Finite‑difference forward modeling of pure qP wave based on new acoustic approximation

For the new acoustic approximation，the velocity of qSV wave in all directions is set to 0，which eliminating residual qSV waves present in traditional acoustic approximations during the simulation process，so it is naturally able to simulate pure qP wave. The spatial approximation method using propagation direction vectors instead of wave number vectors can be used to solve the qP wave dispersion based on the new acoustic approximation in the time - space domain by using finite difference methods，but there may be some theoretical errors. In order to improve the simulation accuracy of pure qP wave，this paper by introducing intermediate variable，the fractional spatial wavenumber domain mixed operator in qP wave dispersion relationship based on the new acoustic approximation is transformed into a linear equation for solving intermediate variables. This converts the complex qP wave dispersion relationship into a simpler form of time-space domain pure qP wave equation group，and the derivation process does not adopt any approximations. Therefore，this equation can accurately simulate the propagation law of qP waves based on the new acoustic approximation，theoretically with higher accuracy，and achieve pure qP wave forward simulation in two-dimensional VTI media through finite difference method. The numerical results also demonstrate that the new pure qP wave equation has higher accuracy. © 2024 Editorial office of Oil Geophysical Prospecting. All rights reserved.