Three-dimensional elastic-waveform inversion of multi-component seismic data is one of the most powerful tools for obtaining high-resolution subsurface velocity models. These compressional- and shear-wave velocity models are crucial for accurate subsurface migration imaging, microseismic location and focal mechanism inversion, and geothermal reservoir characterization. Obtaining a high- accuracy inverted velocity model usually requires seismic data acquired with dense source/receiver arrays. However, seismic sources and/or geophones are often sparsely distributed. To improve velocity inversion with sparse seismic data, we incorporate a compressive sensing technique into elastic- waveform inversion. In our new inversion method, we use an alternating-minimization algorithm to solve the optimization problem. We apply our new inversion method to synthetic 3D vertical seismic profiling (VSP) data for a 3D geophysical model built using geologic features and well log data at the Raft River geothermal field. We compare our results obtained using a sparse source array with those produced with the conventional elastic-waveform inversion for the same sparse data, and show that our new method greatly improves the velocity inversion results for sparse VSP data.

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