Model reduction in geostatistical seismic inversion with functional data analysis

Abstract

In subsurface modeling and characterization, predicting the spatial distribution of subsurface elastic properties is commonly achieved by seismic inversion. Stochastic seismic inversion methods, such as iterative geostatistical seismic inversion (GSI), are widely applied to this end. Global iterative GSI methods are computationally expensive because they require, at a given iteration, the stochastic sequential simulation of the entire inversion grid at once multiple times. Functional data analysis (FDA) is a well-established statistical method suited to model long-term and noisy temporal series. This method allows us to summarize spatiotemporal series in a set of analytical functions with a low-dimension representation. FDA has been recently extended to problems related to geosciences, but its application to geophysics is still limited. We have developed the use of FDA as a model reduction technique during the model perturbation step in global iterative GSI. FDA is used to collapse the vertical dimension of the inversion grid. We illustrate our hybrid inversion method with its application to 3D synthetic and real data sets. The results indicate the ability of our inversion methodology to predict smooth inverted subsurface models that match the observed data at a similar convergence as obtained by a global iterative GSI, but with a considerable decrease in the computational cost. Although the resolution of the inverted models might not be enough for a detailed subsurface characterization, the inverted models can be used as a starting point of global iterative GSI to speed up the inversion or to test alternative geologic scenarios by changing the inversion parameterization and obtaining inverted models in a relatively short time.