A comparison of accuracy and computation time of three-dimensional magnetotelluric modelling algorithms

SUMMARYBecause the magnetotelluric (MT) method uses natural sources, the electric and magnetic fields recorded in the field acquisition are not directly used but usually converted into other MT response functions for interpretation such as inversion. Considering that inversion results are dependent on types of input data, it can be helpful to analyse different characteristics of MT response functions for inversion. In this study, we examine sensitivity patterns of MT response functions used commonly in MT inversion, which are the impedance tensor, apparent resistivity, phase, tipper, effective impedance and phase tensor; and investigate how their sensitivity patterns affect inversion results. We first describe overall tendencies of 3-D sensitivity patterns of the MT response functions, and then classify the MT response functions into six groups based on 2-D sensitivity patterns computed at the surface, which are briefly called ‘surface-sensitivity patterns’ in this study. The ’diagonal components of the impedance’ and ‘off-diagonal components of the phase tensor’, which have four petals-shaped surface-sensitivity patterns along the diagonal directions, belong to Group 1, and contribute to imaging 3-D subsurface structures from receivers installed evenly at the surface. Group 2 contains the ‘xy-components of the impedance, apparent resistivity and phase’ and ‘yy-component of the phase tensor’ whose surface-sensitivity patterns are linear in the y-axis. The ‘yx-components of the impedance, apparent resistivity and phase’ and ‘xx-component of the phase tensor’ that have strong linear surface-sensitivity patterns along the x-axis are classified into Group 3. The MT response functions of Groups 2 and 3 are useful for inversion of structures close to 2-D, whose strike extends along the y- and x-axes, respectively. Groups 4 and 5 include the ‘x- and y-components of tipper’ that possess linearly aligned two petals-shaped surface-sensitivity patterns in the x- and y-axes, respectively. The tipper can be helpful in imaging both 2-D and 3-D structures. The ‘effective impedance’ belongs to Group 6, whose surface-sensitivity patterns appear as a small circle. The surface-sensitivity patterns allow the effective impedance to have an advantage in interpretation of 1-D structures. By using several MT response functions for specific cases of 1-D, 2-D and 3-D interpretation of MT data, we investigate whether characteristics of the sensitivity patterns are reflected in modelling (simulating field data) and inversion results, and then suggest optimal MT response functions for those cases. In doing so, we show how to utilize the characteristics of the sensitivity patterns in inversion, and recommend the input MT response functions for inversion according to MT exploration situations. Our study provides basic information on similarities and differences of major MT response functions for inversion and insights on which MT response functions are suitable to increase the feasibility of MT inversion for different field situations based on the sensitivity patterns.

2D magnetotelluric inversion based on ResNet

SUMMARY Previous inversions of sea-floor magnetotelluric (MT) sounding data have predicted upper mantle electrical conductivities which are more than an order of magnitude higher than laboratory measurements of the conductivity of olivine would suggest, and controlled source-field electromagnetic (CSEM) soundings require a lithospheric mantle conductivity of 3 x lop5 Sm-’, which is so low that the electromagnetic (EM) coast effect would produce more anisotropy in MT soundings than is observed. We address these issues by constructing an olivine mantle model for conductivity and examining the inversion of MT data from three sea-floor sites, and show that the incompatibilities can be largely resolved if the effects of oceans and coastlines are considered. Our mantle model is based on recent measurements of olivine conductivity, the conductivity of tholeiite melt, a thermal model for the upper mantle based on lithospheric cooling and the temperature of a+ a + /3 olivine transition, the pyrolite model of mantle petrology, and conductivities derived from CSEM sounding. We propose Archie’s Law with exponent 2 and interconnected tubes as realistic lower and upper bounds for the effect of partial melt on rock conductivity, and Archie’s Law with exponent 1.5 as the preferred estimate. The 1-D forward response of this model is not compatible with observed sea-floor MT data. Three data sets presented by Oldenburg (1981) pass a test for one-dimensionality based on the size of the residuals when fit with Parker’s D+ algorithm, but two of the three soundings fail a test for independence of residuals. We also find that the presence of the upper mantle ‘high-conductivity zone’ previously inferred from these data is highly dependent on data misfit and not required when the misfit criterion is relaxed a reasonable amount. Re-inversions of the MT data produce models which are incompatible with our petrological model of mantle conductivity. However, by adding an ocean with various coastlines of simple geometry to our petrological model and solving the forward 3-D problem using thin-sheet analysis we predict MT responses which are distorted in a manner that is remarkably similar to the observed data.

The magnetotelluric (MT) method is passive geophysical method that measures natural electromagnetic field to estimate the subsurface resistivity structure. Before conducting 2D MT data inversion, data analysis, dimensionality, including determining the direction of the geoelectrical strike must be performed. It is needed to fulfill the assumption of 2D MT modeling. 2D modeling of magnetotelluric data is an important part because the results can determine the quality of the subsurface interpretation. Therefore, this paper describes the determination of the dimensonality and geoelectrical strike using the phase tensor and tipper strike parameters. The invariant parameters of phase tensor including skew angle (β) and ellipticity are used to get the information about the dimensionality and geoelectrical strike. The results from the phase tensor are plotted in a rose diagram to determine the main direction of the geoelectrical strike. The phase tensor analysis contains ambiguity 90°, therefore tipper strike used to validate the analysis. From the analysis, the result shows the 1D or 2D structures of the MT data in high frequency, meanwhile the lower frequency, the majority of the data show 3D structures. The dominant geoelectrical strike is around N15°E and it is confirmed with the regional structure of the area. Determination of dimensionality and geoelectrical strike are applied to MT data from the geothermal field.

We present the numerical experimental results to investigate the applicability and limitations of two-dimensional (2-D) magnetotelluric (MT) topographic inversion of MT data which is assumed to be acquired in three-dimensional (3-D) topographic environment. For this purpose, we set up a 3-D model, which has a hill and a valley in 3-D shape with a 2-D like anomalous body. We examined the topographic responses for homogenous models and tried 2-D topographic inversion of 3-D data. We compared 2-D inversion results each other with 2-D non-topographic inversion and topographic inversion for data distorted by 3-D topography.

Magnetotelluric data modeling was used for oil and gas exploration. The parameters are apparent resistivity and phase. The magnetotelluric data of this research were line JBS4 with 71 sounding sites and line JBS8 with 66 sounding sites. The magnetotelluric data was completed by remote reference data which used for reducing the noise so that good data could be gotten. The magnetotelluric data was proceed in stage as follow: time series selection, Fourier transform, robust processing, cross power selection, and 2 dimension inversion. The result of this research showed that magnetotelluric method can figured out the sub-surface model well. From the result of interpretation 2D inversion magnetotelluric and other geophysical data (gravity anomaly map), we can conclude that magnetotelluric modeling figured out 2 sub-basins. Those sub basins had thick sediment layer (4000 meter for Bantarkalong Basin and 3000 meter for Citanduy Basin) and the dominant resistivity value was 22-119 Ohm.meter.

The effects of the ocean coast on magnetotelluric (MT) data have been studied and results are described in this article. MT soundings from various sites along coastal plains of Kachchh were acquired where volcanic rocks overlie Mesozoic sediments having potential resource prospects. The region of our study lies in the proximity of Gulf of Kachchh and Arabian Sea. This article describes the effects the presence of a conductive body on the acquired MT data. With the help of synthetic MT modelling and induction arrows we demonstrate the influence of shallow conductive body on the MT data. The modelling results when compared to the field observations show that much of the high frequencies are unaffected by the coast, however low frequencies of the data do seem to be distorted by onshore–offshore resistivity contrasts. The least affect on high frequencies can be attributed to very shallow water depth as well as to the fact that the onshore–offshore resistivity contrasts are not large enough to influence the high frequency data badly. The results presented here report for the first time the effect of the coast on the analysis on MT data from Kachchh. Due to several academic as well as industrial onshore–offshore MT experiments presently being carried out to explore its hydrocarbon potential, our results have an important bearing on designing and acquisition of future MT surveys in this region.

Out-of-quadrant impedance phases (POQ) have been observed in several magnetotelluric (MT) data sets around the world, hampering the modelling and interpretation of the data. These anomalous responses are usually observed in small groups of sites and have been variously interpreted as due to electrical anisotropy, galvanic distortion, 2-D structures with large resistivity contrasts, or 3-D conductive bodies, such as L-shaped conductors. We present here what is possibly a unique land-based MT data set characterized by an exceptionally large number of sites with POQ. The MT data were collected in the southeastern margin of the Capricorn Orogen (Western Australia). This is an area with a complex geological history, which is evident in the MT responses. Given the characteristics of the study area, which includes very high resistivity Archean terrains surrounded by low resistivity Palaeoproterozoic basins, strong resistivity contrasts involving complex 3-D structures are a possible cause of this unusual behaviour. This is confirmed by 3-D forward modelling using models based on the general geology of the study area, as well as by the 3-D inversion results. A comparison of the real and synthetic data, derived from 3-D forward modelling, using the same parameters suggests that the proposed scenario is a realistic explanation for most of the anomalous phases observed in this data set. Synthetic data are not affected by galvanic distortion or electrical anisotropy, so the good match observed between the real and synthetic MT responses is likely due to 3-D inductive effects. Previous explanations for POQ responses, such as blocks with electrical anisotropy and 3-D L-shaped conductors, are not required and are considered to be less likely causes of the POQ responses on geological grounds.

We present electrical resistivity models of the crust and upper mantle from two‐dimensional (2‐D) inversion of magnetotelluric (MT) data collected in the Rio Grande rift, New Mexico, USA. Previous geophysical studies of the lithosphere beneath the rift identified a low‐velocity zone several hundred kilometers wide, suggesting that the upper mantle is characterized by a very broad zone of modified lithosphere. In contrast, the surface expression of the rift (e.g., high‐angle normal faults and synrift sedimentary units) is confined to a narrow region a few tens of kilometers wide about the rift axis. MT data are uniquely suited to probing the depths of the lithosphere that fill the gap between surface geology and body wave seismic tomography, namely the middle to lower crust and uppermost mantle. We model the electrical resistivity structure of the lithosphere along two east‐west trending profiles straddling the rift axis at the latitudes of 36.2 and 32.0°N. We present results from both isotropic and anisotropic 2‐D inversions of MT data along these profiles, with a strong preference for the latter in our interpretation. A key feature of the anisotropic resistivity modeling is a broad (~200‐km wide) zone of enhanced conductivity (<20 Ωm) in the middle to lower crust imaged beneath both profiles. We attribute this lower crustal conductor to the accumulation of free saline fluids and partial melt, a direct result of magmatic activity along the rift. High‐conductivity anomalies in the midcrust and upper mantle are interpreted as fault zone alteration and partial melt, respectively.

We collected long-period magnetotelluric (LMT) data on the 64 stations by using a remotely controlled measurement system in northwestern Anatolia, Türkiye. The data was collected along four nearly parallel 300-km-long lines. In our previous project, we already collected broadband magnetotelluric(MT) data on 358 stations along those four lines. These lines are crossing main tectonic traverses such as North Anatolia Fault Zones, and Intra-Pontid Suture zones.  The remotely controlled MT measurement system provides us to control data quality during measurement and we can change the station location if the data quality is not good in the current stations.  This ensures the good data quality of all MT sites. After the time series analysis and main data processing procedure such as phase tensor decomposition and static shift correction, we interpreted each line's data set by using a two-dimensional inversion algorithm. We also inverted LMT data by using a three-dimensional inversion algorithm. The three-dimensional resistivity model also showed us to main tectonic units as two-dimensional resistivity models. Additionally, crust lithosphere relations were also revealed. We obtained upper and lower crust boundaries by using magnetic data and crust al depth by using gravity data. Those results also validated our resistivity models obtained from MT data inversion. We are going to give preliminary interpretation results of the lithosphere structure of northwest Anatolia in this presentation.Acknowledgement:  This study is supported by TUBITAK (The Scientific and Technological Research Council of Turkey) Project with Grant Number 119Y197. We thanks TUBITAK.

ABSTRACTWe describe an algorithm for inverting magnetotelluric (MT) data in the presence of strong bathymetry or topography. Instead of correcting distortions due to bathymetry or topography we incorporate them directly into the inversion. To achieve a high accuracy in computing MT responses we use finite‐difference approximations that permit sloping discrete boundaries inside model elements. The same approach is applicable to any seafloor electromagnetic calculation and can also be used to incorporate steep topography on land. We test our approach on various topographic features and compare our results to that of a finite element approach. Finally, we present inversion examples that illustrate the effectiveness of our inversion algorithm in recovering true subsurface structures in the presence of strong bathymetry and topography.

Three-dimensional magnetotelluric modeling in anisotropic media using edge-based finite element method

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2002An algorithm for the three‐dimensional inversion of magnetotelluric dataAuthors: Colin G. FarquharsonDouglas W. OldenburgEldad HaberRoman ShekhtmanColin G. FarquharsonUBC‐Geophysical Inversion Facility, U. of British Columbia, Vancouver, Canada, Douglas W. OldenburgUBC‐Geophysical Inversion Facility, U. of British Columbia, Vancouver, Canada, Eldad HaberEMI‐Schlumberger, Richmond, CA, and Roman ShekhtmanUBC‐GIFhttps://doi.org/10.1190/1.1817336 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InReddit Permalink: https://doi.org/10.1190/1.1817336FiguresReferencesRelatedDetailsCited byHybrid mesh for magnetotelluric forward modeling based on the finite element method11 January 2023 | Scientific Reports, Vol. 13, No. 1Fast 3D simulation of magnetotelluric data in anisotropic media using a rational Krylov methodJunjun Zhou, Ningbo Bai, Xiangyun Hu, Tiaojie Xiao, and Zhidan Long17 October 2023 | GEOPHYSICS, Vol. 88, No. 6Processing of passive EM fields acquired during active-source airborne EM surveys4 February 2021 | Exploration Geophysics, Vol. 52, No. 6An efficient parallel algorithm for 3D magnetotelluric modeling with edge-based finite element6 July 2020 | Computational Geosciences, Vol. 25, No. 1A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation1 September 2020 | Geophysical Journal International, Vol. 223, No. 33D inversion of magnetotelluric data by using a hybrid forward-modeling approach and mesh decouplingDeniz Varılsüha11 September 2020 | GEOPHYSICS, Vol. 85, No. 5Subsurface Characterization of the Pennsylvanian Clare Basin, Western Ireland, by Means of Joint Interpretation of Electromagnetic Geophysical Data and Well‐Log Data9 July 2019 | Journal of Geophysical Research: Solid Earth, Vol. 124, No. 7Modeling sferic signals extracted from active-source AEM dataDaniel Sattel and Eric Battig27 August 2018Removal of galvanic distortion effects in 3D magnetotelluric data by an equivalent source techniqueWenwu Tang, Yaoguo Li, Douglas W. Oldenburg, and Jianxin Liu8 February 2018 | GEOPHYSICS, Vol. 83, No. 2The advantages of complementing MT profiles in 3-D environments with geomagnetic transfer function and interstation horizontal magnetic transfer function data: results from a synthetic case study23 September 2016 | Geophysical Journal International, Vol. 207, No. 3Integration of controlled-source and radio magnetotellurics, electric resistivity tomography, and reflection seismics to delineate 3D structures of a quick-clay landslide site in southwest of SwedenChunling Shan, Mehrdad Bastani, Alireza Malehmir, Lena Persson, and Emil Lundberg12 January 2016 | GEOPHYSICS, Vol. 81, No. 13-D inversion of magnetotelluric data using unstructured tetrahedral elements: applicability to data affected by topography29 May 2015 | Geophysical Journal International, Vol. 202, No. 23D marine magnetotelluric modeling and inversion with the finite-difference time-domain methodSébastien de la Kethulle de Ryhove and Rune Mittet8 October 2014 | GEOPHYSICS, Vol. 79, No. 6Magnetotelluric static shift correction using an equivalent source techniqueWenwu Tang, Yaoguo Li, Douglas W. Oldenburg, and Jianxin Liu5 August 2014The inability of magnetotelluric off-diagonal impedance tensor elements to sense oblique conductors in three-dimensional inversion17 December 2013 | Geophysical Journal International, Vol. 196, No. 3Magnetotelluric 3-D inversion—a review of two successful workshops on forward and inversion code testing and comparison14 March 2013 | Geophysical Journal International, Vol. 193, No. 3Methods and algorithms for reconstructing three-dimensional distributions of electric conductivity and polarization in the medium by finite-element 3D modeling using the data of electromagnetic sounding8 May 2013 | Izvestiya, Physics of the Solid Earth, Vol. 49, No. 3The modeling of ZTEM data with 2D and 3D algorithmsDaniel Sattel and Ken Witherly25 October 2012Large-scale inversion of ZTEM dataElliot Holtham and Douglas W. Oldenburg9 July 2012 | GEOPHYSICS, Vol. 77, No. 4Electrical resistivity structure at the northern margin of the Tibetan Plateau and tectonic implications7 December 2011 | Journal of Geophysical Research, Vol. 116, No. B12Application of the 3D magnetotelluric inversion code in a geologically complex area9 June 2010 | Geophysical Prospecting, Vol. 58, No. 6Three‐dimensional inversion of MT and ZTEM dataElliot Holtham and Douglas W. Oldenburg21 October 2010Constructing piecewise-constant models in multidimensional minimum-structure inversionsColin G. Farquharson26 December 2007 | GEOPHYSICS, Vol. 73, No. 1Three‐dimensional forward modelling and inversion of Z‐TEM dataElliot Holtham and Douglas W. Oldenburg15 December 2008Constructing piecewise‐constant models in multi‐dimensional minimum‐structure inversionsColin G. Farquharson6 October 2006Three-Dimensional Electromagnetic Modelling and Inversion from Theory to ApplicationSurveys in Geophysics, Vol. 26, No. 6Three‐dimensional inversion of MT data from the Turquoise Ridge mine, NevadaColin G. Farquharson, Douglas W. Oldenburg, and Peter Kowalczyk3 January 2005 SEG Technical Program Expanded Abstracts 2002 ISSN (print):1052-3812 ISSN (online):1949-4645 Copyright: 2002 Pages: 2478 publication data© 2002 Copyright © 2002 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 03 Jan 2005 CITATION INFORMATION Colin G. Farquharson, Douglas W. Oldenburg, Eldad Haber, and Roman Shekhtman, (2002), "An algorithm for the three‐dimensional inversion of magnetotelluric data," SEG Technical Program Expanded Abstracts : 649-652. https://doi.org/10.1190/1.1817336 Plain-Language Summary PDF DownloadLoading ...

Long‐period magnetotelluric (MT) data can be used to interpret upper mantle temperature, hydrogen content, and the presence of partial melt, all of which strongly influence mantle viscosity. We have collected the first long‐period MT data in Svalbard and have combined them with preexisting broadband MT data to produce a model of the electrical resistivity of Svalbard's upper mantle. Asthenospheric resistivities are low compared to stable continental settings but more comparable to young oceanic asthenosphere, suggesting that the physical state of Svalbard's upper mantle is controlled by its proximity to the Mid‐Atlantic Ridge. Interpretation of the MT model using a petrologically constrained genetic algorithm approach shows that partial melt is present in the uppermost asthenosphere beneath Svalbard. This is the first direct evidence of partial melt in Svalbard's asthenosphere from deep geophysical soundings. Viscosities calculated from the geophysical data show a low viscosity layer (~1018 Pa s) coincident with the partial melt layer, underlain by a higher viscosity layer (~1020 Pa s) extending to the transition zone. Viscosities calculated from glacial isostatic adjustment (GIA) data in Svalbard show a considerable range due mainly to uncertainties in past ice sheet models. Improved constraints on Svalbard's mantle viscosity from geophysical data may help to improve these GIA models.

Summary There has been developed several algorithm for two dimensional (2-D) inverse problem of Magnetotelluric (MT) data. The well-known algorithms are developed by DeGrooth Hedlin and Constable (1990) (OCCAM), Smith and Booker (1991) (RRI), and Mackie et al. (1997) (CG) three of which based on smoothing approximation. However, forward solution and jacobian matrix calculation of the algorithms are different from each other. In addition, while SVD is used in inversion part of the first two algorithms, conjugate gradient solution is used in the third algorithm. Therefore, they generate different result from each other. It is not known exactly what is causing these differences. In this paper, a new code is developed in MATLAB for 2-D inversion of MT data. First, inversion result with different stabilizer is compared in CG algorithm. Then, CG and SVD solution is compared with each other for the sythetic model.