Nonlinear design of geophysical surveys and processing strategies
The principal aim of all scientific experiments is to infer knowledge about a set of parameters of interest through the process of data collection and analysis. In the geosciences, large sums of money are spent on the data analysis stage but much less attention is focussed on the data collection stage. Statistical experimental design (SED), a mature field of statistics, uses mathematically rigorous methods to optimise the data collection stage so as to maximise the amount of information recorded about the parameters of interest. The uptake of SED methods in geophysics has been limited as the majority of SED research is based on linear and linearised theories whereas most geophysical methods are highly nonlinear and therefore the developed methods are not robust. Nonlinear SED methods are computationally demanding and hence to date the methods that do exist limit the designs to be either very simplistic or computationally infeasible and therefore cannot be used in an industrial setting. In this thesis, I firstly show that it is possible to design industry scale experiments for highly nonlinear problems within a computationally tractable time frame. Using an entropy based method constructed on a Bayesian framework I introduce an iteratively-constructive method that reduces the computational demand by introducing one new datum at a time for the design. The method reduces the multidimensional design space to a single-dimensional space at each iteration by fixing the experimental setup of the previous iteration. Both a synthetic experiment using a highly nonlinear parameter-data relationship, and a seismic amplitude versus offset (AVO) experiment are used to illustrate that the results produced by the iteratively-constructive method closely match the results of a global design method at a fraction of the computational cost. This new method thus extends the class of iterative design methods to nonlinear problems, and makes fully nonlinear design methods applicable to higher dimensional industrial scale problems. Using the new iteratively-constructive method, I show how optimal trace profiles for processing amplitude versus angle (AVA) surveys that account for all prior petrophysical information about the target reservoir can be generated using totally nonlinear methods. I examine how the optimal selections change as our prior knowledge of the rock parameters and reservoir fluid content change, and assess which of the prior parameters has the largest effect on the selected traces. The results show that optimal profiles are far more sensitive to prior information about reservoir porosity than information about saturating fluid properties. By applying ray tracing methods the AVA results can be used to design optimal processing profiles from seismic datasets, for multiple targets each with different prior model uncertainties. Although the iteratively-constructive method can be used to design the data collection stage it has been used here to select optimal data subsets post-survey. Using a nonlinear Bayesian SED method I show how industrial scale amplitude versus offset (AVO) data collection surveys can be constructed to maximise the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The results show that the optimal design is highly dependant on the model parameters when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered I find that, in the case of AVO experiments, a design with constant spatial receiver separation is close to optimal. This explains why regularly-spaced, 2D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also as providing data to constrain subsurface petrophysical information. Finally, I discuss the implications of the new methods developed and assess which areas of geophysics would benefit from applying SED methods during the design stage.