Global nonlinear inversion of transient EM data from conducting surroundings using a free‐space plate model

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 783-790 ◽  
Author(s):  
Shashi P. Sharma ◽  
Pertti Kaikkonen
Keyword(s):  
Free Space ◽  
Synthetic Data ◽  
Electromagnetic Response ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Conductive Plate ◽  
Transient Electromagnetic ◽  
Conducting Body ◽  
Geological Conditions ◽  
Very Fast Simulated Annealing

A platelike conducting body in free space is used as a model to invert transient electromagnetic data using the very fast simulated annealing procedure as a global optimization tool. When the host rock conductivity is non‐zero, acceptable fits between the observed and computed responses are difficult to obtain. In general, the conducting body is assigned a lower conductance, larger dimensions (strike length and depth extent) and a smaller depth than the true values. We approximate the response of a conducting host to yield reliable estimates of model parameters as well as a good fit between the observed and computed responses. Our procedure is based on the assumption that the observed electromagnetic response is the sum of the response due to the conductive target and the response due to conducting surroundings (host and overburden). It is also assumed that the host response is laterally invariant, implying a layered earth and fixed source‐receiver geometry. The validity of the superposition assumption is tested against the full solution for a conductive plate in a finite conducting host. The efficacy of our approach is demonstrated using noise‐free and noisy synthetic data and two field examples measured in different geological conditions.

Resistivity-depth imaging of airborne transient electromagnetic method based on an artificial neural network

2020 ◽  
Author(s):  
Jifeng Zhang ◽  
Bing Feng ◽  
Dong Li
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Bp Neural Network ◽  
Apparent Resistivity ◽  
Electromagnetic Method ◽  
Electromagnetic Response ◽  
Model Parameters ◽  
Transient Electromagnetic Method ◽  
Transient Electromagnetic ◽  
Artificial Neural

<p>An artificial neural network, which is an important part of artificial intelligence, has been widely used to many fields such as information processing, automation and economy, and geophysical data processing as one of the efficient tools. However, the application in geophysical electromagnetic method is still relatively few. In this paper, BP neural network was combined with airborne transient electromagnetic method for imaging subsurface geological structures.</p><p>We developed an artificial neural network code to map the distribution of geologic conductivity in the subsurface for the airborne transient electromagnetic method. It avoids complex derivation of electromagnetic field formula and only requires input and transfer functions to obtain the quasi-resistivity image section. First, training sample set, which is airborne transient electromagnetic response of homogeneous half-space models with the different resistivity, is formed and network model parameters include the flight altitude and the time constant, which were taken as input variables of the network, and pseudo-resistivity are taken as output variables. Then, a double hidden layer BP neural network is established in accordance with the mapping relationship between quasi-resistivity and airborne transient electromagnetic response. By analyzing mean square error curve, the training termination criterion of BP neural network is presented. Next, the trained BP neural network is used to interpret the airborne transient electromagnetic responses of various typical layered geo-electric models, and it is compared with those of the all-time apparent resistivity algorithm. After a lot of tests, reasonable BP neural network parameters were selected, and the mapping from airborne TEM quasi-resistivity was realized. The results show that the resistivity imaging from BP neural network approach is much closer to the true resistivity of model, and the response to anomalous bodies is better than that of all-time apparent resistivity numerical method. Finally, this imaging technique was use to process the field data acquired by the airborne transient method from Huayangchuan area. Quasi-resistivity depth section calculated by BP neural network and all-time apparent resistivity is in good agreement with the actual geological situation, which further verifies the effectiveness and practicability of this algorithm.</p>

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.

Resistivity-depth Imaging with the Airborne Transient Electromagnetic Method Based on an Artificial Neural Network

2020 ◽  
Vol 25 (3) ◽  
pp. 355-368
Author(s):  
Bing Feng ◽  
Ji-feng Zhang ◽  
Dong Li ◽  
Yang Bai
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Bp Neural Network ◽  
Apparent Resistivity ◽  
Electromagnetic Method ◽  
Electromagnetic Response ◽  
Model Parameters ◽  
Transient Electromagnetic Method ◽  
Transient Electromagnetic ◽  
Artificial Neural

We developed an artificial neural network to map the distribution of geologic conductivity in the earth subsurface using the airborne transient electromagnetic method. The artificial neural network avoids the need for complex derivations of electromagnetic field formulas and requires only input and transfer functions to obtain a quasi-resistivity image. First, training sample set from the airborne transient electromagnetic response of homogeneous half-space models with different resistivities was formed, and network model parameters, including the flight altitude, time constant, and response amplitude, were determined. Then, a double-hidden-layer back-propagation (BP) neural network was established based on the mapping relationship between quasi-resistivity and airborne transient electromagnetic response. By analyzing the mean square error curve, the training termination criterion of the BP neural network was determined. Next, the trained BP neural network was used to interpret the airborne transient electromagnetic responses of various typical layered geo-electric models, and the results were compared with that from the all-time apparent resistivity algorithm. The comparison indicated that the resistivity imaging from the BP neural network approach was much closer to the true resistivity of the model, and the response to anomalous bodies was better than that from an all-time apparent resistivity. Finally, this imaging technique was used to process field data acquired by employing the airborne transient method from the HuaYin survey area. Quasi-resistivity depth sections calculated with the BP neural network and the actual geological situation were in good.

The transient electromagnetic response of a magnetic or superparamagnetic ground

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 854-860 ◽  
Author(s):  
T. Lee
Keyword(s):  
Transient Response ◽  
Direct Current ◽  
Free Space ◽  
Electromagnetic Response ◽  
Time Constants ◽  
True Value ◽  
Transient Electromagnetic ◽  
Current Value ◽  
The Wire ◽  
Weakly Magnetic

The effect of superparamagnetic minerals on the transient response of a uniform ground can be modeled by allowing the permeability of the ground μ to vary with frequency ω as [Formula: see text] Here [Formula: see text] and [Formula: see text] are the upper and lower time constants for the superparamagnetic minerals and [Formula: see text] is the direct current value of the susceptibility. For single‐loop data it is found that the voltage will decay as 1/t, provided that [Formula: see text] and [Formula: see text] Here, a is the radius of the wire loop and b is the radius of the wire, t represents time and [Formula: see text] is the permeability of free space. Even if a separate transmitter and receiver are used, the transient will still be anomalous. For this case the 1/t term in the equations is less important, and more prevalent now is the [Formula: see text] term. These results show that a uniform ground behaves in a similar way to a ground which only has a thin superparamagnetic layer. A difference is that whereas the amplitude of the 1/t term could be drastically reduced by using a separate receiver, this is not the case for a uniform ground. A magnetic ground for late times will decay as [Formula: see text]. However, if the conductivity of the ground is estimated from apparent conductivities it will be found that the value of the conductivity will be incorrect by a factor that is related to the susceptibility [Formula: see text] of the ground. For a weakly magnetic ground the estimated conductivity [Formula: see text] is related to the true value of the conductivity [Formula: see text].

The effect of a conductive half‐space on the transient electromagnetic response of a three‐dimensional body

Geophysics ◽  
1985 ◽  
Vol 50 (7) ◽  
pp. 1144-1162 ◽  
Author(s):  
William A. SanFilipo ◽  
Perry A. Eaton ◽  
Gerald W. Hohmann
Keyword(s):  
Half Space ◽  
Free Space ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Vertical Component ◽  
The Body ◽  
Electromagnetic Response ◽  
Loop Current ◽  
Transient Electromagnetic ◽  
Space Response

The transient electromagnetic (TEM) response of a three‐dimensional (3-D) prism in a conductive half‐space is not always approximated well by three‐dimensional free‐space or two‐dimensional (2-D) conductive host models. The 3-D conductive host model is characterized by a complex interaction between inductive and current channeling effects. We numerically computed 3-D TEM responses using a time‐domain integral‐equation solution. Models consist of a vertical or horizontal prismatic conductor in conductive half‐space, energized by a rapid linear turn‐off of current in a rectangular loop. Current channeling, characterized by currents that flow through the body, is produced by charges which accumulate on the surface of the 3-D body and results in response profiles that can be much different in amplitude and shape than the corresponding response for the same body in free space, even after subtracting the half‐space response. Responses characterized by inductive (vortex) currents circulating within the body are similar to the response of the body in free space after subtracting the half‐space contribution. The difference between responses dominated by either channeled or vortex currents is subtle for vertical bodies but dramatic for horizontal bodies. Changing the conductivity of the host effects the relative importance of current channeling, the velocity and rate of decay of the primary (half‐space) electric field, and the build‐up of eddy currents in the body. As host conductivity increases, current channeling enhances the amplitude of the response of a vertical body and broadens the anomaly along the profile. For a horizontal body the shape of the anomaly is distorted from the free‐space anomaly by current channeling and is highly sensitive to the resistivity of the host. In the latter case, a 2-D response is similar to the 3-D response only if current channeling effects dominate over inductive effects. For models that are not greatly elongated, TEM responses are more sensitive to the conductivity of the body than galvanic (dc) responses, which saturate at a moderate resistivity contrast. Multicomponent data are preferable to vertical component data because in some cases the presence and location of the target are more easily resolved in the horizontal response and because the horizontal half‐space response decays more quickly than does the corresponding vertical response.

A comparison of performances of linearized and global nonlinear 2-D inversions of VLF and VLF-R electromagnetic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 462-475 ◽  
Author(s):  
P. Kaikkonen ◽  
S. P. Sharma
Keyword(s):  
A Priori ◽  
Low Frequency ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Stable Model ◽  
Very Fast Simulated Annealing ◽  
Iterative Inversion ◽  
Priori Information ◽  
The One ◽  
Nonlinear Joint

The performances of linearized (local) and global nonlinear joint 2-D inversions of very low frequency (VLF) and VLF resistivity electromagnetic measurements are analyzed. A stable iterative inversion scheme is used in linearized inversion while the very fast simulated annealing approach is used in global nonlinear inversion. Synthetic noise‐free and noisy data due to three different models in complexity and two field examples are considered. Synthetic examples show that linearized inversion reveals the subsurface structure better than global nonlinear inversion provided the model has only a few parameters under inversion. Both linearized and global nonlinear inversions must be performed combining all available data in order to obtain the most reliable estimates of the subsurface parameters. Complex models with a large number of parameters are better to invert using global nonlinear inversion although the CPU time needed is always much longer than the one used in linearized inversion. Contrary to global nonlinear inversion, success in linearized inversion requires the good a priori information of all the model parameters under inversion. Noise in data influences the linearized inversion results more than those provided by global inversion. Linearized inversion using as an initial model the mean model due to a few global inversion runs is also a good approach. Even in this case, if there are a large number of model parameters in inversion, linearized inversion can lead to an unstable solution. To overcome such a problem, one can fix the important and stable model parameters from the first step of linearized inversion and then vary and stabilize unstable parameters in the second step.

The Transient Electromagnetic Response Characteristics of Unfavorable Geological Bodies in Tunnels

2011 ◽  
Vol 261-263 ◽  
pp. 1494-1498
Author(s):  
Lu Bo Meng ◽  
Tian Bin Li ◽  
Zheng Duan
Keyword(s):  
Apparent Resistivity ◽  
Electromagnetic Response ◽  
High Resistivity ◽  
Karst Cave ◽  
Geological Body ◽  
Response Characteristics ◽  
Finite Element Software ◽  
Transient Electromagnetic ◽  
Electromagnetic Methods ◽  
Geological Conditions

A numerical model of Transient Electromagnetic Methods, which used to detect geological conditions in tunnels, was created by ANSYS finite element software, and the transient electromagnetic response characteristics of typical unfavorable geological bodies were discussed. The results indicate that the apparent resistivity isoline almost outputs in straight structure, and augments equably with the depth increasing when no unfavorable geological body is in front of the tunnel workface. The apparent resistivity isoline obviously reduces when water-rich karst cave, fault, or fracture exist in the front of the tunnel workface, where water-rich karst cave exists, the apparent resistivity isoline becomes close together, and there is to be an ordered pyramid resistivity-reduced area which can be an evidence of rich water fault. However, it will increase when dry fault or karst cave exist, and the high resistivity area corresponding to dry cave shows some triangles, but this phenomena is hard identified, which need detail analyses according to hydrogeologic data.

Approximate calculations of the transient electromagnetic response from buried conductors in a conductive half‐space

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 918-924 ◽  
Author(s):  
J. D. McNeill ◽  
R. N. Edwards ◽  
G. M. Levy
Keyword(s):  
Half Space ◽  
Free Space ◽  
Target Location ◽  
Electromagnetic Coupling ◽  
Practical Interest ◽  
Electromagnetic Response ◽  
Galvanic Current ◽  
Transient Electromagnetic ◽  
Space Modeling ◽  
Space Response

The transient electromagnetic (TEM) response from a conductive plate buried in a conductive half‐space and energized by a large‐loop transmitter is investigated in a heuristic manner. The vortex and galvanic components are each calculated directly in the time domain using an approximate procedure which ignores the electromagnetic coupling present in the complete solution. In modeling the vortex and galvanic current flows, the plate is replaced with a single‐turn wire loop of appropriate parameters and a distribution of current dipoles, respectively. The results of calculations of the transient magnetic field at the surface of the earth are presented for a few selected cases of practical interest. The relative importance of the vortex and galvanic components varies with the half‐space resistivity. The vortex component dominates if the half‐space is resistive, in which case free‐space algorithms suffice for numerical modeling. Furthermore the measured responses give much useful information about the target, and large depths of exploration should be achieved. As the half‐space resistivity decreases, a significant half‐space response is observed, caused by currents induced in the half‐space itself. This response can be very large. Spatial variations in it caused by relatively small changes in resistivity, i.e., geologic noise, obscure the response from deep targets making them difficult to detect. The effect of the half‐space is also to delay, distort, and reduce the vortex component in comparison with the free‐space response. The behavior of the galvanic component is determined by the haft‐space current flow. The presence of this component explains the large enhancement of overall target response seen at early times over relatively resistive ground and the departure from an exponential decay seen over more conductive ground, again with respect to responses predicted by free‐space modeling. In more conductive ground the galvanic component completely dominates the vortex component, resulting in the loss of useful diagnostic information. Although target location and depth can still be determined, target shape and orientation are poorly defined. Because of galvanic current saturation good conductors are difficult to distinguish from poor ones.

Improvement in MRS parameter estimation by joint and laterally constrained inversion of MRS and TEM data

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB191-WB200 ◽  
Author(s):  
Ahmad A. Behroozmand ◽  
Esben Auken ◽  
Gianluca Fiandaca ◽  
Anders Vest Christiansen
Keyword(s):  
Water Content ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Clear Correlation ◽  
Model Parameters ◽  
Dc Resistivity ◽  
Borehole Data ◽  
Simultaneous Inversion ◽  
Transient Electromagnetic ◽  
Magnetic Resonance Sounding

We developed a new scheme for joint and laterally constrained inversion (LCI) of magnetic resonance sounding (MRS) data and transient electromagnetic (TEM) data, which greatly improves the estimation of the MRS model parameters. During the last few decades, electrical and electromagnetic methods have been widely used for groundwater investigation, but they suffer from some inherent limitations; for example, equivalent layer sequences. Furthermore, the water content information is only empirically correlated to resistivity of the formation. MRS is a noninvasive geophysical technique that directly quantifies the water content distribution from surface measurements. The resistivity information of the subsurface is obtained from a complementary geophysical method such as TEM or DC resistivity methods. The conventional inversion of MRS data assumes the resulting resistivity structure to be correct and considers a constant MRS kernel through the inversion. We found that this assumption may introduce an error to the forward modeling and consequently could result in erroneous parameter estimations in the inversion process. We investigated the advantage of TEM for the joint inversion compared to DC resistivity. A fast and numerically efficient MRS forward routine made it possible to invert the MRS and TEM data sets simultaneously along profiles. Furthermore, by application of lateral constraints on the model parameters, lateral smooth 2D model sections could be be obtained. The simultaneous inversion for resistivity and MRS parameters led to a more reliable and robust estimation of all parameters, and the MRS data diminished the range of equivalent resistivity models. We examined the approach through synthetic data and a field example in Denmark where good agreement with borehole data was demonstrated with clear correlation between the relaxation time [Formula: see text] and the grain size distribution of a sandy aquifer.

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