Applied geophysical inversion

Еllis, Robert G.; Oldenburg, Doug

doi:10.1111/j.1365-246x.1994.tb02122.x

Cited by 179 publications

(107 citation statements)

References 8 publications

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“…The smoothness-constrained least-squares optimization method is frequently used for 2-D and 3-D inversion of resistivity data (deGroot-Hedlin & Constable 1990;Ellis & Oldenburg 1994;Loke et al 2013aLoke et al , 2014b. The 3-D model usually consists of many quadrilateral cells (Loke & Barker 1996).…”

Section: Data Inversion Model Resolution and The 'Compare R' Methodsmentioning

confidence: 99%

Computation of optimized arrays for 3-D electrical imaging surveys

Loke¹,

Wilkinson

Uhlemann

et al. 2014

Geophysical Journal International

141

120

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S U M M A R Y3-D electrical resistivity surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artefacts. Many 3-D surveys use a grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the x-direction. The 'Compare R' array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. The array geometric factor and its relative error are used to filter out potentially unstable arrays in the construction of the comprehensive data set. Comparisons of the conventional (consisting of dipole-dipole and Wenner-Schlumberger arrays) and optimized arrays are made using a synthetic model and experimental measurements in a tank. The tests show that structures located between the lines are better resolved with the optimized arrays. The optimized arrays also have significantly better depth resolution compared to the conventional arrays.

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Section: Data Inversion Model Resolution and The 'Compare R' Methodsmentioning

confidence: 99%

Computation of optimized arrays for 3-D electrical imaging surveys

Loke¹,

Wilkinson

Uhlemann

et al. 2014

Geophysical Journal International

141

120

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“…The L 2 norm or smoothness-constrained least-squares optimisation equation (deGroot-Hedlin and Constable, 1990;Ellis and Oldenburg, 1994) is given by…”

Section: Methodsmentioning

confidence: 99%

“…However, in cases when a sharp transition in the subsurface resistivity is expected (such as an igneous dyke), this method tends to smear out the boundaries. An alternative method is the blocky or L 1 norm optimisation method that tends to produce models with regions that are piecewise constant and separated by sharp boundaries (Ellis and Oldenburg, 1994). This might be more consistent with the known geology in some situations.…”

Section: Introductionmentioning

confidence: 99%

“…A commonly used inversion technique for 2D and 3D resistivity inversion is the regularised least-squares optimisation method (Sasaki, 1989;deGroot-Hedlin and Constable, 1990;Oldenburg and Li, 1994;Loke and Barker, 1996;Li and Oldenburg, 2000). This is a versatile method that allows the user to include available information about the subsurface as constraints on the inversion procedure, so that it will produce results that are closest to the actual subsurface geology (Ellis and Oldenburg, 1994). The use of the regularised least-squares optimisation method with two different constraints is discussed in this paper.…”

Section: Introductionmentioning

confidence: 99%

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A comparison of smooth and blocky inversion methods in 2D electrical imaging surveys

Loke

Acworth²,

Dahlin

2003

Exploration Geophysics

808

396

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Two-dimensional electrical imaging surveys are now widely used in engineering and environmental surveys to map moderately complex structures. In order to adequately resolve such structures with arbitrary resistivity distributions, the regularised least-squares optimisation method with a cell-based model is frequently used in the inversion of the electrical imaging data. The L 2 norm based least-squares optimisation method that attempts to minimise the sum of squares of the spatial changes in the model resistivity is often used. The resulting inversion model has a smooth variation in the resistivity values. In cases where the true subsurface resistivity consists of several regions that are approximately homogenous internally and separated by sharp boundaries, the result obtained by the smooth inversion method is not optimal. It tends to smear out the boundaries and give resistivity values that are too low or too high. The blocky or L 1 norm optimisation method can be used for such situations. This method attempts to minimise the sum of the absolute values of the spatial changes in the model resistivity. It tends to produce models with regions that are piecewise constant and separated by sharp boundaries. Results from tests of the smooth and blocky inversion methods with several synthetic and field data sets highlight the strengths and weaknesses of both methods. The smooth inversion method gives better results for areas where the subsurface resistivity changes in a gradual manner, while the blocky inversion method gives significantly better results where there are sharp boundaries. While fast computers and software have made the task of interpreting data from electrical imaging surveys much easier, it remains the responsibility of the interpreter to choose the appropriate tool for the task based on the available geological information.

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“…One method that is widely used is the linearized least-squares optimization method. (deGroot et al, 1990) and (Ellis et al, 1994), where the relationship between the measured data and model parameters is given by the following equation.…”

mentioning

confidence: 99%