Seismic wavefield modelling of Enceladus to distinguish between interior structures
Authors: Dapré Kat , Irving Jessica C. E. 
Published: July 2021

Introduction

Enceladus' interior structure comprises an icy outer shell, a global water ocean, and a rocky core, with the ice shell thinning significantly at the south pole, and to a lesser extent at the north pole, and with its greatest thickness around the equator. However, there is a large amount of debate over the thicknesses, compositions, and densities of each of these layers. Central to this uncertainty is an imbalance in its thermodynamic energy budget; the energy required to maintain the global ocean and south polar vents is significantly more than that generated by tidal heating assuming a consolidated core, and heating from radiogenic elements is expected to be limited. A porous, hydrothermally altered, and mechanically weaker core has been proposed to increase tidal heating in the core and help sustain the global ocean. This theory is supported by the chemical composition of ejecta from the south polar vents, which indicates water-rock interactions.
Seismic research on Enceladus will benefit from the satellite's innate seismic sources, with high levels of eruptive and seismic activity at the south pole, as well as creaking along existing faults in the ice shell and potential for waves in the subsurface ocean, all generating distinctive seismic signals. The recent increase in Earth-based cryoseismology research can provide useful analogues to assist in characterising these sources and predicting wave propagation through the ice. Enceladus' small size and anticipated axisymmetry both help to minimise the computational resources necessary to produce detailed seismic wavefield simulations. Its 252km radius leads to short propagation distances that should enable even low-amplitude signals to be detected anywhere on the moon, and produces low interior pressures that help reduce the problem of extrapolation of material properties commonly associated with Earth-based seismology.
Models
Initially, an array of existing structural models were collected and quantified in order to draw comparisons between these results. These models, developed by numerous different authors, take various approaches including isostasy, libration, thermodynamics, and compositional constraints, and produce a wide range of results that demonstrate the inability of existing data to constrain a single coherent interior model. Three of these models were then recreated for analysis using the TauP toolkit software [1]: that of &#268;adek et al. [2], model 5 of Vance et al. [3], and model A1 of Neumann and Kruse [4], which are compared in Figure 1. Seismic velocities estimated by St&#228;hler et al. [5] were adopted for these models, using the higher, consolidated core velocity for the entire &#268;adek core, and the maximum ice thickness was assumed for the 1D &#268;adek model.

Ray theoretical results
Travel time predictions are shown in Figure 2. In general, the Vance model, with its thicker ice shell and hydrated upper core layer, enables a larger number of phases to travel further around the moon. Results for the Neumann model are fairly similar, though they show slightly less expansive wavefields. Meanwhile, the &#268;adek model's thinner ice shell terminates most phases by 90 degrees and reduces the difference in travel time between direct phases, such as the direct shear waves (S), and reflected phases, such as shear waves reflected once from the ice-ocean interface (ScS).

If detectable, PKJKP shear core phases, which appear at large distances in all three models, are likely to be useful in distinguishing between attenuation structures in the core to make inferences regarding its porosity. In addition, the thinner porous upper core layer in the Neumann model produces fewer core-underside reflected (PKIIKP) arrivals at any given distance than the thicker layer in the Vance model which, in contrast, produces an array of PKIIKP waves, some of which do not enter the deeper core and are instead reflected within the upper core. The boundary between the hydrated upper core and the consolidated deeper core has been specified to be sharp; however, a more gradational interface may suppress the number of these PKIIKP phases, and could be a useful diagnostic tool.
Ray theoretical travel time predictions alone cannot provide insight into how detectable, and therefore useful, each phase may be. In addition, the 1D models necessarily omit known complexities such as variations in ice shell thickness with latitude, as well as smaller length-scale heterogeneities suggested by surface features. However, this early stage of modelling has already demonstrated the effects that different hypothesised seismic structures may have on a seismic survey of Enceladus, and these discrepancies are likely to become more reliably diagnostic with a higher-dimension model.
Full wavefield simulations
Enceladus' main structural heterogeneities appear to vary primarily with latitude, for example in the thinning of the ice shell at the poles. In addition, the anticipated primary sources of seismic activity, in the form of fault reactivation and plume emissions, are located at the south pole. Beyond using ray theory, this research also employs the axisymmetric full waveform simulation code AxiSEM [6] to assess the seismic wavefields generated by quakes at the south pole of Enceladus. Initial investigations assess the detectability of different phases in the 1D models described above. Input parameters to AxiSEM can be modified to investigate the effect of variables such as attenuation properties and degree of core porosity or serpentinisation. The introduction of attenuation structures based on terrestrial measurements and expectations will improve the prediction of geographical variation in the detectability of key phases. Different types of source mechanisms can be explored in AxiSEM to describe the sources present on Enceladus. Comparison of the 2.5D wavefields generated by AxiSEM with the 1D TauP models will help to evaluate the impact of full wavefield modelling on our understanding of Enceladus.
References
[1] H. P. Crotwell, T. J. Owens, J. Ritsema, Seismological Research Letters 70, 154&#8211;160 (1999).[2] O. &#268;adek et al., Geophysical Research Letters 43, 5653&#8211;5660 (2016).[3] S. D. Vance et al., Journal of Geophysical Research: Planets 123, 180&#8211;205 (2018).[4] W. Neumann, A. Kruse, The Astrophysical Journal 882, 47 (2019).[5] S. C. St&#228;hler et al., Journal of Geophysical Research: Planets 123, 206&#8211;232 (2018).[6] T. Nissen-Meyer et al., Solid Earth 5, 425&#8211;445 (2014).