3D elastic full-waveform inversion of small-scale heterogeneities in transmission geometry

Three-dimensional elastic full-waveform inversion aims to reconstruct elastic material properties of 3D structures in the subsurface with high resolution. Here we present an implementation of 3D elastic full-waveform inversion based on the adjoint-state method. The code is optimized regarding runtime and storage costs by using a time-frequency approach. The gradient is computed from monochromatic frequency-domain particle-velocity wavefields calculated with a time-domain velocity-stress finite-difference scheme. The 3D full-waveform inversion was applied to data of a complex random medium model, which resembles a realistic crystalline rock environment. We show synthetic inversion results of P-wave and S-wave velocities for two transmission geometries: (1) a 3D acquisition geometry with planes of sources and receivers and (2) a 2D geometry with two lines of sources and receivers, resembling a realistic two-borehole geometry. The 3D inversion of data acquired with 3D source-receiver geometry is capable to reconstruct differently sized 3D structures of shear and compressional velocities with resolution of about a wavelength. The 3D random medium data recorded with 2D acquisition geometry were inverted using 3D inversion and 2D full-waveform inversion for comparison. The 2D inversion suffers from strong artefacts that are caused by 3D scattering. The multiparameter 3D inversion, by contrast, is capable to invert the 3D scattered waves and to reconstruct 3D structures up to about 1-2 wavelengths adjacent to the plane between sources and receivers. The resolution is lower compared to the 3D acquisition geometry result. Still, a 3D inversion of cross-hole data can be beneficial compared to a 2D inversion in the presence of complex 3D small-scale heterogeneities, as it is capable to resolve 3D structures next to the source-receiver plane.