Elastic wavefield tomography with probabilistic petrophysical clustering

Abstract

Full waveform inversion (FWI) aims to use all information provided by seismic data to deliver high resolution models of subsurface parameters. However, multiparameter FWI suffers from an inherent trade-off between parameters and from ill-posedness due to the highly nonlinear nature of FWI. Also, the models recovered using elastic FWI are subject to local minima if the initial models are far from the optimal solution. In addition, an objective function purely based on the misfit between recorded and modeled data may honor the seismic data, but disregard the geological context. Hence, the inverted models may be geologically inconsistent, and not represent feasible lithological units. We propose that all the aforementioned difficulties can be alleviated by explicitly incorporating petrophysical information into the inversion through a penalty function based on multiple probability density functions (PDFs), where each PDF represents a different lithology with distinct properties. We treat lithological units as clusters and use unsupervised K-means clustering to separate the petrophysical information into different units of distinct lithologies are not easily distinguishable. Through several synthetic examples, we demonstrate that the proposed framework leads FWI to elastic models that are superior to models obtained either without incorporating petrophysical information, or with a probabilistic penalty function based on a single PDF.