Computer Modelling of Electrical Conductivity Structures

Williamson, Karina; Hewlett, C. W.; Tammemagi, Hans

doi:10.1111/j.1365-246x.1974.tb04102.x

Cited by 21 publications

(9 citation statements)

References 3 publications

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“…In doing so we believe we have uncovered some misconceptions and errors (other than the one pointed out by Williamson et al (1974)) in previously published work.…”

Section: Introductionmentioning

confidence: 79%

“…By doing this they have generously enabled other researchers to use the program directly for solving particular induction problems, but as a result they have exposed the algebraic details of their own work to greater scrutiny than that of other authors. An error in their finite difference representation of second derivatives for variable grid spacings was discovered by Williamson, Hewlett & Tammemagi (1974). Jones & Thomson (1974) have shown that its effect on calculated results is much reduced when a numerical grid whose spacings are not too irregular is used.…”

Section: Introductionmentioning

confidence: 99%

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On the finite difference solution of two-dimensional induction problems

Brewitt-Taylor

Weaver

1976

Geophysical Journal International

125

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The numerical solution by finite differences of two-dimensional problems in electromagnetic induction is reexamined with a view to generalizing the method to three-dimensional models. Previously published work, in which fictitious values were used to derive the finite difference equations, is discussed and some errors in the theory which appear to have gone undetected so far, are pointed out. It is shown that the previously published Bpolarization formulas are incorrect at points where regions of different conductivity meet, and that the E-polarization formulas are inaccurate when the step sizes of the numerical grid around the point are uneven. An appropriately-modified version of the two-dimensional theory is developed on the assumption that the Earth's conductivity is a smoothly-varying function of position, a method which naturally lends itself to three-dimensional generalization. All the required finite-difference formulas are derived in detail, and presented in a form which is suitable for programming. A simple numerical calculation is given to illustrate the application of the method and the results are compared with those obtained from previous work.

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“…In doing so we believe we have uncovered some misconceptions and errors (other than the one pointed out by Williamson et al (1974)) in previously published work.…”

Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

On the finite difference solution of two-dimensional induction problems

Brewitt-Taylor

Weaver

1976

Geophysical Journal International

125

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“…To check the influence of the source fields on the transfer functions is certainly necessary. Many calculations relevant to such a relationship using a 3-D model have been developed by Everett and Hyndman (1967), Williamson et al (1974), Honkura (1979), Liley and Arora (1982), Chen and Fung (1985, 1986, 1989. Several models with different dimensions and conductivity have been set to calculate its theoretic values of the induction arrows and total intensity.…”

Section: Discussionmentioning

confidence: 99%

Geomagnetic anomaly at Lunping before the 1999 Chi-Chi earthquake (M w = 7.6) in Taiwan

et al. 2011

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A strong earthquake with a magnitude of 7.6 (M L = 7.3) occurred on September 21, 1999, in central Taiwan. In order to discern any potential precursors before this earthquake, geomagnetic data at Lunping (LNP), Taiwan, Geomagnetic Observatory situated 100 km from the epicenter are examined using two methods, i.e., the traditional induction arrows and complex demodulation. Our results show that the remarkable temporal variation of real induction arrows appear to be strong prior to the great earthquake over the previous 24 months. After the great earthquake, the magnitudes of induction arrows decreased to the normal (mean of 8 years) levels. In other words, the direction of real induction arrows of the periods 30 and 20 min rotated 85°and 40°anticlockwise, respectively, before the Chi-Chi earthquake and returned to mean direction of last 10 years after the earthquake. A horizontal source field model using the finite difference method for 3-D shows that the variation of the real induction arrows might be ascribed to the conductivity variation body, which is 5 km buried at the epicenter area of the Chi-Chi earthquake, changing its conductivity from 0.002S/m to 0.06 S/m. The ratios of modulus (demodulated by using the complex demodulation method) over a period 12, and 8 h relative to the period of 24 h reveal a remarkable change that appeared 4-5 months prior to this strong earthquake. They increased gradually from the beginning of 1999 to August 1999 and decreased again to a (8 years) mean level after the strong earthquake occurrence. We consider that the variation of the induction arrow might be ascribed to the conductivity anomaly, which is buried 5 km at the south-east side of LNP with a conductivity change of 0.06 S/m. We propose that this elevation might be related to the preparation process of the great earthquake.

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“…Calculated magnetotelluric responses of 2-D model structures have been compared with the observed responses along the transect AB in the following way. The finite-difference method described by Jones & Pascoe (1971) and Pascoe & Jones (1972), modified to benefit from criticisms by Williamson, Hewlett & Tammemagi (1974) and Brewitt-Taylor & Weaver (1976), was used to calculate pseudosections (PSDs) of apparent resistivity and phase for incident fields polarized both with electric field (E-pol) and magnetic field (B-pol) along the infinite axis of the model. These calculated PSDs were then compared with PSDs from the field data from sites close to transect AB, the model was modified, and the procedure repeated in the usual forwardmodelling process.…”

Section: Model C a L C U L A T I O N Smentioning

confidence: 99%

A Model of Crustal Conductive Structure In the Canadian Cordillera

Majorowicz

Gough

1994

Geophysical Journal International

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S U M M A R YResults from magnetotelluric soundings in t h e frequency range 0.016-160 H z are used t o model conductive structure in the upper and middle crust along a section across strike of the Canadian Cordillera, a region of continental accretion associated with three successive subductions over the last 200 Ma. 2-D finite-difference modelling is applied t o secure a first-order fit to observed phase and apparent resistivity pseudosections in two polarizations, with t h e electric field along geological strike (E-polarization) and across strike (B-polarization). T h e fit to observed fields, and its limitations, are shown in detail by comparing calculated and observed pseudosections. T h e misfits are instructive and a r e t o b e expected where 2-D modelling is fitted t o 3-D structure in the Earth. T h e model nevertheless indicates two major resistive and three major conductive blocks in t h e upper and middle crust. T h e larger resistive block probably represents granitoid plutons of the Coast Plutonic Belt, which are shown t o continue beneath the adjoining Intermontane Belt. T h e three conductive blocks a r e believed t o result from saline water in fractures. T h e block under the Coast Plutonic Belt may draw its water from the currently active subduction offshore, whereas t h e block in line with the Fraser Fault may draw its water from the atmosphere a n d the block under the Omineca Belt from a global-scale upcurrent in the mantle.

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Computer Modelling of Electrical Conductivity Structures

Cited by 21 publications

References 3 publications

On the finite difference solution of two-dimensional induction problems

On the finite difference solution of two-dimensional induction problems

Geomagnetic anomaly at Lunping before the 1999 Chi-Chi earthquake (M w = 7.6) in Taiwan

A Model of Crustal Conductive Structure In the Canadian Cordillera

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