A Hybrid Regularization Operator and Its Application in Seismic Inversion

Seismic inversion is an effective tool to estimate the properties of subsurface strata from seismograms. However, the intrinsic ill-posedness of the inversion problem causes the inverted subsurface properties to be easily polluted by inversion errors due to the random noise in the observed data. The inversion errors make it difficult to interpret the geological features of subsurface strata, especially their boundaries and textures. To recover high-fidelity inversion results from noisy observed data, we developed a hybrid total-variation (HTV) regularization operator in this research. Compared with the conventional total-variation (TV) regularization, the HTV regularization has two advantages when applied in seismic inversion. One advantage is that HTV regularization overcomes the typical staircase effect of conventional TV regularization while maintaining the advantage of TV regularization in edge-preserving properties. The determination of regularization parameters is also a difficult problem in seismic inversion with conventional TV regularization. A large regularization parameter may lead to an oversmoothed inversion result, while a small value leads to a noisy inversion result. Another advantage of HTV regularization is that it can generate proper inversion results even if a regularization parameter that is too large is adopted, which makes it easy to set the value of the regularization parameter. Numerical examples demonstrate the performance of the HTV regularization method proposed in this research.