Trapezoid coordinate finite difference modeling of acoustic wave propagation using the CPML boundary condition

Due to compaction of clastic sedimentary rocks caused by gravitational forces, the wave propagation velocity tends to gradually increase with depth. Based on this observation, a trapezoid coordinate system is built to integrate the general velocity variation, and an acoustic wave equation is derived in the new coordinate system. Numerically, a conventional uniform rectangular grid FD scheme can be evoked to solve the new equation. Physically, a variable grid mesh is used: that is, fine grids for shallow areas with low velocity and coarse grids for deep areas with high velocity. This method is free of artificial reflections caused by the transition of different grid sizes. Furthermore, the Convolutional Perfectly Matched Layer (CPML) boundary condition is adapted to eliminate artificial boundary reflections. A homogeneous velocity model is used to verify the effectiveness of the CPML boundary. Tests using the Marmousi benchmark model show that with the demonstrated comparable accuracy, the proposed method is 2.9 times as fast as the conventional physical uniform grid FD algorithm while saving as much as 75% of the computer memory.