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The nearly analytic discrete (NAD) method is a kind of finite difference method with advantages of high accuracy and stability. Previous studies have investigated the NAD method for simulating wave propagation in the time-domain. This study applies the NAD method to solving three-dimensional (3D) acoustic wave equations in the frequency-domain. This forward modeling approach is then used as the “engine” for implementing 3D frequency-domain full waveform inversion (FWI). In the numerical modeling experiments, synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods. Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods. The inversion results show that the NAD method is more suitable than traditional methods, in terms of computational cost and stability, for 3D frequency-domain FWI, and represents an effective approach for inversion of subsurface model structures.

Energy loss in porous media containing fluids is typically caused by a variety of dynamic mechanisms. In the Biot theory, energy loss only includes the frictional dissipation between the solid phase and the fluid phase, resulting in underestimation of the dispersion and attenuation of the waves in the low frequency range. To develop a dynamic model that can predict the high dispersion and strong attenuation of waves at the seismic band, we introduce viscoelasticity into the Biot model and use fractional derivatives to describe the viscoelastic mechanism, and finally propose a new wave propagation model. Unlike the Biot model, the proposed model includes the intrinsic dissipation of the solid frame. We investigate the effects of the fractional order parameters on the dispersion and attenuation of the P- and S-waves using several numerical experiments. Furthermore, we use several groups of experimental data from different fluid-saturated rocks to testify the validity of the new model. The results demonstrate that the new model provides more accurate predictions of high dispersion and strong attenuation of different waves in the low frequency range.