Bayesian estimation of resistivities from seismic velocities
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I address the problem of finding a background model for the estimation of resistivities in the earth from controlled-source electromagnetic (CSEM) data by using seismic data and well logs as constraints. Estimation of resistivities is normally done by trial-and-error, in a process called “inversion”, by finding a model of the earth whose responses match the data to within an acceptable error; what comes out of the inversion is what is put into the model by the geophysicist: it does not come out of the data directly. The premise underlying this thesis is that an earth model can be found that satisfies not only the CSEM data but also the seismic data and any well logs. I present a methodology to determine background resistivities from seismic velocities using rock physics, structural constraints, and depth trends. The physical parameters of the seismic wave equation are different from those in the electromagnetic diffusion equation, so there is no direct link between the governing equations. I therefore use a Bayesian framework to incorporate not only the errors in the data and our limited knowledge of the rock parameters, but also the uncertainty of our chosen and calibrated velocity-to-resistivity transform. To test the methodology I use a well log from the North Sea Harding South oil and gas field to calibrate the transform, and apply it to seismic velocities of the nearby Harding Central oil and gas field. I also use short-offset CSEM inversions to estimate the electric anisotropy and to improve the shallow part of the resistivity model, where there is no well control. Three-dimensional modelling of this resistivity model predicts the acquired CSEM data within the estimated uncertainty. This methodology makes it possible to estimate background resistivities from seismic velocities, well logs, and other available geophysical and geological data. Subsequent CSEM surveys can then focus on finding resistive anomalies relative to this background model; these are, potentially, hydrocarbon-bearing formations.