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Development of Specialized Nonlinear Inversion Algorithms, Basis Functions, Eikonal Solvers, and Their Integration for Use in Joint Seismic and Gravitational Tomographic Inversion

  • Author(s): Abatchev, Zagid
  • Advisor(s): Davis, Paul M
  • et al.

Many approaches and packages have been developed for tomographic inversion of seismic data and have consistently remained in high demand in both academic and industrial geophysics for subsurface imaging. However, our survey of published implementations has shown them to suffer from shortcomings. They include: low computational efficiency leading to overreliance on gradient-based inversion methods, non-robust forward models, and overparametrization of invertible fields leading to overconfidence in parameter resolvability and susceptibility to local minima. Additionally, many suffer from poor algorithmic documentation, lacking source code availability, and complicated dependencies of many published packages, resulting in difficulty with their reproducibility, testing, and adaptation. Finally, most available packages do not incorporate different measurement sets, such as gravitational anomaly data, to better constrain seismic inversion.

To address these issues, we have developed our own implementation and integration of an improved set of algorithms for seismic and gravitational tomography and applied it to a seismic data set from the Peruvian Andes obtained in a joint experiment with Caltech between 2008 and 2013. A summary of the work completed includes the development and/or demonstration of:

An efficiently parametrized scalar field basis function incorporating 2D and 3D Natural Neighbor Interpolation specialized for mantle tomography and mapping of irregular discontinuities such as a perturbed Moho. An emphasis on perturbation continuity and smoothness makes it suitable for use with appropriately damped gradient based inversion methods.

A hybrid Eikonal solver first arrival forward model, based primarily on the Fast Marching Method (FMM)(Sethian, 1997) and utilizing key elements of Vidale Finite Difference Method (VFD)(Vidale, 1991) in order to reduce model error. We demonstrate a simple and common velocity configuration in which VFD experiences a catastrophic failure, while our variant (designated FMM-VFD) performs with well constrained and small model error.

A hybrid inversion algorithm incorporating iterating sequential application of a custom Damped Gauss-Newton (DGN) algorithm and a Markov Chain Monte Carlo (MCMC) method, which allows for problem specific balancing of inversion robustness versus efficiency. Integration of the above into a joint gravitational, local seismic, and teleseismic master inversion algorithm.

In a tangential development with potential for future integration, we developed an experimental O(n^3*log(n)) quasi-parallel and sparse implementation of an Acoustic Wave Equation solver wavefront arrival model using FMM-VFD field pre-initialization.

Full disclosure and publication of key source code, written in a maximally simplified manner with no dependencies outside the C++ standard template library, included in a fully commented form to promote its verification, adaptation, and free use by others.

Local and teleseismic arrivals, as well as the published gravitational anomaly field over Peru have been used to invert jointly for local event locations, 3D mapping of the Moho, and mantle velocity perturbation structure, showing features consistent with the subducting Nazca slab. From the obtained results, we believe to have potentially identified the region in which the subduction of the Nazca plate undergoes flattening.

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