Stochastic Image-guided Structure-constrained Inversion

Abstract:

The inverse problem we often focus on in geophysics is to try to recover a subsurface model with data obtained from one or more geophysical survey methods, e.g. seismic or electrical methods, while the model parameters are corresponding petrophysical properties, e.g. density, velocity or electrical resistivity. If any prior information about the subsurface structure is given, for instance a guiding image believed to reflects the true structure features is available, we can incorporate it into the regularization term in the inversion, construct the model covariance and perform a structure-constrained inversion. Previous works have shown that compared to conventional inversion algorithms which use homogeneous and stationary regularization term, the image-guided structure-constrained inversion result not only honor the structure features of subsurface, but also tend to better recover the value of the petrophysical parameters of interest. So far, we have considered the guiding image to be perfectly known. If we reverse the concept, instead of trying to find the best geophysical model under constraint of known structure, we assume the subsurface structure is unknown and try to look for the image (or the set of images) which has the highest probability to be correct. This process can be achieved using a Bayesian approach of image-guided inversion. The idea is to parameterize structure features such as faults and sediment layer boundaries into random variables, each of which has a prior probability density. The data vector collected from geophysical survey is fixed, but each random vector of those structure parameters corresponds to a different guiding image, hence generates a different image-guided inversion result. An adaptive Metropolis MCMC algorithm will automatically and efficiently find the proposal distributions of the structure parameters, of which the corresponding images will result in inverted models with less data misfit, hence more possible to be the right image. We will discuss in details the theory of image-guided structure-constrained inversion and the Bayesian scheme. Using electrical resistivity data as an example, one synthetic case and one field case will be investigated. Structural modeling through this effective technique can be very helpful to all kinds of geophysical characterizations.