A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data

Rodi, William

doi:10.1111/j.1365-246x.1976.tb03669.x

Cited by 161 publications

(92 citation statements)

References 10 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the Gauss-Newton method, a locally linear misfit functional is assumed (Kormendi & Dietrich, 1991;Menke, 1989;Aster et al, 2005), which allows the second order term of the Hessian to be dropped (Virieux & Operto, 2009). We obtain explicitly the sensitivity matrix J by perturbing each model parameter at each layer depth; the resulting partial derivative wavefield is propagated from the secondary virtual sources to the receivers' position (Rodi, 1976;Sheen et al, 2006;Operto et al, 2013). The effectiveness of this approach in scaling and weighting the gradient is higher than the steepest-descent and quasi-Newton methods, because the approximate Hessian J T J is computed rather than statistically estimated.…”

Section: Gauss-newton Seismic Inversionmentioning

confidence: 99%

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

Provenzano

Vardy

Henstock

2017

Geophysical Journal International

View full text Add to dashboard Cite

SUMMARYThe full waveform inversion (FWI) of seismic reflection data aims to reconstruct a detailed physical properties model of the subsurface, fitting both the amplitude and traveltime of the reflections generated at physical discontinuities in the propagation medium. Unlike reservoirscale seismic exploration, where seismic inversion is a widely adopted remote characterisation tool, ultra high frequency (UHF, 0.2-4.0 kHz) multi-channel marine reflection seismology is still most often limited to a qualitative interpretation of the reflections' architecture. Here we propose an elastic full waveform inversion methodology, custom-tailored for pre-stack UHF marine data in vertically heterogeneous media to obtain a decimetric-scale distribution of Pimpedance, density and Poisson's ratio within the shallow sub-seabed sediments. We address the deterministic multi-parameter inversion in a sequential fashion. The complex trace instantaneous phase is first inverted for the P-wave velocity to make-up for the lack of low-frequency in the data and reduce the non-linearity of the problem. This is followed by a short-offset Pimpedance optimisation and a further step of full offset range Poisson's ratio inversion. Provided that the seismogram contains wide reflection angles (> 40 degrees), we show that it is possible to invert for density and decompose a-posteriori the relative contribution of P-wave velocity and density to the P-impedance. A broad range of synthetic tests is used to prove the potential of the methodology and highlights sensitivity issues specific to UHF seismic. An example application to real data is also presented. In the real case, trace normalisation is applied to minimise the systematic error deriving from an inaccurate source wavelet estimation. G. Provenzano et al.The inverted model for the top 15 meters of the sub-seabed agrees with the local lithological information and core-log data. Thus we can obtain a detailed remote characterisation of the shallow sediments using a multi-channel sub-bottom profiler within a reasonable computing cost and with minimal pre-processing. This has the potential to reduce the need of extensive geotechnical coring campaigns.

show abstract

Section: Gauss-newton Seismic Inversionmentioning

confidence: 99%

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

Provenzano

Vardy

Henstock

2017

Geophysical Journal International

View full text Add to dashboard Cite

show abstract

“…The forward modeling is based on the same numerical implementation of the finite difference method as of Zhdanov et al [1982] and de Lugao et al [1997]. We use the reciprocity principle [Madden, 1972;Rodi, 1976;McGillivray and Oldenburg, 1990;de Lugao and Wannamaker, 1996;de Lugao et al, 1997] for Frechet derivative calculations. Note that according to the construction the minimum support functional generates a stable solution that tends to produce the smallest possible anomalous domain.…”

Section: Regularized Solution Of a Discrete Mt Inverse Problemmentioning

confidence: 99%

“…where F ik are the elements of the Frechet derivative matrix computed, for example, using the reciprocity principle [Madden, 1972;Rodi, 1976;McGillvray and Oldenburg, 1990;McGillvary et al, 1994;de Lugao and Wannamaker, 1996;de Lugao et al, 1997]. Following Mehanee et al…”

Section: Formulation Of the Weighted Inverse Solutionmentioning

confidence: 99%

Two‐dimensional magnetotelluric inversion of blocky geoelectrical structures

Mehanee

Zhdanov

2002

J. Geophys. Res.

View full text Add to dashboard Cite

[1] This paper demonstrates that there are alternative approaches to the magnetotelluric (MT) inverse problem solution based on different types of geoelectrical models. The traditional approach uses smooth models to describe the conductivity distribution in underground formations. In this paper, we present a new approach, based on approximating the geology by models with blocky conductivity structures. We can select one or another class of inverse models by choosing between different stabilizing functionals in the regularization method. The final decision, whose approach may be used for the specific MT data set, is made on the basis of available geological information. This paper describes a new way of stabilizing two-dimensional MT inversion using a minimum support functional and shows the improvement that it provides over traditional methods for geoelectrical models with blocky structures. The new method is applied to MT data collected for crustal imaging in the Carrizo Plain in California and to MT data collected for mining exploration by INCO Exploration.

show abstract

“…The computer code is based on that of OGAWA (1988) which follows the finite element method described in RODI (1976). The weighted inversion and the ABIC-minimization schemes are added.…”

Section: The Modelmentioning

confidence: 99%

Smooth 2-D Inversion for Magnetotelluric Data Based on Statistical Criterion ABIC.

Uchida

1993

J. geomagn. geoelec

View full text Add to dashboard Cite

We often apply a smoothness constraint to a two-dimensional (2-D) linearized least-squares inversion of magnetotelluric (MT) data to achieve a stable result. A substantial problem with this scheme lies in the choice of the optimum smoothness, and in this paper, a statistical approach which is very versatile for this purpose is presented. It uses a statistical criterion called ABIC (Akaike's Bayesian Information Criterion), which was derived by introducing the entropy-maximization theorem into the Bayes statistics. On applying the Bayesian procedure to 2-D MT inversion, we seek simultaneous minimization of data misfit and model roughness. ABIC works as a number that represents goodness, or an entropy, of a model in a sense of this simultaneous minimization. Tests with both synthetic and real field data have revealed the effectiveness of this method for non-linear inversion problems. Regardless of the magnitude of the observation error, the method objectively adjusts the tradeoff between the misfit and the roughness, and stable convergence is attained.

show abstract

A Technique for Improving the Accuracy of Finite Element Solutions for Magnetotelluric Data

Cited by 161 publications

References 10 publications

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

Two‐dimensional magnetotelluric inversion of blocky geoelectrical structures

Smooth 2-D Inversion for Magnetotelluric Data Based on Statistical Criterion ABIC.

Contact Info

Product

Resources

About