Modeling and inversion of seismic data using multiple scattering, renormalization and homotopy methods

In the last couple of decades we have witnessed an increased use of 4D seismic data. Traditionally, the result of successful interpretation of 4D seismic data has been a better understanding of the oil saturation in the reservoir, leading to identification of the water-flooded areas and pockets of remaining oil, and an improved understanding of compartmentalization of the reservoir. This reservoir has been crucial in making decisions for drilling new wells. The success in use of 4D seismic data can be judged by the willingness to invest in such data. An example of such investments is the fact that a handful of fields at the Norwegian Continental Shelf are or are going to be equipped with permanent sub-sea monitoring equipment. The quantification of uncertainties in 4D seismic data is highly non-trivial, since the so-called seismic data are often the result of a complicated seismic processing or inversion task. Utilizing 4D seismic data for updating reservoir models has been done at different levels. The use of full waveform inversion methods can help us to obtain a better understanding of the propagation of uncertainties along the seismic processing chain.

Seismic scattering theory plays an important role in seismic forward modeling and is the theoretical foundation for various seismic imaging methods. Full waveform inversion is a powerful technique for obtaining a high-resolution model of the subsurface. In computational geophysics, many applications involve the use of seismic scattering theory. The Born scattering series is obtained by expanding the Lippmann-Schwinger equation in terms of an iterative solution based on perturbation theory. Such an expansion assumes weak scattering and may have the problems of convergence in strongly scattering media.

The first goal of this project is to develop seismic forward modeling methods for strongly scattering and strongly anisotropic media. The second goal of the project is to develop efficient methods for time-lapse full waveform inversion. Another goal is to estimate the uncertainty and multiparameter trade-offs in anisotropic elastic full waveform inversion based on integral equation approaches and the iterated extended Kalman filter. This includes: Develop a Kalman filter approach for Bayesian seismic waveform inversion suitable for application with the existing T-matrix approach to seismic modeling in scalar media with constant density and variable velocity, assess the uncertainty quantification for this approach by comparing it with a more rigorous approach for non-linear Bayesian inversion on suitable (simplified) cases, develop techniques for reducing computational costs and strategies for dealing with time-lapse seismic data. Develop an existing generalized T-matrix approach to seismic modeling in elastic media with variable density and elastic parameters; investigate the use of various approximations for speeding up the calculations and comparison with finite difference simulations; start with elastic FWI based on this forward model.