The finite-difference method in microseismic modeling: Fundamentals, implementation, and applications

Abstract

The complexity of the seismic model around most reservoirs poses significant challenges for ray methods, even for 1D model structures. Scattering, waveguide, and near-field effects potentially create waveforms that can only be modeled adequately by the full elastic wave equation. Finite-difference modeling can form the basis of a new class of interpretation tool for these scenarios. Although used extensively in reverse time migration and full-waveform inversion algorithms, it is not commonly used in microseismic applications. Microseismic modeling places more stringent demands on the finite-difference method than its more conventional applications in surface seismic imaging. A finite-difference scheme can meet these requirements by carefully accounting for the main potential sources of error in modeled results. We examine the accuracy of finite-difference seismograms through comparisons with analytical results in a dip-slip modeling example. The value of this approach as an interpretation tool in microseismic modeling is demonstrated in a survey design example from the Fayetteville Shale, where scattering and waveguide phenomena have a significant effect on the observed amplitudes. We advise placing arrays at locations where amplitudes are robust to these effects when deploying real-time ray-based inversion methods in the field.