Joint waveform inversion with the separated upgoing and downgoing wavefields of VSP data

Abstract

Abstract Waveform inversion of Vertical Seismic Profiling (VSP) data, including upgoing and downgoing wavefields, is a challenging technique for building an accurate model. During the inversion process, upgoing and downgoing wavefields have different contributions to the objective function due to an energy imbalance between them that may cause the upgoing field to not be used effectively. Therefore, we propose a method of joint waveform inversion with the separated upgoing and downgoing wavefields of VSP data based on the establishment of a multiobjective function without introducing weight coefficients. The separating step with direct simulation of upgoing and downgoing wavefields of VSP data by the reflectivity method simplifies the complexity of separating wavefields. Specially, the zero-offset VSP data can be obtained in the τ−p domain to reduce computational cost greatly. Establishment of a multiobjective function of the difference between upgoing and downgoing wavefields can overcome the energy imbalance problem for them. The joint inversion step with a multiobjective optimization method avoids insufficient or incomplete information from just using an upgoing or downgoing wavefield alone. Numerical tests applied on synthetic models indicate that this method has the potential to increase the accuracy of estimating the velocity and density.