Christina Morency

Computational poroelasticity — A review

Computational physics has become an essential research and interpretation tool in many fields. Particularly in reservoir geophysics, ultrasonic and seismic modeling in porous media is used to study the properties of rocks and to characterize the seismic response of geologic formations. We provide a review of the most common numerical methods used to solve the partial differential equations describing wave propagation in fluid-saturated rocks, i.e., finite-difference, pseudospectral, and finite-element methods, including the spectral-element technique. The modeling is based on Biot-type theories of dynamic poroelasticity, which constitute a general framework to describe the physics of wave propagation. We explain the various techniques and discuss numerical implementation aspects for application to seismic modeling and rock physics, as, for instance, the role of the Biot diffusion wave as a loss mechanism and interface waves in porous media.

Elastic imaging and time-lapse migration based on adjoint methods

We have drawn connections between imaging in exploration seismology, adjoint methods, and emerging finite-frequency tomography. All of these techniques rely on spatial and temporal constructive interference between observed and simulated waveforms to map locations of structural anomalies. Modern numerical methods and computers have facilitated the accurate and efficient simulation of 3D acoustic, (an)elastic, and poroelastic wave propagation. Using a 2D cross section of the SEG/EAGE salt model, we have determined how such waveform simulations might be harnessed to improve onshore and offshore seismic imaging strategies and capabilities. We have found that the density sensitivity kernel in adjoint tomography is related closely to the imaging principle in exploration seismology, and that in elastic modeling the impedance kernel actually is a better diagnostic tool for reflector identification. The shear- and compressional-wave speed sensitivity kernels in adjoint tomography are related closely to finite-frequency banana-doughnut kernels, and these kernels are well suited for mapping larger-scale structure, i.e., for transmission tomography. These ideas have been substantiated by addressing problems in subsalt time-lapse migration.

Seismic modeling and imaging based upon spectral-element and adjoint methods

The overarching goal of exploration geophysics is to map or “image” geological structures. Seismic migration, which attempts to map reflected and/or refracted signals to their actual spatial origin, plays a central role in imaging. Migration techniques are frequently based upon approximations to the seismic wave equation (e.g., ray-theory-based Kirchhoff migration or acoustic/first-arrival wavefield continuation methods).