Numerical simulation of velocity gradient scattering waves in visco-acoustic smooth media based on F-K domain integration method

A popular attenuation velocity model for complete waveform inversion and seismic migration, the visco-acoustic (VA) smooth velocity model has first-order or high-order partitioned continuous derivatives. To compute the gradient scattering field caused by velocity gradient changes in the acoustic smooth velocity, we provide an integral technique in the acoustic F-K domain. We conduct Taylor expansion on the disturbance term and transform the velocity disturbance term into a velocity gradient term, in contrast to the conventional F-K domain integration approach that retrieves the scattering field caused by medium disturbance. Next, we compute the gradient scattering field in the VA smooth velocity model using the phase-shift interpolation (PSPI) technique. We examine the propagation law of gradient scattering waves in VA medium using the F-K domain integration technique in combination with the Futterman model. We provide a simulation approach for velocity gradient scattering wave numbers in the VA smooth medium, based on the numerical simulation technique in the F-K domain. The numerical study's results demonstrate that the viscosity of VA medium reduces the amplitude of seismic waves in that medium. The thicker seismic wave phase axis indicates the loss of certain high-frequency components. The amplitude of the seismic gradient scattering waves decreases in the smooth velocity model. After smoothing, the velocity gradient shift is relatively small, and the amplitude of the gradient scattering wave signal in the forward modeling of the viscous F-K domain method is greater than that in VA FD and VA Generalized Born approximation (VA GB) methods. The results of the numerical analysis have validated the effectiveness of the method.