scholarly journals Multidimensional inversion of loop-loop frequency-domain EM data for resistivity and magnetic susceptibility

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. F213-F223 ◽  
Author(s):  
Yutaka Sasaki ◽  
Jung-Ho Kim ◽  
Seong-Jun Cho
Keyword(s):  
Magnetic Susceptibility ◽  
Frequency Domain ◽  
Synthetic Data ◽  
Staggered Grid ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Small Loop ◽  
Em Induction ◽  
Airborne Em

Electromagnetic (EM) induction measurements are affected by resistivity and magnetic susceptibility. Thus, inverting EM data for resistivity alone can give misleading models if susceptible effects are strong. An inversion algorithm is presented to simultaneously recover multidimensional distributions of resistivity and susceptibility from various types of loop-loop frequency-domain EM data. The algorithm adopts a staggered-grid finite-difference method for the 3D forward solutions and computes the sensitivities with respect to resistivity and susceptibility from the forward solutions using the reciprocity principle. The algorithm is tested on synthetic data sets from ground-based small-loop, airborne, and Slingram EM surveys. It is shown that the simultaneous inversion of the small-loop EM data collected at a singleheight is unstable and likely to produce unreliable susceptibility models because the effect of susceptibility is nearly independent of the frequency. However, if the data are obtained for multiple heights or different loop configurations, simultaneous inversion can produce more reliable susceptibility and resistivity models even if the data are contaminated by offset errors. It is also shown that although the simultaneous inversion of airborne EM data is relatively stable, adding data obtained at different heights helps to increase the reliability of the resistivity and susceptibility models. Among the loop-loop EM methods discussed here, the Slingram method is relatively insensitive to susceptibility anomalies and thus cannot be used to recover the susceptibility distribution via inversion even if the data are obtained using different loop configurations.

Quasi-2D inversion of DCR and TDEM data for shallow investigations

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. F239-F250 ◽  
Author(s):  
Fernando A. Monteiro Santos ◽  
Hesham M. El-Kaliouby
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Data Sets ◽  
Complex Environments ◽  
Inversion Algorithm ◽  
2D Inversion ◽  
New Approach ◽  
Earth Models ◽  
Time Domain Electromagnetic ◽  
Inversion Techniques

Joint or sequential inversion of direct current resistivity (DCR) and time-domain electromagnetic (TDEM) data commonly are performed for individual soundings assuming layered earth models. DCR and TDEM have different and complementary sensitivity to resistive and conductive structures, making them suitable methods for the application of joint inversion techniques. This potential joint inversion of DCR and TDEM methods has been used by several authors to reduce the ambiguities of the models calculated from each method separately. A new approach for joint inversion of these data sets, based on a laterally constrained algorithm, was found. The method was developed for the interpretation of soundings collected along a line over a 1D or 2D geology. The inversion algorithm was tested on two synthetic data sets, as well as on field data from Saudi Arabia. The results show that the algorithm is efficient and stable in producing quasi-2D models from DCR and TDEM data acquired in relatively complex environments.

2.5‐D inversion of frequency‐domain electromagnetic data generated by a grounded‐wire source

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1753-1768 ◽  
Author(s):  
Yuji Mitsuhata ◽  
Toshihiro Uchida ◽  
Hiroshi Amano
Keyword(s):  
Frequency Domain ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Statistical Criterion ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Gas Field ◽  
Data Set ◽  
Transient Electromagnetic

Interpretation of controlled‐source electromagnetic (CSEM) data is usually based on 1‐D inversions, whereas data of direct current (dc) resistivity and magnetotelluric (MT) measurements are commonly interpreted by 2‐D inversions. We have developed an algorithm to invert frequency‐Domain vertical magnetic data generated by a grounded‐wire source for a 2‐D model of the earth—a so‐called 2.5‐D inversion. To stabilize the inversion, we adopt a smoothness constraint for the model parameters and adjust the regularization parameter objectively using a statistical criterion. A test using synthetic data from a realistic model reveals the insufficiency of only one source to recover an acceptable result. In contrast, the joint use of data generated by a left‐side source and a right‐side source dramatically improves the inversion result. We applied our inversion algorithm to a field data set, which was transformed from long‐offset transient electromagnetic (LOTEM) data acquired in a Japanese oil and gas field. As demonstrated by the synthetic data set, the inversion of the joint data set automatically converged and provided a better resultant model than that of the data generated by each source. In addition, our 2.5‐D inversion accounted for the reversals in the LOTEM measurements, which is impossible using 1‐D inversions. The shallow parts (above about 1 km depth) of the final model obtained by our 2.5‐D inversion agree well with those of a 2‐D inversion of MT data.

Determination of relative angles and anisotropic resistivity using multicomponent induction logging data

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 898-908 ◽  
Author(s):  
Zhiyi Zhang ◽  
Liming Yu ◽  
Berthold Kriegshäuser ◽  
Lev Tabarovsky
Keyword(s):  
Sensitivity Analysis ◽  
Azimuth Angle ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Simultaneous Inversion ◽  
Induction Logging ◽  
Em Induction ◽  
Whole Space ◽  
Dip Angle

We have developed a new algorithm that retrieves information about relative dip angle, relative azimuth angle, vertical resistivity, and horizontal resistivity from multicomponent EM induction logging data. To investigate how relative dip and azimuth angles affect multicomponent induction logging data, we performed a sensitivity analysis using an anisotropic whole space model. Based upon the sensitivity analysis, we designed a two‐step procedure to recover relative dip, relative azimuth, horizontal resistivity, and vertical resistivity. In the first step, the observed data are transformed into a new data set independent of the azimuth angle; a simultaneous inversion method recovers relative dip angle, vertical resistivity, and horizontal resistivity. In the second step, a 1D line search is performed to decide relative azimuth angle. Synthetic and field data tests indicate that the new inversion algorithm can extract information about relative dip and azimuth angles as well as the anisotropic resistivity structure from multicomponent induction loggingdata.

Reconstruction of 1-D conductivity from dual‐loop EM data

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 492-501 ◽  
Author(s):  
Zhiyi Zhang ◽  
Partha S. Routh ◽  
Douglas W. Oldenburg ◽  
David L. Alumbaugh ◽  
Gregory A. Newman
Keyword(s):  
Inverse Problem ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Geological Structures ◽  
Electromagnetic Data ◽  
Independent Information ◽  
The Individual ◽  
Data Constraints

Inversions of electromagnetic data from different coil configurations provide independent information about geological structures. We develop a 1-D inversion algorithm that can invert data from the horizontal coplanar (HC), vertical coplanar, coaxial (CA), and perpendicular coil configurations separately or jointly. The inverse problem is solved by minimizing a model objective function subject to data constraints. Tests using synthetic data from 1-D models indicate that if data are collected at a sufficient number of frequencies, then the recovered models from individual inversions of different coil systems can be quite similar. However, if only a limited number of frequencies are available, then joint inversion of data from different coils produces a better model than the individual inversions. Tests on 3-D synthetic data sets indicate that 1-D inversions can be used as a fast and approximate tool to locate anomalies in the subsurface. Also for the test example presented here, the joint inversion of HC and CA data over a 3-D conductivity provided a better model than that produced by the individual inversion of the data sets.

3-D inversions of magnetic gradiometer data in archeological prospecting: Possibilities and limitations

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 849-860 ◽  
Author(s):  
Jörg Herwanger ◽  
Hansruedi Maurer ◽  
Alan G. Green ◽  
Jürg Leckebusch
Keyword(s):  
Magnetic Susceptibility ◽  
Synthetic Data ◽  
Vertical Gradient ◽  
Magnetic Data ◽  
Data Sets ◽  
Northern Switzerland ◽  
Recorded Data ◽  
Susceptibility Contrast ◽  
Depth Extent ◽  
Archeological Site

A vertical‐gradient magnetic system based on optically pumped Cesium sensors has been used to map subtle magnetic anomalies across infilled pit houses and ditches at a medieval archeological site in northern Switzerland. For estimating the locations and dimensions of these features from the recorded data, we have designed and implemented an appropriate inversion scheme. Tests of this scheme on realistic synthetic data sets suggested that suitable minimum magnetic susceptibility contrasts and smoothing parameters for the inversion may be directly extracted from the data. Inversions with minimum magnetic susceptibility contrasts generated causative bodies with maximum plausible sizes. By using higher magnetic susceptibility contrasts, a complete suite of models that matched the data equally well was produced. To constrain better the magnetic susceptibility constrast within a selected area of the archeological site, shallow samples of topsoil and sediment were analyzed in the laboratory. An inversion based on the measured magnetic susceptibility contrast yielded reliable estimates of the locations, 3-D geometries, and sizes of two small pit houses. The depth extent of one pit house was subsequently verified by shallow drilling. We concluded that inversions of vertical‐gradient magnetic data constrained by magnetic susceptibility or shallow borehole information are rapid and inexpensive means of providing key knowledge on the depth distribution of inductively magnetized bodies.

Simultaneous 1D inversion of loop–loop electromagnetic data for magnetic susceptibility and electrical conductivity

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1857-1869 ◽  
Author(s):  
Colin G. Farquharson ◽  
Douglas W. Oldenburg ◽  
Partha S. Routh
Keyword(s):  
Magnetic Susceptibility ◽  
Objective Function ◽  
Sum Of Squares ◽  
Magnetic Data ◽  
Data Sets ◽  
Low Frequencies ◽  
Simultaneous Inversion ◽  
Electromagnetic Data ◽  
Susceptibility Effects ◽  
Logarithmic Barrier

Magnetic susceptibility affects electromagnetic (EM) loop–loop observations in ways that cannot be replicated by conductive, nonsusceptible earth models. The most distinctive effects are negative in‐phase values at low frequencies. Inverting data contaminated by susceptibility effects for conductivity alone can give misleading models: the observations strongly influenced by susceptibility will be underfit, and those less strongly influenced will be overfit to compensate, leading to artifacts in the model. Simultaneous inversion for both conductivity and susceptibility enables reliable conductivity models to be constructed and can give useful information about the distribution of susceptibility in the earth. Such information complements that obtained from the inversion of static magnetic data because EM measurements are insensitive to remanent magnetization. We present an algorithm that simultaneously inverts susceptibility‐affected data for 1D conductivity and susceptibility models. The solution is obtained by minimizing an objective function comprised of a sum‐of‐squares measure of data misfit and sum‐of‐squares measures of the amounts of structure in the conductivity and susceptibility models. Positivity of the susceptibilities is enforced by including a logarithmic barrier term in the objective function. The trade‐off parameter is automatically estimated using the generalized cross validation (GCV) criterion. This enables an appropriate fit to the observations to be achieved even if good noise estimates are not available. As well as synthetic examples, we show the results of inverting airborne data sets from Australia and Heath Steele Stratmat, New Brunswick.

Which data residual norm for robust elastic frequency-domain full waveform inversion?

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. R37-R46 ◽  
Author(s):  
Romain Brossier ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Sampling Interval ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Fitting Procedure ◽  
Full Waveform ◽  
Threshold Criterion

Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model, definition of multiparameter classes, and inaccurate modeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm [Formula: see text], the least-absolute-values norm [Formula: see text], and combinations of both (the Huber and so-called hybrid criteria) with reference to two noisy offshore (Valhall model) and onshore (overthrust model) synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion (FWI), where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the [Formula: see text]-norm provided the most reliable models for P- and S-wave velocities ([Formula: see text] and[Formula: see text]), even when strongly decimated data sets that correspond to few frequencies were used in the inversion and when outliers polluted the data. The [Formula: see text]-norm can provide reliable results in the presence of uniform white noise for [Formula: see text] and [Formula: see text] if the data redundancy is increased by refining the frequency sampling interval in the inversion at the expense of computational efficiency. The [Formula: see text]-norm and the Huber and hybrid criteria, unlike the [Formula: see text]-norm, allow for successful imaging of the [Formula: see text] model from noisy data in a soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The [Formula: see text]-norm provides a robust alternative to the [Formula: see text]-norm for inverting decimated data sets in the framework of efficient frequency-domain FWI.

A holistic approach to inversion of frequency-domain airborne EM data

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. G301-G312 ◽  
Author(s):  
Ross Brodie ◽  
Malcolm Sambridge
Keyword(s):  
Frequency Domain ◽  
Synthetic Data ◽  
Holistic Approach ◽  
Data Sets ◽  
Data Set ◽  
Zero Level ◽  
Airborne Electromagnetic ◽  
Available Information ◽  
Airborne Electromagnetic Data ◽  
Parameter Values

We have developed a holistic method for simultaneously calibrating, processing, and inverting frequency-domain airborne electromagnetic data. A spline-based, 3D, layered conductivity model covering the complete survey area was recovered through inversion of the entire raw airborne data set and available independent conductivity and interface-depth data. The holistic inversion formulation includes a mathematical model to account for systematic calibration errors such as incorrect gain and zero-level drift. By taking these elements into account in the inversion, the need to preprocess the airborne data prior to inversion is eliminated. Conventional processing schemes involve the sequential application of a number of calibration corrections, with data from each frequency treated separately. This is followed by inversion of each multifrequency sample in isolation from other samples.By simultaneously considering all of the available information in a holistic inversion, we are able to exploit interfrequency and spatial-coherency characteristics of the data. The formulation ensures that the conductivity and calibration models are optimal with respect to the airborne data and prior information. Introduction of interfrequency inconsistency and multistage error propagation stemming from the sequential nature of conventional processing schemes is also avoided. We confirm that accurate conductivity and calibration parameter values are recovered from holistic inversion of synthetic data sets. We demonstrate that the results from holistic inversion of raw survey data are superior to the output of conventional 1D inversion of final processed data. In addition to the technical benefits, we expect that holistic inversion will reduce costs by avoiding the expensive calibration-processing-recalibration paradigm. Furthermore, savings may also be made because specific high-altitude zero-level observations, needed for conventional processing, may not be required.

A simultaneous inversion for background velocity and impedance maps

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 458-469 ◽  
Author(s):  
D. Cao ◽  
W. B. Beydoun ◽  
S. C. Singh ◽  
A. Tarantola
Keyword(s):  
Traditional Approach ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Seismic Velocities ◽  
Inversion Algorithm ◽  
Seismic Reflection Data ◽  
Simultaneous Inversion ◽  
Highly Nonlinear

Full‐waveform inversion of seismic reflection data is highly nonlinear because of the irregular form of the function measuring the misfit between the observed and the synthetic data. Since the nonlinearity results mainly from the parameters describing seismic velocities, an alternative to the full nonlinear inversion is to have an inversion method which remains nonlinear with respect to velocities but linear with respect to impedance contrasts. The traditional approach is to decouple the nonlinear and linear parts by first estimating the background velocity from traveltimes, using either traveltime inversion or velocity analysis, and then estimating impedance contrasts from waveforms, using either waveform inversion or conventional migration. A more sophisticated strategy is to obtain both the subsurface background velocities and impedance contrasts simultaneously by using a single least‐squares norm waveform‐fit criterion. The background velocity that adequately represents the gross features of the medium is parameterized using a sparse grid, whereas the impedance contrasts use a dense grid. For each updated velocity model, the impedance contrasts are computed using a linearized inversion algorithm. For a 1-D velocity background, it is very efficient to perform inversion in the f-k domain by using the WKBJ and Born approximations. The method performs well both with synthetic and field data.

Sign in / Sign up

Export Citation Format

Share Document