A study of nonlinearity with spectral element method and linear slip effective medium theory

In exploration seismology, mapping the Earth’s interior structure in more detail is of great interest. The rocks’ microstructures, such as cracks, play an essential rule in oil and gas exploration and production. We study elastic nonlinearity because the microstructures are the main reason for this phenomenon. Nonlinearity is also related to the velocity change due to perturbations in the stress filed within the rocks. Many studies have observed the nonlinearity in field data as well as experimental data. However, the exact underlying mechanism of this phenomenon is not well understood. In this study, we provide some numerical examples of wave-perturbed cracked rocks and study the effects of crack aperture size, change of velocity inside crack, and crack orientation on the medium velocity change to better understand this phenomenon. Similar to a few other studies, we study the travel-time delay in a small wave caused by the propagation of a stronger wave. We show that there is a strong dependency between the crack parameters and the travel-time delay