3D marine magnetotelluric inversion: A hybrid impedance and direct-field approach

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. E335-E346
Author(s):  
Lutz Mütschard ◽  
Ketil Hokstad ◽  
Torgeir Wiik ◽  
Bjørn Ursin
Keyword(s):  
Electric Field ◽  
Real Data ◽  
Source Distribution ◽  
Impedance Tensor ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Source ◽  
Field Approach ◽  
Impedance Inversion ◽  
Field Inversion

The measured electromagnetic field in magnetotellurics (MT) is composed of the natural source field and its subsurface response. Commonly, the data are represented as impedances, the complex ratio between the horizontal electric and magnetic fields. This measure is independent of the source distribution because the impedance-tensor estimation contains a deconvolution operator. We have used a Gauss-Newton-type 3D MT inversion scheme to compare impedance-data inversion with an inversion using the recorded electric field directly. The use of the observed electric field is beneficial to the inversion algorithm because it simplifies the estimation of the sensitivities. The direct-field approach permits the use of the observed data without processing, but it presumes knowledge of the source distribution. A method to estimate the time-variable strength and polarization of the incoming plane-wave source is presented and tested on synthetic and real-data examples. The direct-field inversion is successfully applied to a synthetic and a real data set within marine settings. A comparison with the conventional impedance inversion is conducted. The results of the synthetic data example are very similar, with a slightly more accurate reconstruction of the model in the impedance case, whereas the direct-field inversion produces a smoother inversion result when compared with the impedance case. The mapping of a resistive salt structure in the real-data example indicates deviations in the final conductivity models. The impedance inversion suggests a deeper rooted resistive structure, whereas the direct-field inversion predicts a more compact structure limited to the overburden. We have evaluated the advantages of the new approach like the simplification of the sensitivity calculation, limitations, and disadvantages like knowledge of the source distribution.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

scholarly journals Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. M1-M10 ◽  
Author(s):  
Leonardo Azevedo ◽  
Ruben Nunes ◽  
Pedro Correia ◽  
Amílcar Soares ◽  
Luis Guerreiro ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Metric Space ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Algorithm ◽  
Data Set ◽  
The Real ◽  
Geostatistical Inversion ◽  
Impedance Models

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a cross-validation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

Nonlinear impedance inversion for attenuating media

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. R111-R117 ◽  
Author(s):  
Sérgio Oliveira ◽  
Luiz Loures ◽  
Fernando Moraes ◽  
Carlos Theodoro
Keyword(s):  
Amplitude Spectrum ◽  
Real Data ◽  
Alternative Formulation ◽  
Nonlinear Inversion ◽  
Inversion Algorithm ◽  
Impedance Inversion ◽  
Reflectivity Function ◽  
Analytical Formulas ◽  
Zero Offset ◽  
Internal Multiples

Applications of seismic impedance inversion normally assume the data are free of multiples and transmission effects, requiring knowledge of the seismic pulse that is assumed to be stationary. An alternative formulation for impedance inversion is based on an exact frequency-domain, zero-offset reflectivity function for a 1D medium. Analytical formulas for the Fréchet derivatives are derived for efficient implementation of an iterative nonlinear inversion. The exact zero-offset reflectivity accounts for internal multiples and transmission effects in the data. Absorption and dispersion are also conveniently handled if a reasonable estimate for the quality [Formula: see text] factor of the medium is available. A series of convenient features are included in the inversion algorithm: an automatic estimation of the amplitude spectrum of the seismic pulse, an impedance transform that makes the inversion independent from the initial smooth model, and a practical approach to estimate the regularization weight. Numerical tests using synthetic and real data show that the method is stable and needs only a few iterations to converge.

Fast 2-D ray+Born migration/inversion in complex media

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Philippe Thierry ◽  
Stéphane Operto ◽  
Gilles Lambaré
Keyword(s):  
Numerical Approximation ◽  
Reference Model ◽  
Real Data ◽  
Model Parameters ◽  
Complex Media ◽  
Inversion Algorithm ◽  
Numerical Approximations ◽  
Data Set ◽  
Cpu Time ◽  
Computational Evaluation

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

Structurally constrained impedance inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T577-T589 ◽  
Author(s):  
Haitham Hamid ◽  
Adam Pidlisecky
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Field Data ◽  
A Priori ◽  
Structural Constraints ◽  
Inversion Algorithm ◽  
Data Set ◽  
Impedance Inversion ◽  
Single Trace ◽  
Complex Geology

In complex geology, the presence of highly dipping structures can complicate impedance inversion. We have developed a structurally constrained inversion in which a computationally well-behaved objective function is minimized subject to structural constraints. This approach allows the objective function to incorporate structural orientation in the form of dips into our inversion algorithm. Our method involves a multitrace impedance inversion and a rotation of an orthogonal system of derivative operators. Local dips used to constrain the derivative operators were estimated from migrated seismic data. In addition to imposing structural constraints on the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We investigated this algorithm on a complex synthetic 2D model as well as a seismic field data set. We compared the result obtained with this approach with the results from single trace-based inversion and laterally constrained inversion. The inversion carried out using dip information produces a model that has higher resolution that is more geologically realistic compared with other methods.

scholarly journals Array analysis of magnetic and electric field observatories in China: estimation of magnetotelluric impedances at very long periods

2020 ◽  
Vol 222 (1) ◽  
pp. 305-326
Author(s):  
Hui Wang ◽  
Gary Egbert ◽  
Yusong Yao ◽  
Jiulong Cheng
Keyword(s):  
Electric Field ◽  
Data Acquisition ◽  
Electric Fields ◽  
Principal Component ◽  
Array Analysis ◽  
Data Set ◽  
Wave Source ◽  
Long Period ◽  
Noise Characteristics ◽  
Almost All

SUMMARY Ten years (2008–2017) of continuous measurements from 40 electric and 36 magnetic sites collected in China for earthquake prediction research represent a unique EM array data set, which can be used to explore the challenging problem of very long-period MT data acquisition, to study source characteristics, and ultimately to learn about electric conductivity of Earth's mantle beneath East Asia. In this study, we focus on basic noise and signal characteristics in this data set, and on estimation of the MT impedances. We report a novel method to fix the numerous timing errors in the electric data caused by limitations in instrumentation and data acquisition. Then, we use multivariate array analysis to study signal and noise characteristics for periods from 250 s to 3.5 × 105 s (4 d). Signal-to-noise ratios (SNR) are above 30 dB in magnetic fields for the first two dominant modes, which correspond roughly to N–S and E–W quasi-uniform sources. SNRs for electric fields are lower, especially at very long periods, and especially for N–S electric components. There are clear peaks in signal strength at the daily variation (DV) periods, but source structure becomes more complex, and significant biases in MT impedance tensors are more often seen at these periods. The MT quasi-impedance, computed using the closest magnetic site for each electric site, is estimated by robust remote reference techniques (RR) and by using linear combinations of PCA (principal component analysis) modes that best approximate a uniform or plane-wave source (PW). For almost all sites, smooth impedances are obtained for periods up to 104 s using either approach. This result, and a more detailed analysis of impedances estimates obtained with shorter-wavelength (gradient) sources extracted from the array, suggests that source effects in MT impedances are minimal for periods below 104 s, at least at the latitude of China. At many sites curves can be extended a decade further, to 105 s, but here results are improved by carefully omitting DV bands and (at a few sites) with the PW approach. For longer periods (>105 s) SNR is very low in electric field channels at most sites, making estimation challenging. However, at a few sites, even some near big cities (e.g. including a site within 40 km of Beijing) smooth impedance components related to N–S magnetic sources (Zxx and Zyx) are obtained to periods to 3.5 × 105 s (4 d). This result suggests that cultural noise may not be the main impediment to collecting very long-period MT data.

Transient electromagnetic inversion: A remedy for magnetotelluric static shifts

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1242-1250 ◽  
Author(s):  
Louise Pellerin ◽  
Gerald W. Hohmann
Keyword(s):  
Electric Field ◽  
Apparent Resistivity ◽  
Parametric Representation ◽  
Impedance Tensor ◽  
Static Shift ◽  
Electrode Arrays ◽  
Data Set ◽  
Low Frequencies ◽  
Transient Electromagnetic ◽  
Correction Scheme

Surficial bodies can severely distort magnetotelluric (MT) apparent resistivity data to arbitrarily low frequencies. This distortion, known as the MT static shift, is due to an electric field generated from boundary charges on surficial inhomogeneities, and persists throughout the entire MT recording range. Static shifts are manifested in the data as vertical, parallel shifts of log‐log apparent resistivity sounding curves, the impedance phase being unaffected. Using a three‐dimensional (3-D) numerical modeling algorithm, simulated MT data with finite length electrode arrays are generated. Significant static shifts are produced in this simulation; however, for some geometries they are impossible to identify. Techniques such as spatial averaging and electromagnetic array profiling (EMAP) are effective in removing static shifts, but they are expensive, especially for correcting a previously collected MT data set. Parametric representation and use of a single invariant quantity, such as the impedance tensor determinant, are only useful in limited circumstances and can lead the MT interpreter astray. Transient electromagnetic (TEM) sounding data are relatively inexpensive to collect, do not involve electric field measurements, and are only affected at very early times by surficial bodies. Hence, using TEM data acquired at the same location provides a natural remedy for the MT static shift. We describe a correction scheme to shift distorted MT curves to their correct values based on 1-D inversion of a TEM sounding taken at the same location as the MT site. From this estimated 1-D resistivity structure an MT sounding is computed at frequencies on the order of 1 Hz and higher. The observed MT curves are then shifted to the position of the computed curve, thus eliminating static shifts. This scheme is accurate when the overlap region between the MT and TEM sounding is 1-D, but helpful information can be gleaned even in multidimensional environments. Other advantages of this scheme are that it is straightforward to ascertain if the correction scheme is being accurately applied and it is easy to implement on a personal computer.

Multisite, multifrequency tensor decomposition of magnetotelluric data

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 158-173 ◽  
Author(s):  
Gary W. McNeice ◽  
Alan G. Jones
Keyword(s):  
Computing Time ◽  
Regional Scale ◽  
Synthetic Data ◽  
Real Data ◽  
Impedance Tensor ◽  
Small Scale ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Distortion Parameters ◽  
Galvanic Distortion

Accurate interpretation of magnetotelluric data requires an understanding of the directionality and dimensionality inherent in the data, and valid implementation of an appropriate method for removing the effects of shallow, small‐scale galvanic scatterers on the data to yield responses representative of regional‐scale structures. The galvanic distortion analysis approach advocated by Groom and Bailey has become the most adopted method, rightly so given that the approach decomposes the magnetotelluric impedance tensor into determinable and indeterminable parts, and tests statistically the validity of the galvanic distortion assumption. As proposed by Groom and Bailey, one must determine the appropriate frequency‐independent telluric distortion parameters and geoelectric strike by fitting the seven‐parameter model on a frequency‐by‐frequency and site‐by‐site basis independently. Although this approach has the attraction that one gains a more intimate understanding of the data set, it is rather time‐consuming and requires repetitive application. We propose an extension to Groom‐Bailey decomposition in which a global minimum is sought to determine the most appropriate strike direction and telluric distortion parameters for a range of frequencies and a set of sites. Also, we show how an analytically‐derived approximate Hessian of the objective function can reduce the required computing time. We illustrate application of the analysis to two synthetic data sets and to real data. Finally, we show how the analysis can be extended to cover the case of frequency‐dependent distortion caused by the magnetic effects of the galvanic charges.

Self-constrained inversion of potential fields through a 3D depth weighting

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. G143-G156
Author(s):  
Andrea Vitale ◽  
Maurizio Fedi
Keyword(s):  
Weighting Function ◽  
Real Data ◽  
Whole Body ◽  
Source Distribution ◽  
Potential Fields ◽  
Bottom Surface ◽  
Data Set ◽  
Scaling Properties ◽  
Local Homogeneity ◽  
Complex Source

A new method for inversion of potential fields is developed using a depth-weighting function specifically designed for fields related to complex source distributions. Such a weighting function is determined from an analysis of the field that precedes the inversion itself. The algorithm is self-consistent, meaning that the weighting used in the inversion is directly deduced from the scaling properties of the field. Hence, the algorithm is based on two steps: (1) estimation of the locally homogeneous degree of the field in a 3D domain of the harmonic region and (2) inversion of the data using a specific weighting function with a 3D variable exponent. A multiscale data set is first formed by upward continuation of the original data. Local homogeneity and a multihomogeneous model are then assumed, and a system built on the scaling function is solved at each point of the multiscale data set, yielding a multiscale set of local-homogeneity degrees of the field. Then, the estimated homogeneity degree is associated to the model weighting function in the source volume. Tests on synthetic data show that the generalization of the depth weighting to a 3D function and the proposed two-step algorithm has great potential to improve the quality of the solution. The gravity field of a polyhedron is inverted yielding a realistic reconstruction of the whole body, including the bottom surface. The inversion of the aeromagnetic real data set, from the Mt. Vulture area, also yields a good and geologically consistent reconstruction of the complex source distribution.

Transformation of VLF anomaly maps into apparent resistivity and phase

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 497-505 ◽  
Author(s):  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Magnetic Field ◽  
Plane Wave ◽  
Electric Field ◽  
Transfer Functions ◽  
Magnetic Data ◽  
Impedance Tensor ◽  
Wave Source ◽  
Layered Earth ◽  
Magnetic Transfer ◽  
The Magnetic Field

We investigate a transformation of magnetic transfer functions into the tangential‐electric mode part of the impedance tensor in the scope of the plane‐wave electromagnetic tensor–VLF method. The transformation, which is applicable to any 2D data representing the response of arbitrary 3D geoelectric structures, overcomes the difficulties of quantitative interpretation of magnetic transfer functions, which predominantly provide a measure of the lateral changes of the electrical conductivity in the earth. We require densely sampled magnetic transfer functions of one frequency as input data. These may be decomposed into their normal and anomalous parts (deviation from the response of a layered earth) for a unit external plane‐wave source field using the Hilbert transform relationship between the magnetic field components. Faraday's law then directly provides the anomalous toroidal electric field. Unfortunately, there is no chance to estimate the normal electric field from magnetic data, since the magnetic field is not sensitive to a layered earth. This constant must be provided as a boundary condition, e.g., from one ground measurement, to derive an impedance tensor and related apparent resistivities and phases.

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