基于一阶弹性波方程的能量互相关成像条件

The energy cross-correlation imaging condition based on first-order elastic wave equations

基于地震波场能量构建的能量互相关成像条件,具有易实现、物理意义明确及背向散射压制效果明显等优势.但是,目前构建的能量互相关成像条件仅适用于二阶弹性波方程,难以直接应用于一阶弹性波方程.为此,本文针对一阶弹性波方程,基于能量守恒定理及能量密度,构建以速度-应力为参数的能量范数以表征弹性波场能量,将速度-应力能量范数拓展为能量内积以提取弹性波场反射能量.震源端与检波端的基矢量正方向保持一致的基础上,构建得到可有效压制背向散射的弹性波能量成像条件.数值模拟结果表明:该成像条件可以得到背向散射压制、振幅有效保持的能量成像结果.

The energy cross-correlation imaging condition,which takes the advantages of easy realization and suppressing the backscattering effectively,permits to generate images with definite physical meanings.However,such a condition designed by the second-order elastic wave equation cannot be used directly in the first-order elastic wave equation.To solve this problem,based on the energy conservation theorem and energy density,we construct an energy norm characterized by velocity-stress fields,representing the elastic wavefield energy.As for the source wavefield and the receive wavefield,we extend the velocity-stress energy norm to the energy inner product.Combined with the propagation direction of the forward and backward velocity-stress fields,the energy cross-correlation imaging condition is proposed to attenuate the backscattering.Numerical experiments indicate that this condition allow us to extract the results of reflected wavefield energy without extra computation and to suppress backscattering noise effectively.