Bayesian inversion of CSEM and magnetotelluric data

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. E33-E42 ◽  
Author(s):  
Arild Buland ◽  
Odd Kolbjørnsen
Keyword(s):  
Prior Knowledge ◽  
Inversion Method ◽  
Earth Model ◽  
Magnetotelluric Data ◽  
Inversion Result ◽  
Electromagnetic Data ◽  
Magnetic Components ◽  
Resistivity Model ◽  
Frequency Components ◽  
Inversion Procedure

We have developed a Bayesian methodology for inversion of controlled source electromagnetic (CSEM) data and magnetotelluric (MT) data. The inversion method provided optimal solutions and also the associated uncertainty for any sets of electric and magnetic components and frequencies from CSEM and MT data. The method is based on a 1D forward modeling method for the electromagnetic (EM) response for a plane-layered anisotropic earth model. The inversion method was also designed to invert common midpoint (CMP)-sorted data along a 2D earth profile assuming locally horizontal models in each CMP position. The inversion procedure simulates from the posterior distribution using a Markov chain Monte Carlo (McMC) approach based on the Metropolis-Hastings algorithm. The method that we use integrates available geologic prior knowledge with the information in the electromagnetic data such that the prior model stabilizes and constrains the inversion according to the described knowledge. The synthetic examples demonstrated that inclusion of more data generally improves the inversion results. Compared to inversion of the inline electric component only, inclusion of broadside and magnetic components and an extended set of frequency components moderately decreased the uncertainty of the inversion. The results were strongly dependent on the prior knowledge imposed by the prior distribution. The prior knowledge about the background resistivity model surrounding the target was highly important for a successful and reliable inversion result.

Automatic 1-D inversion of magnetotelluric data: Finding the simplest possible model that fits the data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 773-782 ◽  
Author(s):  
Laust B. Pedersen ◽  
Mehran Gharibi
Keyword(s):  
Plane Wave ◽  
Theoretical Data ◽  
Small Error ◽  
Earth Model ◽  
Model Parameters ◽  
Random Errors ◽  
Magnetotelluric Data ◽  
Near Surface ◽  
Resolution Power ◽  
Inversion Procedure

We demonstrate that automatic layered inversion of plane‐wave electromagnetic data can be carried out by modifying standard least‐squares inversion schemes. The modifications include a logarithmic reparameterization of the unknown model parameters, whereby all layer parameters are forced to remain within given bounds. However, the most important modification to help the optimization process find the best model and to avoid local minima is to split the data into several subbands, starting from the highest frequencies. By this stripping procedure, the shallower part of the model becomes well estimated first. As more data are introduced, more layers may be required to improve the data fit. The new inversion procedure has been applied to many sets of theoretical data representing increasingly complicated layering that is often found in near‐surface studies. The main result of these simulations is that there is a very strong coupling between the resolution power of plane‐wave data and their random errors. Particularly at small error levels around 1–2%, the resolution power increases greatly. For larger error levels the fine layering of the models becomes smeared, and only the variations in thickness of the upper layer can be resolved. A comparison with the popular “Occam” procedure shows, not unexpectedly, that a blocky earth is best represented by a blocky earth model rather than by a smooth model.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

Three‐dimensional inversion of magnetotelluric data for a resistivity model with arbitrary anisotropy

2021 ◽  
Author(s):  
Wenxin Kong ◽  
Handong Tan ◽  
Changhong Lin ◽  
Martyn Unsworth ◽  
Benjamin Lee ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Magnetotelluric Data ◽  
Resistivity Model ◽  
Arbitrary Anisotropy

2-D and 3-D resistivity image reconstruction using crosshole data

Geophysics ◽  
1992 ◽  
Vol 57 (10) ◽  
pp. 1270-1281 ◽  
Author(s):  
Hiromasa Shima
Keyword(s):  
Field Test ◽  
Numerical Models ◽  
Electrical Potential ◽  
Nonlinear Least Squares ◽  
Three Dimensions ◽  
Inversion Method ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Resistivity Model

Theoretical changes in the distribution of electrical potential near subsurface resistivity anomalies have been studied using two resistivity models. The results suggest that the greatest response from such anomalies can be observed with buried electrodes, and that the resistivity model of a volume between boreholes can be accurately reconstructed by using crosshole data. The distributive properties of crosshole electrical potential data obtained by the pole‐pole array method have also been examined using the calculated partial derivative of the observed apparent resistivity with respect to a small cell within a given volume. The results show that for optimum two‐dimensional (2-D) and three‐dimensional (3-D) target imaging, in‐line data and crossline data should be combined, and an area outside the zone of exploration should be included in the analysis. In this paper, the 2-D and 3-D resistivity images presented are reconstructed from crosshole data by the combination of two inversion algorithms. The first algorithm uses the alpha center method for forward modeling and reconstructs a resistivity model by a nonlinear least‐squares inversion. Alpha centers express a continuously varying resistivity model, and the distribution of the electrical potential from the model can be calculated quickly. An initial general model is determined by the resistivity backprojection technique (RBPT) prior to the first inversion step. The second process uses finite elements and a linear inversion algorithm to improve the resolution of the resistivity model created by the first step. Simple 2-D and 3-D numerical models are discussed to illustrate the inversion method used in processing. Data from several field studies are also presented to demonstrate the capabilities of using crosshole resistivity exploration techniques. The numerical experiments show that by using the combined reconstruction algorithm, thin conductive layers can be imaged with good resolution for 2-D and 3-D cases. The integration of finite‐element computations is shown to improve the image obtained by the alpha center inversion process for 3-D applications. The first field test uses horizontal galleries to evaluate complex 2-D features of a zinc mine. The second field test illustrates the use of three boreholes at a dam site to investigate base rock features and define the distribution of an altered zone in three dimensions.

Deep electrical structure of northern Alberta (Canada): implications for diamond exploration

2009 ◽  
Vol 46 (2) ◽  
pp. 139-154 ◽  
Author(s):  
Erşan Türkoğlu ◽  
Martyn Unsworth ◽  
Dinu Pana
Keyword(s):  
Subduction Zone ◽  
Upper Mantle ◽  
Lithospheric Mantle ◽  
Three Dimensional ◽  
Diamond Formation ◽  
Magnetotelluric Data ◽  
Diamond Exploration ◽  
Upper Mantle Structure ◽  
Resistivity Model ◽  
Northern Alberta

Geophysical studies of upper mantle structure can provide constraints on diamond formation. Teleseismic and magnetotelluric data can be used in diamond exploration by mapping the depth of the lithosphere–asthenosphere boundary. Studies in the central Slave Craton and at Fort-à-la-Corne have detected conductors in the lithospheric mantle close to, or beneath, diamondiferous kimberlites. Graphite can potentially explain the enhanced conductivity and may imply the presence of diamonds at greater depth. Petrologic arguments suggest that the shallow lithospheric mantle may be too oxidized to contain graphite. Other diamond-bearing regions show no upper mantle conductor suggesting that the correlation with diamondiferous kimberlites is not universal. The Buffalo Head Hills in Alberta host diamondiferous kimberlites in a Proterozoic terrane and may have formed in a subduction zone setting. Long period magnetotelluric data were used to investigate the upper mantle resistivity structure of this region. Magnetotelluric (MT) data were recorded at 23 locations on a north–south profile extending from Fort Vermilion to Utikuma Lake and an east–west profile at 57.2°N. The data were combined with Lithoprobe MT data and inverted to produce a three-dimensional (3-D) resistivity model with the asthenosphere at 180–220 km depth. This model did not contain an upper mantle conductor beneath the Buffalo Head Hills kimberlites. The 3-D inversion exhibited an eastward dipping conductor in the crust beneath the Kiskatinaw terrane that could represent the fossil subduction zone that supplied the carbon for diamond formation. The low resistivity at crustal depths in this structure is likely due to graphite derived from subducted organic material.

BAYESIAN MAGNETOTELLURIC INVERSION USING METHYLENE BLUE STRUCTURAL PRIORS FOR IMAGING SHALLOW CONDUCTORS IN GEOTHERMAL FIELDS

Geophysics ◽  
2021 ◽  
pp. 1-66
Author(s):  
Alberto Ardid ◽  
David Dempsey ◽  
Edward Bertrand ◽  
Fabian Sepulveda ◽  
Flora Solon ◽  
...  
Keyword(s):  
Methylene Blue ◽  
Clay Content ◽  
3D Models ◽  
Bayesian Inversion ◽  
Inversion Method ◽  
Geothermal Fields ◽  
Geological Information ◽  
Resistivity Model ◽  
Irreducible Uncertainty ◽  
Clay Cap

In geothermal exploration, magnetotelluric (MT) data and inversion models are commonly used to image shallow conductors typically associated with the presence of an electrically conductive clay cap that overlies the main reservoir. However, these inversion models suffer from non-uniqueness and uncertainty, and the inclusion of useful geological information is still limited. We develop a Bayesian inversion method that integrates the electrical resistivity distribution from MT surveys with borehole methylene blue data (MeB), an indicator of conductive clay content. MeB data is used to inform structural priors for the MT Bayesian inversion that focus on inferring with uncertainty the shallow conductor boundary in geothermal fields. By incorporating borehole information, our inversion reduces non-uniqueness and then explicitly represents the irreducible uncertainty as estimated depth intervals for the conductor boundary. We use Markov chain Monte Carlo (McMC) and a one-dimensional three-layer resistivity model to accelerate the Bayesian inversion of the MT signal beneath each station. Then, inferred conductor boundary distributions are interpolated to construct pseudo-2D/3D models of the uncertain conductor geometry. We compared our approach against a deterministic MT inversion software on synthetic and field examples and showed good performance in estimating the depth to the bottom of the conductor, a valuable target in geothermal reservoir exploration.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Transient electromagnetic search engine for real-time imaging

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. E277-E285 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Jie Zhang ◽  
Xiong Zhang
Keyword(s):  
Real Time ◽  
Search Engine ◽  
Solution Space ◽  
Inversion Method ◽  
Model Parameters ◽  
Transient Electromagnetic ◽  
Model Solutions ◽  
Resistivity Model ◽  
2D Resistivity ◽  
Engine Method

To image the resistivity distribution of the subsurface, transient electromagnetic (TEM) surveying has been established as an effective geophysical method. Conventionally, an inversion method is applied to resolve the model parameters from the available measurements. However, significant time and effort are involved in preparing and executing an inversion and this prohibits its use as a real-time decision-making tool to optimize surveying in the field. We have developed a search engine method to find approximate 1D resistivity model solutions for circular central-loop configuration TEM data in real time. The search engine method is a concept used for query searches from large databases on the Internet. By extension, approximate solutions to any input TEM data can be found rapidly by searching a preestablished database. This database includes a large number of forward simulation results that represent the possible model solutions. The database size is optimized by the survey depth of investigation and the sensitivity analysis of the model layers. The fast-search speed is achieved by using the multiple randomized [Formula: see text]-dimensional tree method. In addition to its high speed in finding solutions, the search engine method provides a solution space that quantifies the resolutions and uncertainties of the results. We apply the search engine method to find 1D model solutions at different data points and then interpolate them to a pseudo-2D resistivity model. We tested the method with synthetic and real data.

Traveltime inversion of offset vertical seismic profiles—A feasibility study

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 250-264 ◽  
Author(s):  
L. R. Lines ◽  
A. Bourgeois ◽  
J. D. Covey
Keyword(s):  
Inverse Method ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Inversion Method ◽  
Earth Model ◽  
Seismic Profiles ◽  
Traveltime Inversion ◽  
Vertical Seismic Profiles ◽  
Inversion Techniques

Traveltimes from an offset vertical seismic profile (VSP) are used to estimate subsurface two‐dimensional dip by applying an iterative least‐squares inverse method. Tests on synthetic data demonstrate that inversion techniques are capable of estimating dips in the vicinity of a wellbore by using the traveltimes of the direct arrivals and the primary reflections. The inversion method involves a “layer stripping” approach in which the dips of the shallow layers are estimated before proceeding to estimate deeper dips. Examples demonstrate that the primary reflections become essential whenever the ratio of source offset to layer depth becomes small. Traveltime inversion also requires careful estimation of layer velocities and proper statics corrections. Aside from these difficulties and the ubiquitous nonuniqueness problem, the VSP traveltime inversion was able to produce a valid earth model for tests on a real data case.

An efficient data‐subspace inversion method for 2-D magnetotelluric data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 791-803 ◽  
Author(s):  
Weerachai Siripunvaraporn ◽  
Gary Egbert
Keyword(s):  
Significant Loss ◽  
Inversion Method ◽  
Data Sets ◽  
Reduced Basis ◽  
Sensitivity Matrix ◽  
Approximate Methods ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Data Space ◽  
Occam’S Inversion

There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much more efficient variant on the OCCAM scheme. By expressing the solution as a linear combination of rows of the sensitivity matrix smoothed by the model covariance (the “representers”), we transform the linearized inverse problem from the M-dimensional model space to the N-dimensional data space. This method is referred to as DASOCC, the data space OCCAM’s inversion. Since generally N ≪ M, this transformation by itself can result in significant computational saving. More importantly the data space formulation suggests a simple approximate method for constructing the inverse solution. Since MT data are smooth and “redundant,” a subset of the representers is typically sufficient to form the model without significant loss of detail. Computations required for constructing sensitivities and the size of matrices to be inverted can be significantly reduced by this approximation. We refer to this inversion as REBOCC, the reduced basis OCCAM’s inversion. Numerical experiments on synthetic and real data sets with REBOCC, DASOCC, NLCG, RRI, and OCCAM show that REBOCC is faster than both DASOCC and NLCG, which are comparable in speed. All of these methods are significantly faster than OCCAM, but are not competitive with RRI. However, even with a simple synthetic data set, we could not always get RRI to converge to a reasonable solution. The basic idea behind REBOCC should be more broadly applicable, in particular to 3-D MT inversion.

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