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UBC Theses and Dissertations

Inversion of em data to recover 1-d conductivity and geometric survey parameter Walker, Sean Eugene


The presence of geometrical survey parameter errors can cause problems when attempting to invert electromagnetic (EM) data. There are two types of data which are of particular interest: airborne EM (AEM) and ground based horizontal loop EM (HLEM). When dealing with AEM data there is a potential for errors in the measurement height. The presence of measurement height errors can result in distortions in the conductivity models recovered via inversion. When dealing with HLEM there is a potential for errors in the coil separation. This can cause the inphase component of the data to be distorted. Distortions such as these can make it impossible for an inversion algorithm to predict the inphase data. Examples of these types of errors can be found in the Mt. Milhgan and Sullivan data sets. The Mt. Milligan data are contaminated with measurement height errors and the Sullivan data are contaminated with coil separation errors. In order to ameliorate the problems associated with geophysical survey parameter errors a regularized inversion methodology is developed through which it is possible to recover both a function and a parameter. This methodology is applied to the 1-D EM inverse problem in order to recover both 1-D conductivity structure and a geometrical survey parameter. The algorithm is tested on synthetic data and is then applied to the field data sets. Another problem which is commonly encountered when inverting geophysical data is the problem of noise estimation. When solving an inverse problem it is necessary to fit the data to the level of noise present in the data. The common practice is to assign noise estimates to the data a priori. However, it is difficult to estimate noise by observation alone and therefore, the assigned errors may be incorrect. Generalized cross validation is a statistical method which can be used to estimate the noise level of a given data set. A non-linear inversion methodology which utilizes GCV to estimate the noise level within the data is developed. The methodology is applied to 1-D EM inverse problem. The algorithm is tested on synthetic examples in order to recover 1-D conductivity and also to recover 1-D conductivity as well as a geometrical survey parameter. The strengths and limitations of the algorithm are discussed.

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