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Register a new userSeismic wave propagation in icy ocean worlds
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Seismology was developed on Earth and shaped our model of the Earths interior over the 20th century. With the exception of the Philae lander, all in situ extraterrestrial seismological effort to date was limited to other terrestrial planets. All have in common a rigid crust above a solid mantle. The coming years may see the installation of seismometers on Europa, Titan and Enceladus, so it is necessary to adapt seismological concepts to the setting of worlds with global oceans covered in ice. Here we use waveform analyses to identify and classify wave types, developing a lexicon for icy ocean world seismology intended to be useful to both seismologists and planetary scientists. We use results from spectral-element simulations of broadband seismic wavefields to adapt seismological concepts to icy ocean worlds. We present a concise naming scheme for seismic waves and an overview of the features of the seismic wavefield on Europa, Titan, Ganymede and Enceladus. In close connection with geophysical interior models, we analyze simulated seismic measurements of Europa and Titan that might be used to constrain geochemical parameters governing the habitability of a sub-ice ocean.
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Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exaspirated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the methods applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.
Achieving desirable receiver sampling in ocean bottom acquisition is often not possible because of cost considerations. Assuming adequate source sampling is available, which is achievable by virtue of reciprocity and the use of modern randomized (simultaneous-source) marine acquisition technology, we are in a position to train convolutional neural networks (CNNs) to bring the receiver sampling to the same spatial grid as the dense source sampling. To accomplish this task, we form training pairs consisting of densely sampled data and artificially subsampled data using a reciprocity argument and the assumption that the source-site sampling is dense. While this approach has successfully been used on the recovery monochromatic frequency slices, its application in practice calls for wavefield reconstruction of time-domain data. Despite having the option to parallelize, the overall costs of this approach can become prohibitive if we decide to carry out the training and recovery independently for each frequency. Because different frequency slices share information, we propose the use the method of transfer training to make our approach computationally more efficient by warm starting the training with CNN weights obtained from a neighboring frequency slices. If the two neighboring frequency slices share information, we would expect the training to improve and converge faster. Our aim is to prove this principle by carrying a series of carefully selected experiments on a relatively large-scale five-dimensional data synthetic data volume associated with wide-azimuth 3D ocean bottom node acquisition. From these experiments, we observe that by transfer training we are able t significantly speedup in the training, specially at relatively higher frequencies where consecutive frequency slices are more correlated.
The structure of the icy shells of ocean worlds is important for understanding the stability of their underlying oceans as it controls the rate at which heat can be transported outward and radiated to space. Future spacecraft exploration of the ocean worlds (e.g., by NASAs Europa Clipper mission) will allow for higher-resolution measurements of gravity and shape than currently available. In this paper, we study the sensitivity of gravity-topography admittance to the structure of icy shells in preparation for future data analysis. An analytical viscous relaxation model is used to predict admittance spectra given different shell structures determined by the temperature-dependent viscosity of a tidally heated, conductive shell. We apply these methods to the ocean worlds of Europa and Enceladus. We find that admittance is sensitive to the mechanisms of topography support at different wavelengths and estimate the required gravity performance to resolve transitions between these mechanisms. We find that the Airy isostatic model is unable to accurately describe admittance universally across all wavelengths when the shell thickness is a significant fraction of bodys radius. Our models suggest that measurements of admittance at low spherical harmonic degrees are more sensitive to thick shells with high tidal dissipation, and may complement ice-penetrating radar measurements in constraining shell thickness. Finally, we find that admittance may be used to constrain the tidal dissipation within the icy shell, which would be complementary to a more demanding measurement of the tidal phase lag.
Enceladus is characterised by a south polar hot spot associated with a large outflow of heat, the source of which remains unclear. We compute the viscous dissipation resulting from tidal and libration forcing in the moons subsurface ocean using the linearised Navier-Stokes equation in a 3-dimensional spherical model. We conclude that libration is the dominant cause of dissipation at the linear order, providing up to about 0.001 GW of heat to the ocean, which remains insufficient to explain the (about) 10 GW observed by Cassini. We also illustrate how resonances with inertial modes can significantly augment the dissipation. Our work is an extension to Rovira-Navarro et al. [2019] to include the effects of libration. The model developed here is readily applicable to the study of other moons and planets.
This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial condition of sufficient symmetry, this provides a valuable check for the validity of the numerical method that follows. A particular initial condition is found which allows for a new closed-form solution. A numerical scheme is then presented which combines a spectral (Fourier) representation for displacement components and wave-speed parameters, a fourth order Runge-Kutta integration method, and an absorbing boundary layer. The resulting large system of differential equations is solved in parallel on suitable enhanced performance desktop hardware in a new software implementation. This provides an alternative approach to forward modelling of waves within isotropic media which is efficient, and tailored to rapid and flexible developments in modelling seismic structure, for example, shallow depth environmental applications. Visual comparisons of the analytic solution and the numerical scheme are presented.
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