Geomechanical Modeling Using a Damped Finite Difference Method and Seismic Imaging Using Secondary Scattered Waves

Modeling dynamic and static responses of an elastic medium often employs different numerical schemes. The elastic properties obtained from the dynamic propagation method are usually frequency dependent. To get the static solution, I introduced a damping parameter to the dynamic modeling process. By introducing damping into the system, I showed how the widely used time-marching staggered finite difference (FD) approach in solving the elastodynamic wave equation can be used to model time-independent elastostatic problems. I verified the damped FD approach by comparing results against the analytical solutions for several models, such as a simple homogenous and isotropic model, a borehole model, a laminated model, and the Hashin and Shtrikman model. I also validated my approach numerically for an inclusion model by comparing the results computed by the finite element (FE) method. The damped FD showed excellent agreement with both the analytical results and the FE results. I then applied the geomechanical modeling to a deep earthquake problem. Recent work using earthquake radiation patterns showed that the subducting slabs hosting deep earthquakes are strongly anisotropic. Such anisotropy may be caused by aligned fluid or melt inclusions of carbonates. If it is the case, I showed that the shear modulus of the inclusion must be less than one-tenth of the matrix shear modulus in order to achieve the strong anisotropy observed. It infers that the inclusion is highly possible to be carbonatite melt or other aqueous fluids. These discoveries constrain the amount of subducted carbon into the Earth carried by slabs. My second line of research is on seismic imaging. Steeply dipping faults, salt flanks, and subsalt sediments are important geological structures in energy exploration. Conventional seismic imaging in such areas is known to have challenges in imaging those features, due to poor illumination because of the use of singly scattered waves/primary reflections. I proposed to use multiply scattered waves, especially the secondary scattered waves, in the reverse time migration (RTM), to enhance the seismic illumination for imaging the steep faults and subsalt areas. I applied the method on two synthetic models, a trapezoidal model and the Sigsbee2B model. These two synthetic examples show that the new method achieves better imaging of steep faults and subsalt areas than the traditional RTM.