Elastic Wave Full-Waveform Inversion Method With Body-Fitted Grid On Undulating Ground

Full waveform inversion(FWI)uses the full wavefield information from seismic data to reconstruct the velocity of subsurface medium.It is a highly accurate velocity reconstruction method as it makes full use of the dynamics and kinematics of the seismic wavefield.The method obtains synthetic seismic records by means of elastic wave-equation forward modeling method,whose model is iteratively updated using a gradient descent optimization algorithm to minimize the difference between the observed and simulated data,thus obtains highly accurate velocity and other parameters.The conventional forward modeling method simulates the undulating surface wavefield by using a regular rectangular grid to finely dissect the undulating surface morphology,which causes spurious scattering during forward modeling and reduces the accuracy of forward modeling.In order to avoid these problems and to better adapt to the undulating surface conditions,this paper implements an elastic wave-equation forward modeling method based on the body-fitted coordinate system,and presents a difference format for forward modeling in the body-fitted system,together with the free boundary condition and absorbing boundary condition in this finite difference format,and applies it to multi-scale undulating surface FWI.The gradient expression for the FWI of elastic waves in the body-fitted coordinate system is derived and combined with an optimization algorithm to conduct elastic wave FWI based on the body-fitted system.In addition,a curvilinear-rectangular grid coupling mechanism is developed in this paper,which not only allows the construction of undulating surface patterns,but also saves computational cost.On the basis of the curvilinear-rectangular grid coupling mechanism,free surface conditions are considered and a simple model is tested in the FWI.The model test results demonstrate that the velocity with undulating surface can be achieved by FWI in the body-fitted coordinate system,which not only improves the simulation accuracy of the forward modeling,but also the accuracy of the reconstructed velocity model.