Effective Media for Transversely Isotropic Models Based on Homogenization Theory: With Applications to Borehole Sonic Logs

Sonic log records, including measurements of wave speeds in boreholes, provide critical input to the geological, geophysical, and petrophysical studies of a region under exploration. 1D background models are routinely built based on sonic log records for applications such as seismic imaging of hydrocarbon reservoirs and microseismic source inversions. Smoothing or 'upscaling' techniques are required to produce models in coarser scales than the very fine layers in the raw log data. In this paper, we follow the recently popular homogenization theory, derive its application to the special case of 1D TI models for both P-SV and SH waves, and show that it is consistent with the Backus averaging technique commonly used to upscale 1D fine-layered models. We examine a study case of sonic log data from a well in the Horn River Basin in northeastern British Columbia, a region known for its tight shale-gas deposit. We demonstrate the computational accuracy and efficiency gained by proper upscaling procedures for spectral-element simulations of seismic wave propagation, and discuss the effect of control parameters on wavefield recovery.