝜇 & 𝜆) in each voxel aremodel parameters

OrthogonalParallelWaveform inversion•

Source parameter: GCMT (Global Centroid MomentTensor) solution•

Initial model: PREM (Dziewonski+ 1981)•

Compute synthetic waveforms using DSM (DirectSolution Method; Kawai+ 2006)•

Compute partial derivatives using the algorithm of Geller+(1993) & Borgeaud+ (2019)•Solve the inverse problem using the CG (ConjugateGradient) method•Use AIC (Akaike’s Information Criterion) to truncate theCG expansion•Since the amount of data for estimating model parameters are different (about 17,000 waveforms for 𝜇 and about 3000 waveforms for𝜆) and since 𝜕𝑢! ⁄𝜕𝜇 & 𝜕𝑢! ⁄𝜕𝜆 are not independent of each other, 𝜆 cannot be resolved when we infer 𝜇 & 𝜆 simultaneously using T &Z components of data.

•We conduct a two-step inversion. In the first step, we infer only 𝜇 using the T & Z components of data, and in the second step, weinfer 𝜆 using inferred 𝜇 and only the Z components of data.

•This method is based on the assumptions that 𝜇 is well constrained by the first step and that the remaining residuals between
observed waveforms and synthetics are due to the perturbation of 𝜆.

Reference••••

Borgeaud, A. F. E., Kawai, K., & Geller, R. J. (2019). Three‐dimensional S velocity structure of the mantle transition zone beneath Central America and the Gulf of Mexico inferred using waveform inversion.
Journal of Geophysical Research: Solid Earth, 124, 9664-9681. https://doi.org/10.1029/2018JB016924
Dziewonski, A. M., & Anderson, D. L. (1981). Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25(4), 297-356. https://doi.org/10.1016/0031-9201(81)90046-7
Geller, R. J., & Hara, T. (1993). Two efficient algorithms for iterative linearized inversion of seismic waveform data. Geophysical Journal International, 115(3), 699- 710. https://doi.org/10.1111/j.1365246X.1993.tb01488.x
Kawai, K., Takeuchi, N., & Geller, R. J. (2006). Complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media. Geophysical Journal International, 164(2), 411-424.
https://doi.org/10.1111/j.1365-246X.2005.02829.x

Inversion results
VpVs

Inversion results. Each model is sliced 50 km radially from the CMB to 400 km above the CMB. The blue and red colors indicate faster andslower seismic velocity than PREM. The shadowed regions indicate where the model parameter is not resolved.
•Vs is resolved in a wide region, while Vp is resolved in the region densely sampled by P-wave

Discussion•The two high-velocity anomalies (CA & VZ) and a low-velocity
anomaly (MX) just above the CMB are consistent with ourprevious Vs model (Borgeaud+ 2017)•

Our inferred model images the sheet-like high-velocity structure(CA′) interpreted as paleo-Farallon slabs

Our model

Borgeaud+ (2017)

Reference•

Borgeaud, A. F. E., Kawai, K., Konishi, K., & Geller, R. J. (2017). Imaging paleoslabs in the D″ layer beneath Central America and the Caribbean using seismic waveform inversion. Science Advances, 3(11).
https://doi.org/10.1126/sciadv.1602700