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UNIVERSITY OF CALIFORNIA Los Angeles Development of Specialized Nonlinear Inversion Algorithms, Basis Functions, Eikonal Solvers, and Their Integration for Use in Joint Seismic and Gravitational Tomographic Inversion A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Geophysics and Space Physics by Zagid Abatchev 2019 c Copyright by Zagid Abatchev 2019 ABSTRACT OF THE DISSERTATION Development of Specialized Nonlinear Inversion Algorithms, Basis Functions, Eikonal Solvers, and Their Integration for Use in Joint Seismic and Gravitational Tomographic Inversion by Zagid Abatchev Doctor of Philosophy in Geophysics and Space Physics University of California, Los Angeles, 2019 Professor Paul M. Davis, Chair 1 Abstract 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 docu- mentation, 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 ii 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 disconti- nuities 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 cus- tom 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 exper- imental O(n3log(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 iii 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. iv The dissertation of Zagid Abatchev is approved. David D. Jackson Troy A. Carter Gilles F. Peltzer Paul M. Davis, Committee Chair University of California, Los Angeles 2019 v Contents 1 Abstract ii 2 Introduction 1 3 Methods 13 4 Waveform Pre-processing and Timing 16 5 Basis Function 22 5.1 NNI implementation algorithm . 22 6 Forward Models 30 6.1 Model Error Constraints . 30 6.2 Seismic Forward Model Survey . 32 6.3 Seismic Model Summary . 32 6.4 Seismic Model Selection . 36 6.5 Forward Model Algorithm Implementation . 36 6.6 Seismic Forward Model Testing . 41 6.7 Gravity Model . 45 7 Inversion Algorithms 49 7.1 Damped Gauss Newton Algorithm . 50 7.2 Markov Chain Monte Carlo Algorithm . 53 8 Top Level Integration and Tomographic Inversion 56 8.1 Parameter Initialization . 58 9 Synthetic Testing 62 10 Inversion Results and Error Estimation 65 vi 10.1 Figure Types . 66 10.2 Inversion Plots . 67 11 Conclusions 106 12 Prospective Research 110 12.1 Prior Knowledge Constraints . 110 12.2 Other Objectives . 114 13 Bibliography 116 13.1 Publications . 116 13.2 Online Data and Software Sources . 119 vii List of Figures 1 Peru Subduction Experiment (Source: Robert Clayton, Caltech). Colored circles indicate locations of seismic stations deployed by Caltech and UCLA by their designated line. Data collected between 2008 and 2013. 1 2 Philips et al. 2014: 2D first arrival tomographic inversion using selected data from PeruSE . 4 3 Philips et al. 2014: 2D receiver function inversion using selected data from PeruSE . 5 4 Peru reporting stations(black), USGS PDE catalog event coordinates and starting depths(color). 13 5 Single station local arrival pick aligned with local cluster wave stack median (20 samples/second). 17 6 Single station teleseismic arrival pick aligned with local cluster wave stack median (20 samples/second). 18 7 Five station local cluster of aligned teleseismic arrival wave forms (20 samples/second). 18 8 Top left: master waveform and aligned component wave forms. Top right: all traces phase centered at TauP arrival time. Bottom left: Full phase shifted cross correlated trace set. Bottom right: Picked-TauP residuals across early stage PeruSE network . 19 9 (a) Define Voronoi diagram of field nodes. (b) Define sample p, compute Voronoi cell (c) Compute area fractions of u[i] in u. (d) Weighted avg=field value at p. (Park,2006) . 23 10 Sample 2D NNI wire-mesh plot using 79 floating Voronoi nodes mapping the Moho surface/manifold (PeruSE network stations in black for reference) . 23 11 Sample 2D NNI color-map plot using 79 floating Voronoi nodes representing the Moho surface. Node locations in white . 24 viii 12 Side progression through sample 2 layer rendering of 79 floating 2D NNI Voronoi nodes representing the Moho manifold, and 109 floating 3D NNI Voronoi nodes representing a sample mantle p-wave velocity perturbation(spatial units are in grid scale, with 10km point spacing). 25 13 Side progression through sample 2 layer rendering of 79 floating 2D NNI Voronoi nodes representing the Moho manifold, and 109 floating 3D NNI Voronoi nodes representing a sample full density perturbation field versus standard earth density distribution(spatial units are in grid scale, with 10km point spacing, color bar scale is in grams/cc.) . 26 14 GPU implemented AWE prototype propagation. 33 15 GPU implemented AWE prototype propagation. 33 16 GPU implemented AWE prototype propagation. 33 17 Grid structure in FMM: Sethian, 1997. 36 18 Update procedure in a binary minheap: Sethian, 1997. 37 19 Travel time computation schemes: Vidale, 1990. 38 20 Upwind Eikonal solver scheme: Sethian, 1997. 39 21 FMM travel times through uniform medium. 42 22 1st order Eikonal FMM % error through uniform medium. 42 23 2nd order Eikonal FMM % error through uniform medium. 43 24 FMM-VFD hybrid forward model % error through uniform medium. 43 25 VFD forward model % error through 2 layer medium. 44 26 FMM-VFD hybrid forward model % error through 2 layer medium. 44 27 WGM2012 Bouguer anomaly mapping of Peru used for inversion. 46 28 Sample gravity forward model anomaly using test data. 47 29 Fractional error for sample density field render using fp32 GPU versus fp64 CPU implementations. 49 30 Block diagram of subroutines and models used in our inversion hierarchy. 61 ix 31 Synthetic data generating field using Gaussian perturbed halfspace model velocity parametrization. Gaussian perturbation amplitude: 1km/s; characteristic length: 60km. 63 32 3rd iteration of damped inversion using synthetic time data produced using 31. Gaussian perturbation amplitude: 1km/s; characteristic length: 60km. 63 33 Synthetic data generating field using Gaussian perturbed 2 layer model velocity parametrization. Gaussian perturbation amplitude: 1km/s; characteristic length: 60km. 64 34 3rd iteration of damped inversion using synthetic data field and perturbed 2 layer model velocity parametrization. Gaussian perturbation amplitude: 1km/s; characteristic length: 60km. 64 35 Single layer 3D view of relative node field uncertainty. 3rd iteration. Using locals, teleseisms. 68 36 Single layer Vp cross sections. 3rd iteration. Using locals. 69 37 Single layer 3D view of relative node field uncertainty. 3rd iteration. Using locals. 70 38 Top down gravity misfit(left), Moho depth(right) map. 0th iteration (initial conditions). Using locals, gravity. 71 39 Vp cross sections. 0th iteration (initial conditions).

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