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Unformatted text preview: Non-linear inversion of electrical resistivity data in a layered earth model Stanford University Department of Energy Resources Engineering 1 Introduction As is often the case in the Earth Sciences, engineers or geophysists are asked to quantify the subsurface on the basis of some remote sensing data. Under remote sensing we un- derstand that the medium (earth) has been sensed/tested/explored from a source that is a given distance away from the medium that we would like to characterize. For exam- ple, during a well test, the response of a reservoir to changing production conditions is monitored (pressure response over time). That response is (somehow) depending on the intrinsic properties of the reservoir rock nearby the well but also further away as the test progresses. In this case the intrinsic properties could be permeability and porosity of the reservoir layers. In geophysics, the same process takes place. For example, in the use of resistivity sounding data, one tries to infer the electrical resistivity properties of the subsurface in order to find certain anomalies, which might indicate ore bodies, gas and oil reservoirs. The response measured is now a potential at the surface, given an injected current into the subsurface. The subsurface then conducts or prohibits the conduction of currents in the subsurface, just as permeability allows flow in the subsurface for the well test case. The configuration of the geophysical device determines the depth at which you are sensing, just as the time variable in well test determines how far in the reservoir the well test operates. The important task of the class project is to invert the subsurface medium from remotely sensed data. We focus on resistivity sounding because the models are math- ematically well known and tractable compared to a well-test that often require the use 1 of flow-simulators. An example of inversion of flow data will be looked at later in the class. It is important to recognize that the methods we are going to develop for resistivity sounding data are similar as that for well-test or other remote sensing technique. The idea is to develop the methodology as you learn new techniques in class and apply them to a dataset. So after you have learned a new set of optimization techniques, you will apply them to the project, with the intention that at the end of the class you have a good overview of the various optimization methods for solving these kind of problems. Keep therefore in mind that the idea of this project is not to learn about resistivity sounding but to understand problems/pitfalls involved with optimization and inverse modelling in general. 2 Inverse modelling and optimization in general Inverse modelling in general has applications that reach far beyond Earth Sciences. The mathematics of inverse modelling has existed a long time, yet large scale applications have only become possible since the advent of modern computers....
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- Spring '10
- earth sciences, Inverse problem, apparent resistivity