大地电磁法反演方法回顾-胡祥云

Generalized RRI method, Kazunobu Yamane,1996
Advantages:High speed, acceptable accuracy • RRI starts by J. T.Smith,J.R. Booker (1991), applicable to 2D and 3D MT inversion, developed to GRRI(1996), used to CSAMT, which approximates horizontal derivatives with their values calculated from the fields of previous iteration • The GRRI algorithm offers a new way to directly convert MT data acquired over rough terrain with variable topography into subsurface images. It is possible to reconstruct these resistivity images with a relatively small amount of computer resources. • When compared with the original RRI method, the GRRI method does not require additional computation time, and the inverted image has higher resolution because the new scheme is based on a locally 2-D analysis.
Data space conjugate gradient inversion for 2-D MT data, Weerachai Siripunvaraporn,2007
• A data space approach to MT inversion reduces the size of the system of equations that must be solved from M×M, as required for a model space approach, to only N×N, where M is the number of model parameter and N is the number of data. • The data space Occam’s (DASOCC) inversion has been successfully applied to 2-D (2000) and 3-D (2004) MT inversion. • Computational efficiency is assessed and compared to the DASOCC inversion by counting the number of forward modeling calls. • Experiments with synthetic data showthat although DCG requires significantly less memory, it generally requires more forward problem solutions than a scheme such as DASOCC, which is based on a full computation of J.
Nonlinear conjugate gradients algorithm for 2-D MT inversion, W. Rodi,2001
• Minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity • More efficient than the Gauss-Newton algorithm in terms of both computer memory requirements and CPU time
Reciprocal principle-using values obtained form forward modeling(Philip E. Wannamaker,1996) • Approximation by using of half space analytic formula • Approximate sensitivities for the electromagnetic inverse problem(C. G. Farquharson,D. W. Oldenburg,1996)
Inversion-historical developments
• • Starts from 1-D inversion by Wu(1968) 1970s:from 1-D to 2-D – Bostick inversion – Various local optimization methods,Generalized inversion, Jupp and Vozoff (1975) – anisotropy 1980s:2-D inversion – Joint inversion:Apparent resistivity and phase, TE+TM mode – Smoothness constrained inversion-Occam, Smith and Booker (1988) and Constable(1987) – Seismic analogy inversion(migration,Wang, Oldenburg,1988) 1990s:from 2-D to 3-D – RRI inversion:by Smith and Booker (1991), is one of the best approximate methods, provides reasonable solutions, with less computing resources, because partial derivatives are obtained from a perturbation analysis which uses only the cross terms of the horizontal gradient. – Mackie and Madden (1993) implemented an iterated, linearized inversion algorithm for 3-DMTdata, – forward modelling and Frechet derivatives by Quasi linear Approximation – Electromagnetic migration – Global optimization – Rebocc 2000s: 3-D inversion – Non-linear conjugate gradient, W. Rodi,2001, R.L. Mackie, T.R. Madden, G.A. Newman, D.L. Alumbaugh, – Data space method, Weerachai Siripunvaraporn,2007 – BBI inversion(Constable (2004)) – Joint Inversion(conductivity , magnetic permitivity, polarization, density, velocity
• Computational costs associated with construction and inversion of model-space matrices make a model-space Occam approach to 3D MT inversion impractical • With the transformation to data space it becomes feasible to invert modest 3D MT data sets on a PC
Three-dimensional magnetotelluric inversion using non-linear conjugate gradients Gregory A. Newman,2000
ቤተ መጻሕፍቲ ባይዱ
From Model space to Data space
Three-dimensional magnetotelluric inversion: dataspace method, Weerachai Siripunvaraporna,2005
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Outline of this section
• • • • • • • • • • Nonlinear conjugate gradients Data space algorithm RRI(Rapid Relaxation Inversion) Approximated calculation of Frechet derivatives M.S.Zhdanov from MT to Magnetic D.W. Oldenburg from MT to Gravity Considering Static shift Boundary Based inversion Application of ANN Combination of SVD after CG
Bayesian inversion with Markov chains-I. The MT 1-D case, H. Grandis,1999
• To assess the uncertainty, the inversion process should be cast into a statistical setting. A Bayesian setting is a natural choice for many geophysical inverse problems, where it is possible to combine available prior knowledge with the information contained in the measured data(Bayesian time-lapse inversion, Arild Buland,2006) • The MT 1-D inverse problem is a classical problem, and it has already been addressed by many authors. Various algorithms based on deterministic or probabilistic approachs are at present available • However, it is still of great importance not only for 2-D and 3-D inversion but also especially for Earth deep sounding
Computing Jacobian:important inclusion of Inversion
• Two computational roadblocks encountered when solving an inverse problem: (Oldenburg,1994)
(1)calculation of the sensitivity matrix and (2) solution of the resultant large system of equations.