A generic 1-D imaging method for transient electromagnetic data

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 438-447 ◽  
Author(s):  
Niels Bøie Christensen
Keyword(s):  
Time Derivative ◽  
Step Response ◽  
Imaging Method ◽  
Nonlinear Inversion ◽  
Inversion Algorithm ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Dependent Part ◽  
Space Step ◽  
Forward Mapping

This paper presents a fast approximate 1-D inversion algorithm for transient electromagnetic (EM) data that can be applied for all measuring configurationsand transmitter waveforms and for all field components. The inversion is based on an approximate forward mapping in the adaptive Born approximation. The generality is obtained through a separation of the forward problem into a configuration-independent part, mapping layer conductivities into apparent conductivity, and a configuration-dependent part, the half-space step response. The EM response from any waveform can then be found by a convolution with the time derivative of the waveform. The approach does not involve inherently unstable deconvolution computations or nonunique transformations, and it is about 100 times faster than ordinary nonlinear inversion. Nonlinear model responses of the models obtained through the approximate inversion fit the data typically within 5%.

Imaging quasi‐layered conductive structures by simple processing of transient electromagnetic data

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 545-554 ◽  
Author(s):  
James Macnae ◽  
Yves Lamontagne
Keyword(s):  
Delay Time ◽  
A Priori ◽  
Step Response ◽  
Layered Earth ◽  
Electromagnetic Data ◽  
Apparent Conductivity ◽  
Data Inversion ◽  
Transient Electromagnetic ◽  
Static Zone ◽  
The Cost

An “imaged” conductivity section of a layered earth can be obtained by simple transformation of step‐response electromagnetic data measured in the quasi‐static zone. This method of data transformation is presented as an alternative to conventional apparent conductivity transformations. At each delay time, the variation of the step response as a function of geometry (transmitter and receiver location) is transformed to an equivalent reference depth h, which can be related to the depth of electromagnetic field diffusion. The behavior of h as a function of delay time is nearly independent of the source‐receiver geometry. The slowness dt/dh divided by the magnetic permeability is almost exactly proportional to the cumulative conductance measured from the surface down to a depth h. Thus we can estimate an apparent conductivity, which we call the “imaged conductivity,” at depth to be [Formula: see text]. The cost of this transformation is a fraction of the cost of conventional data inversion, and it does not require an a priori constraint on the number of parameters used in the inversion. The empirically developed technique was used successfully to process UTEM field data measured over a quasi‐layered earth.

An Array Source TEM Apparent Resistivity Conversion and Differential Conductivity Imaging Method and its Potential Applications

2019 ◽  
Vol 24 (4) ◽  
pp. 579-592
Author(s):  
Zhipeng Qi ◽  
Xiu Li ◽  
Yingying Zhang ◽  
He Li ◽  
Naiquan Sun
Keyword(s):  
Apparent Resistivity ◽  
Fdtd Method ◽  
Inverse Function ◽  
Imaging Method ◽  
Inversion Algorithm ◽  
Electromagnetic Device ◽  
Transient Electromagnetic ◽  
Potential Applications ◽  
Anomalous Bodies ◽  
Differential Imaging

In this study, for the purpose of accurately detecting fissured disaster sources and diversion channels during tunnel construction, an array source transient electromagnetic device is proposed. Then, an apparent resistance conversion method and an approximate inversion algorithm for the proposed transient electromagnetic device are presented. First, a finite-difference time-domain (FDTD) method is used for the forward modeling of the proposed array source transient electromagnetic device, and the electromagnetic responses of the cracks and water-conducting channels are obtained. When compared with the transient electromagnetic square responses of the traditional loop sources, it is found that the data confirmed that the responses to the anomalies of the proposed array source transient electromagnetic device are more apparent. Then, the transformation from the array source transient electromagnetic field to the apparent resistivity is realized according to the principle of inverse function. In order to clearly identify the boundaries of the targeted anomalous bodies, a multi-source S-inversion algorithm is used to realize the array source transient electromagnetic differential imaging. The method is validated using a theoretical model. It was determined that the results of the differential imaging had effectively identified the boundaries of the anomalous bodies, and the apparent resistivity imaging had successfully determined the resistivity distributions of the anomalous bodies. Furthermore, a combination of the aforementioned methods is used to effectively identify the faults and water-flowing fractures in the model. This study's proposed algorithm was applied to the actually measured data, and the interpretation results were found to be consistent with the excavation results, which fully demonstrated the feasibility of the proposed method.

Computer Application in Geosciences: Imaging of the Subsurface by Structural Coupled Inversion of Potential Field Data

2014 ◽  
Vol 644-650 ◽  
pp. 2670-2673
Author(s):  
Jun Wang ◽  
Xiao Hong Meng ◽  
Fang Li ◽  
Jun Jie Zhou
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Gravity Data ◽  
Computer Application ◽  
Magnetic Data ◽  
Imaging Method ◽  
Inversion Algorithm ◽  
Constant Property ◽  
Near Surface ◽  
Potential Field Data

With the continuing growth in influence of near surface geophysics, the research of the subsurface structure is of great significance. Geophysical imaging is one of the efficient computer tools that can be applied. This paper utilize the inversion of potential field data to do the subsurface imaging. Here, gravity data and magnetic data are inverted together with structural coupled inversion algorithm. The subspace (model space) is divided into a set of rectangular cells by an orthogonal 2D mesh and assume a constant property (density and magnetic susceptibility) value within each cell. The inversion matrix equation is solved as an unconstrained optimization problem with conjugate gradient method (CG). This imaging method is applied to synthetic data for typical models of gravity and magnetic anomalies and is tested on field data.

Improved Hybrid Particle Swarm Optimizer With Sine-Cosine Acceleration Coefficients For Transient Electromagnetic Inversion

2021 ◽  
Vol 16 ◽  
Author(s):  
Ruiheng Li ◽  
Qiong Zhuang ◽  
Nian Yu ◽  
Ruiyou Li ◽  
Huaiqing Zhang
Keyword(s):  
Learning Strategy ◽  
Particle Swarm ◽  
Population Diversity ◽  
Nonlinear Inversion ◽  
Test Functions ◽  
Particle Swarm Optimizer ◽  
Local Optima ◽  
Hybrid Particle ◽  
Transient Electromagnetic ◽  
Stability And Accuracy

Background: Recently, particle swarm optimization (PSO) has been increasingly used in geophysics due to its simple operation and fast convergence. Objective: However, PSO lacks population diversity and may fall to local optima. Hence, an improved hybrid particle swarm optimizer with sine-cosine acceleration coefficients (IH-PSO-SCAC) is proposed and successfully applied to test functions and in transient electromagnetic (TEM) nonlinear inversion. Method: A reverse learning strategy is applied to optimize population initialization. The sine-cosine acceleration coefficients are utilized for global convergence. Sine mapping is adopted to enhance population diversity during the search process. In addition, the mutation method is used to reduce the probability of premature convergence. Results: The application of IH-PSO-SCAC in the test functions and several simple layered models are demonstrated with satisfactory results in terms of data fit. Two inversions have been carried out to test our algorithm. The first model contains an underground low-resistivity anomaly body and the second model utilized measured data from a profile of the Xishan landslide in Sichuan Province. In both cases, resistivity profiles are obtained, and the inverse problem is solved for verification. Conclusion: The results show that the IH-PSO-SCAC algorithm is practical, can be effectively applied in TEM inversion and is superior to other representative algorithms in terms of stability and accuracy.

Inversion of helicopter electromagnetic data to a magnetic conductive layered earth

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1211-1223 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Magnetic Permeability ◽  
Field Data ◽  
Model Parameters ◽  
Relative Importance ◽  
Magnetic Polarization ◽  
Inversion Algorithm ◽  
Layered Earth ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
True Values

Inversion of airborne electromagnetic (EM) data for a layered earth has been commonly performed under the assumption that the magnetic permeability of the layers is the same as that of free space. The resistivity inverted from helicopter EM data in this way is not reliable in highly magnetic areas because magnetic polarization currents occur in addition to conduction currents, causing the inverted resistivity to be erroneously high. A new algorithm for inverting for the resistivity, magnetic permeability, and thickness of a layered model has been developed for a magnetic conductive layered earth. It is based on traditional inversion methodologies for solving nonlinear inverse problems and minimizes an objective function subject to fitting the data in a least‐squares sense. Studies using synthetic helicopter EM data indicate that the inversion technique is reasonably dependable and provides fast convergence. When six synthetic in‐phase and quadrature data from three frequencies are used, the model parameters for two‐ and three‐layer models are estimated to within a few percent of their true values after several iterations. The analysis of partial derivatives with respect to the model parameters contributes to a better understanding of the relative importance of the model parameters and the reliability of their determination. The inversion algorithm is tested on field data obtained with a Dighem helicopter EM system at Mt. Milligan, British Columbia, Canada. The output magnetic susceptibility‐depth section compares favorably with that of Zhang and Oldenburg who inverted for the susceptibility on the assumption that the resistivity distribution was known.

scholarly journals A parallel finite‐difference approach for 3D transient electromagnetic modeling with galvanic sources

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1192-1202 ◽  
Author(s):  
Michael Commer ◽  
Gregory Newman
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Electric Fields ◽  
Time Derivative ◽  
Stable Solution ◽  
Parallel Computer ◽  
Staggered Grid ◽  
Electromagnetic Modeling ◽  
Transient Electromagnetic

A parallel finite‐difference algorithm for the solution of diffusive, three‐dimensional (3D) transient electromagnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily complicated distributions of conductivity and magnetic permeability. Using a staggered grid and a modified DuFort‐Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate‐gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the initial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence‐free condition is enforced for both the magnetic‐field time derivative and the total conduction‐current density, providing accurate results at late times. In order to simulate large realistic earth models, the algorithm has been designed to run on parallel computer platforms. The upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two‐dimensional parallel fast Fourier transform. Example simulations are compared with analytical, integral‐equation and spectral Lanczos decomposition solutions and demonstrate the accuracy of the scheme.

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