Waveform inversion for orthorhombic anisotropy with P-waves: feasibility & resolution
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Earth Science and Engineering Program
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AbstractVarious parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.
CitationKazei V, Alkhalifah T (2018) Waveform inversion for orthorhombic anisotropy with P-waves: feasibility & resolution. Geophysical Journal International. Available: http://dx.doi.org/10.1093/gji/ggy034.
SponsorsWe thank Alexey Stovas and Daniel Kohn for their constructive and helpful reviews of the manuscript. We are grateful to Ju-Won Oh, Nabil Masmoudi and Ramzi Djebbi of SWAG, KAUST for helpful discussions as well. Vladimir Kazei is also grateful to Oleg Ovcharenko and Veronica Tremblay of KAUST for their suggestions on improving the manuscript readability. Finally, we thank KAUST for support and its HPC resources.
PublisherOxford University Press (OUP)