Multi-dimensional, Multi-Constraint Seismic Inversion of Acoustic Impedance Using Fuzzy Clustering Concepts

Abstract. In the process of transforming seismic data into vital information about subsurface rock and fluid properties, seismic inversion is a crucial tool. This motivates researchers to develop several seismic inversion methods and software. Since the seismic data are band-limited, seismic inversion is ill-posed, and the results are not unique, each method tries to use initial information and assumes expected conditions for the results. Satisfying a general low-frequency trend and having a smooth model or step-wise results are some of the assumptions that these methods add as constraints to the inversion process. Well-logs, geological studies, and models from other geophysical methods can add important insight into the seismic inversion results. We introduce an objective function that applies the clustering properties of the prior information as a constraint to the seismic inversion process as well as other common constraints. An optimal solution to the objective function is explained. We applied the Gustafson-Kessel fuzzy C-means as one of the possible clustering methods for clustering term. Numerical synthetic and real data examples show the efficiency of the proposed method in the inversion of seismic data. In addition to the acoustic impedance model, the proposed seismic inversion method creates reliable deconvolved and denoised versions of the input seismic data. Additionally, the membership section output from the inversion process shows high potential in the seismic interpretation. Further research on selecting an optimum fuzziness, updating wavelet, and the potential of the membership sections to track horizons, distinguish sequences and layers, identify possible contents of the layers, and other possible applications are recommended.