Full waveform inversion in fractured media based on velocity-stress wave equations in the time domain

In the process of seismic wave propagation, the presence of fractures will cause a seismic wave response associated with fracture compliance. Full waveform inversion (FWI) is an effective way to quantitatively obtain fracture compliance values, which can simulate seismic wave propagation in a fractured medium and compute the gradient expression of the fracture compliance parameters. To obtain the fracture compliance parameters quantitatively, a new technique based on FWI needs to be proposed. Based on linear slip theory, a new finite-difference scheme using a rotated grid has been developed to simulate the propagation of seismic waves in fractured media. The corresponding adjoint equation for FWI and the gradient of fracture parameter expression are presented. The crosstalk between normal compliance and tangential compliance is analysed in a homogeneous background medium. Numerical simulations in double-layer media show that the new gradient equation is effective.