A General Approach for Exchanging Structural Information - From A-Priori Data to a new Joint Inversion Algorithm
The inversion of geophysical data is usually non-unique, i.e., a variety of models is able to explain the data. We restrict the ambiguity assumptions such as smoothness constraints or by additional information. Often we have only structural information as from boreholes or other geophysical data. We...
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| Published in: | Eos (Washington, D.C.) Vol. 88; no. 25 (2007 Joint Assembly |
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| Main Authors: | , |
| Format: | Magazine Article |
| Language: | English |
| Published: |
19.06.2007
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| ISSN: | 0096-3941 |
| Online Access: | Get full text |
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| Summary: | The inversion of geophysical data is usually non-unique, i.e., a variety of models is able to explain the data. We restrict the ambiguity assumptions such as smoothness constraints or by additional information. Often we have only structural information as from boreholes or other geophysical data. We present a generalized minimization approach, which can be solved by any minimizer such as the Gauss- Newton method or conjugate gradients. In addition to the error-weighted residuals between data and model response, a roughness term is included. The derivative matrix, which can be formulated for any parameterization such as unstructured meshes, is weighted on model and constraint side by a model matrix and a constraint matrix. On one hand the model control weights or combines individual model cells and can be used for reparameterization or active constraint balancing. On the other hand, a boundary control defines the weight of the individual model boundaries. For example it can be set to zero for a known or assumed structural change. The first example is from a ground-water based study where fine-grained and coarse-grained sediments are to be separated by dc resistivity measurements. Four boreholes show this materials and a conductive basement at depth. At the layer positions allowed boundaries are introduced that help to improve the result significantly. Structural information may also come from other techniques such as seismics. We present an example where a refraction study has been carried out over a resistive lime stone to estimate the overlying volume. The refractor is introduced as allowed change in the resistivity survey and we see a good accordance in most regions, whereas in other the resistivity shows deviances. This proves structural information allows for but does not enforce abrupt changes. The latter is a basis for a new joint inversion algorithm where two tomographic properties are connected structurally. We use the techniques of robust modelling, i.e., the iteratively reweighted least squares. The roughness vector of one parameter is used to determine the weights for the other such that model gradients in both models are preferred. An example using dc resistivity and seismic refraction data shows a significant improvement of the images compared to independent inversion. Both images are finally combined by means of cluster analysis. |
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| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 SourceType-Scholarly Journals-2 ObjectType-Feature-2 ObjectType-Conference Paper-1 SourceType-Conference Papers & Proceedings-1 ObjectType-Article-3 |
| ISSN: | 0096-3941 |