Pre-stack full wavefield inversion for elastic parameters of TI media

Abstract

Pre-stack full wavefield inversion for the elastic parameters of transversely isotropical media is implemented. The Jacobian matrix is derived directly with the finite element method, just like the full wavefield forward modelling. An absorbing boundary scheme combining Liao's transparent boundary condition with Sarma's attenuation boundary condition is applied to the forward modelling and Jacobian calculation. The input data are the complete ground-recorded wavefields containing full kinematic and dynamic information for the seismic waves. Inversion with such data is desirable as it should improve the accuracy of the estimated parameters and also reduce data pre-processing, such as wavefield identification and separation. A scheme called energy grading inversion is presented to deal with the instability caused by the large energy difference between different arrivals in the input data. With this method, parameters in the shallow areas, which mainly affect wave patterns with strong energy, converge before those of deeper media. Thus, the number of unknowns in each inversion step is reduced, and the stability and reliability of the inversion process is greatly improved. As a result, the scheme is helpful to reduce the non-uniqueness in the inversion. Two synthetic examples show that the inversion system is reliable and accurate even though initial models deviate significantly from the actual models. Also, the system can accurately invert for transversely isotropic model parameters even with the introduction of strong random noise.