Structure-, stratigraphy- and fault-guided regularization in geophysical inversion

Geophysical inversion is often ill-posed because of inaccurate and insufficient data. Regularization is often applied to the inversion problem to obtain a stable solution by imposing additional constraints on the model. Common regularization schemes impose isotropic smoothness on solutions and may have difficulties in obtaining geologically reasonable models that are often supposed to be anisotropic and conform to subsurface structural and stratigraphic features. I introduce a general method to incorporate constraints of seismic structural and stratigraphic orientations and fault slips into geophysical inversion problems. I first use a migrated seismic image to estimate structural and stratigraphic orientations and fault slip vectors that correlate fault blocks on opposite sides of a fault. I then use the estimated orientations and fault slips to construct simple and convenient anisotropic regularization operators in inversion problems to spread information along structural and stratigraphic orientations and across faults. In this way, we are able to compute inverted models that conform to seismic reflectors, faults and stratigraphic features such as channels. The regularization is also helpful to integrate well-log properties into the inversion by spreading the measured rock properties away from the well-log positions into the whole inverted model across faults and along structural and stratigraphic orientations. I use a 3-D synthetic example of impedance inversion to illustrate the structure-, stratigraphy- and fault-guided regularization method. I further applied the method to estimate seismic interval velocity and to compute structure- and stratigraphy-oriented semblance.