Modelling and inversion -progress, problems, and challenges

Raiche, Art

doi:10.1007/bf00689859

Cited by 14 publications

(3 citation statements)

References 45 publications

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“…In fact, various algorithms based on deterministic or probabilistic approaches are at present available (see e.g. Tarlowski 1982; Parker 1983); Oldenburg 1990; Raiche 1994). To our knowledge, however, none of them involves the use of Markov chains.…”

Section: The Algorithmmentioning

confidence: 99%

Bayesian inversion with Markov chains-I. The magnetotelluricone-dimensional case

Grandis

Menvielle

Roussignol³

1999

Geophys. J. Int.

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We use Monte Carlo Markov chains to solve the Bayesian MT inverse problem in layered situations. The domain under study is divided into homogeneous layers, and the model parameters are the conductivity of each layer. We use an a priori distribution of the parameters which favours smooth models. For each layer, the a priori and a posteriori distributions are digitized over a limited set of conductivity values. The Markov chain relies on updating the model parameters during successive scanning of the domain under study. For each step of the scanning, the conductivity is updated in one layer given the actual value of the conductivity in the other layers. Thus we designed an ergodic Markov chain, the invariant distribution of which is the a posteriori distribution of the parameters, provided the forward problem is completely solved at each step. We have estimated the a posteriori marginal probability distributions from the simulated successive values of the Markov chain. In addition, we give examples of complex magnetotelluric impedance inversion in tabular situations, for both synthetic models and field situations, and discuss the influence of the smoothing parameter.

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Section: The Algorithmmentioning

confidence: 99%

Bayesian inversion with Markov chains-I. The magnetotelluricone-dimensional case

Grandis

Menvielle

Roussignol³

1999

Geophys. J. Int.

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“…For example, layer 5 from the 8 layer model in figure 4b has a low importance and was removed for final inversion seed models used for inversion of the full data set. As expected, the shallow conductive layers will have the greatest effect on the outcome of the inversion and must be included in the layer discretisation for seed model input to the inversion (Gavin, 2010, Raiche, 1993. Once the analysis of inversion input parameters was complete, a simplified 6 layer model was constructed as the best general seed model for large sub areas and the inversion was completed on the full data set.…”

Section: Methodolgymentioning

confidence: 99%

Airborne TEM for the recovery of basin scale solute distribution; Perth Basin, Western Australia.

Martin

Harris

Schäfer

2012

ASEG Extended Abstracts

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“…The analytical expression of the EM fields is in a complicated form involving special functions that hinder physical intuition regarding the solution. This kind o f complicated analytical expression is also difficult to implement numerically (Raiche 1994). More importantly, the analytical approach can not be generalized to an arbitrary 3-D earth containing multiple bending conductors of finite-length line.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic modelling of buried line conductors using an integral equation

Qian

Boerner

1995

Geophysical Journal International

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S U M M A R YAn integral equation is derived to represent the electromagnetic response of line conductors buried below the surface of a horizontally stratified earth. By permitting several finite-length line conductors of arbitrary topology, this representation is free of the limitations imposed by analytic solutions. The integral equation is formulated in terms of excess electric current (scattering current) flowing along the line conductor and is solved numerically by dividing the line conductor into many small segments. In general, the excess electric current is controlled by both the internal and external impedance of the line conductor. The internal impedance is the longitudinal resistance of the line conductor. The exterpal impedance is caused by galvanic and inductive coupling between the line conductor and its local environment. The galvanic resistance to current channelling is spatially variable with a minimum in the centre of a uniform line conductor and is determined by conductor geometry and the host conductivity structure. The inductive external impedance is proportional to frequency and quadrature dominant. It is a function of lineconductor geometry, cross-section and burial environment. The inductive impedance effectively reduces the spatial dependence of the external impedance at high frequency by presenting a large reactance (which is uniform at all points along the conductor) to the exciting electric field.Within the quasi-static limit (i.e. where displacement current can be neglected), electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far field). The excess electric current in the line conductor will always be inversely proportional to frequency for these types of sources at sufficiently high frequencies where the inductive external impedance is dominant. Horizontal magnetic dipole and vertical electric dipole sources generate primary electric fields that are proportional to the square root of frequency in the high-frequency limit of the quasi-static domain and the excess electric current excited by such sources will decrease as the inverse of the square root of frequency.

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Modelling and inversion -progress, problems, and challenges

Cited by 14 publications

References 45 publications

Bayesian inversion with Markov chains-I. The magnetotelluricone-dimensional case

Bayesian inversion with Markov chains-I. The magnetotelluricone-dimensional case

Airborne TEM for the recovery of basin scale solute distribution; Perth Basin, Western Australia.

Electromagnetic modelling of buried line conductors using an integral equation

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