Simulation of microseismic wave propagation using high-order finite difference velocity implementation on both source and media

Yao, Y., Wang, Y., Xue, Q.F. and Chang, X., 2021. Simulation of microseismic wave propagation using high-order finite difference velocity implementation on both source and media. Journal of Seismic Exploration, 30: 45-64. The characteristics of micro-seismic wave propagation of different source types have raised the interest of seismologists in the past few decades. When using staggered grid finite difference method as simulator, we need to establish a computational staggered grid which has N-th order accuracy and then do source implementation on this grid. There are two kinds of source implementations. One is the stress implementation, which applies the body force onto stress grid directly, and the other is the velocity implementation, which needs to convert body force into velocity component first and then applies the converted velocity component onto velocity grid. The existing velocity implementations mostly do the force-to-velocity conversion based on second-order accuracy, and this kind of implementation is fine when the wave propagation simulator also has second-order accuracy. However, with the increasing accuracy of finite difference simulator, there will be increasing errors due to the calculation order difference between wave propagation simulator and force-to-velocity conversion. We propose a N-th order staggered grid finite difference simulation formula which also has N-th order accuracy of force-to-velocity conversion. We make comparisons with analytical solutions in 3D homogeneous medium, and the results show the effectiveness and high accuracy of proposed approach.
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