Horizontal Electric Dipole Source Research Articles

Three-Dimensional Forward Modeling of Transient Electromagnetic Method Considering Induced Polarization Effect Based on Spectral Element Method

The transient electromagnetic method (TEM) is widely used in the exploration of mineral, petroleum, and geothermal resources due to its sensitivity to low-resistivity bodies, limited site constraints, and strong resistance to interference. In practical applications, the TEM often uses a long wire source instead of an idealized horizontal electric dipole (HED) source as the excitation source. This is due to the complex external conditions and the relatively large distance between the receiving zone and the transmitter source. Compared to the HED, the long wire source can provide a larger excitation current, generating stronger signals to meet the requirements of a higher signal-to-noise ratio or deeper exploration. It also produces longer-duration signals, thereby providing better resolution. Additionally, for the interpretation of TEM data, three-dimensional forward modeling plays a crucial role. However, the mature traditional TEM forward method is based on a simple, sometimes inappropriate model, as it is well established that the induced polarization (IP) effect is widely present in the deep earth, especially in oil and gas reservoirs. The presence of the IP effect results in negative responses in field data that do not conform to the traditional theoretical decay law of TEM, which can significantly impact data processing and inversion results. To address this issue, a TEM forward modeling method considering the IP effect based on the spectral element method (SEM) has been developed in this study. Firstly, starting from the Helmholtz equation satisfied by the time domain electric field, we introduce the Debye model with polarization information into the forward modeling by utilizing the differential form of Ohm’s law. As a result, we derive the boundary value problem for the time domain electric field that considers the induced polarization effect. Using Gauss–Lobatto–Legendre (GLL) polynomials as the basis functions, the SEM is employed to discretize the governing equations at each time step and obtain spectral element discretization equations. Then, temporal discretization equations are derived using the second-order backward Euler formula, and the linear system of equations is solved using the Pardiso direct solver. Finally, the electromagnetic responses at any time channel are obtained via SEM interpolation and numerical integration, thereby achieving three-dimensional TEM forward modeling considering the IP effect. The results indicate that this method can effectively reflect the spatial distribution of polarizable subsurface media. It provides valuable references for studying the polarization parameters of subsurface media and performing a three-dimensional inversion of TEM data considering the induced polarization effect.

3D controlled-source electromagnetic inversion in the radio-frequency band

The classical radio-magnetotelluric (RMT) method is nowadays routinely applied to various environmental, engineering, and exploration problems. The technique uses radio transmitters broadcasting in the frequency range of 10 kHz to 1 MHz, and the measurements are carried out in the far field. The well-known disadvantages of RMT are a lack of robust radio transmitters in remote areas; the absence of transmitters broadcasting below 10 kHz, which limits the penetration depth; and a possible low signal-to-noise ratio. To overcome these difficulties, controlled sources can be used (controlled-source RMT [CSRMT]). We extend the CSRMT method to perform measurements not only in the far field but also in the transition zone. In CSRMT practice, it often is challenging to maintain far-field conditions for logistical reasons. Therefore, part of the measured data contains signatures of the source field, which cannot be interpreted with magnetotelluric software. In addition, the source placed directly in the survey area allows us to increase the signal-to-noise ratio and resolution. Such CSRMT in the transition zone is, in fact, a controlled-source electromagnetic method but with full impedance tensor and tipper vector transfer functions. We develop new procedures for the 3D modeling and inversion of the tensor radio-frequency data measured in the transition zone of two perpendicular horizontal electric dipole sources. In this case, the geometry of the source must be considered in the forward modeling. The developed modeling and inversion software is tested on a synthetic 3D model. The 3D resistivity models derived from the real data confirm the geologic settings and are consistent with the available borehole information. Therefore, we conclude that the CSRMT approach extended to include the source field is feasible and that the developed procedures are reliable.

A Feasibility Study of CSEM in Geological Advance Forecast with Horizontal Casing Well

With the rapid exploitation of deep mines by digging new tunnels, the advance forecast of water inrush has become increasingly important. The land-based controlled source electromagnetic method (CSEM) is commonly used to detect water-bearing structures. To increase its sensitivity, we propose a new measuring configuration for CSEM by placing EM sensors in an underground steel-cased well. The numerical modeling is conducted by COMSOL to overcome the difficulties of investigating the feasibility of the measuring configuration. The current distribution and electromagnetic field along an in-seam horizontal casing are investigated based on a synthesis three-layered model. The results illustrate that the casing can be treated as antennas that enhance the electric fields at large depths. The water-bearing structures can be observed by a magnetic field (with a perpendicularly horizontal electric dipole (HED) source) rather than an electric field (with a parallelly HED source). Numerical simulations demonstrate that the proposed method is a feasible and effective technique for the detection of water-bearing structures during deep mineral exploration.

Three-dimensional Land FD-CSEM Regularized Inversion Based on Edge Finite-element Method

There is a desire to obtain rapid and stable inversion results and clearly reconstruct subsurface resistivity structure in frequency domain (FD) electromagnetics. Three-dimensional modeling of land FD controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic responses collected in increasingly complex geologic settings. Three-dimensional inversion of land FD-CSEM data is a mathematically non-unique problem with instability, due to the noise contained in the data and its inherent incompleteness. The main difference between our method and those from previous work is that the edge finite-element approach is applied to solve the three-dimensional FD-CSEM generated by a horizontal electric dipole source. Firstly, we formulate the edge finite-element equation through the Galerkin method, based on the Helmholtz equation of the electric fields. Secondly, in order to check the validity of the modeling code, we compare the numerical results with the analytical solutions for a homogeneous half-space model. For further tests, we calculate the electromagnetic responses for another two models with more practical structures. Finally, the three-dimensional inversion is carried out based on a regularization method with smoothness-constraints to obtain stable solutions.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys, based on a finite-element discretization of the Helmholtz equation for the electric fields, has been developed. The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source. Firstly, the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields. Secondly, in order to check the validity of the modeling code, the numerical results are compared with the analytical solutions for a homogeneous half-space model. Finally, other three models are simulated with three-dimensional electromagnetic responses. The results indicate that the method can be applied for solving three-dimensional electromagnetic responses. The algorithm has been demonstrated, which can be effective to modeling the complex geo-electrical structures. This efficient algorithm will help to study the distribution laws of 3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses

The inverse Laplace transform is one of the methods used to obtain time-domain electromagnetic (EM) responses in geophysics. The Gaver-Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver-Stehfest algorithm, even when using double-precision arithmetic, is relatively low at late times due to round-off errors. To overcome this issue, we have applied variable-precision arithmetic in the MATLAB computing environment to an implementation of the Gaver-Stehfest algorithm. This approach has proved to be effective in terms of improving accuracy, but it is computationally expensive. In addition, the Gaver-Stehfest algorithm is significantly problem dependent. Therefore, we have turned our attention to two other algorithms for computing inverse Laplace transforms, namely, the Euler and Talbot algorithms. Using as examples the responses for central-loop, fixed-loop, and horizontal electric dipole sources for homogeneous and layered mediums, these two algorithms, implemented using normal double-precision arithmetic, have been shown to provide more accurate results and to be less problem dependent than the standard Gaver-Stehfest algorithm. Furthermore, they have the capacity for yielding more accurate time-domain responses than the cosine and sine transforms for which the frequency-domain responses are obtained by interpolation between a limited number of explicitly computed frequency-domain responses. In addition, the Euler and Talbot algorithms have the potential of requiring fewer Laplace- or frequency-domain function evaluations than do the other transform methods commonly used to compute time-domain EM responses, and thus of providing a more efficient option.

Delineation of Hydrocarbon with Variation of Overburden Thickness for Sea Bed Logging Applications

There are various methods being used to model and study behavior of electromagnetic (EM) waves in controlled source electromagnetic (CSEM) environment. Sea Bed logging (SBL) is using CSEM technique in detecting and characterizing hydrocarbon bearing reservoirs in deep water areas. It uses a mobile horizontal electric dipole (HED) source called transmitter that transmits low frequency of 0.1Hz to 10Hz, 30m - 40m above sea bed and an array of seafloor electric field receivers. These signals depend on the resistivity structure beneath the sea bed as hydrocarbon is known to have high resistivity value of 30 500 Ωm in contrast to sea water layer of 0.5 2 Ωm and sediments of 1-2 Ωm. Array of seafloor receivers detect EM energy that propagates through the sea and subsurface. Data collected is used for processing and modeling purposes to predict depth of resistive bodies. In this paper, synthetics data generated from developed simulator that is able to replicate SBL environment is compared to synthetics data generated from Computer Simulation Software (CST) and COMSOL software with same parameter setting to study trends between them. Percentage differences between data with hydrocarbon and without hydrocarbon are calculated and comparisons are made. Overburden thickness is varied from 1000m to 3000m (incremented by 500m) at frequency of 0.125Hz. It was found that all the data generated either from simulator, CST software and COMSOL showing the same trends. From these findings it shall conclude that the simulator is a reliable tool to model any sea bed logging environment and predicting present of hydrocarbon reservoir in SBL environment.

Electromagnetic Response for Horizontal Electric Dipole Source Considering Conduct & Displacement Current

Electromagnetic (EM) field is often referred to diffusion (quasi-static assumption) that displacement currents are neglected during data processing in geophysical application, while the ratio of conduct currents to displacement currents is higher than 10, that is ,we think EM field is diffusion dominated and wave dominate for the ratio less than 0.1. Our simulating with Horizontal Electric Dipole Field indicated that frequency range of wave dominated is that the ratio is less than 0.007, the magnitude curves of EM component and impedance referring to diffusion and wave are different from those of diffusion. And in transform zone () the curves are different from those of wave and diffusion.

Transient marine electromagnetics in shallow water: A sensitivity and resolution study of the vertical electric field at short ranges

We analyzed the sensitivity of transient step-off responses of shallow-water marine controlled-source electromagnetic configurations, specifically, horizontal electric dipole sources and vertical electric dipole receivers in the near field of the time domain ([Formula: see text]). The capabilities of this configuration were compared with commonly used configurations, specifically, horizontal electric dipole sources and horizontal electric dipole receivers in the frequency domain ([Formula: see text]). By examining some simplified models of local hydrocarbon reservoirs representing separate resistive bodies of limited size buried at different depths in the conductive sediments, and an example of a complex 3D geologic structure, the applications of [Formula: see text] and [Formula: see text] configurations and their limitations in terms of depth, size, and transverse resistance were evaluated.

Three Dimensional Electromagnetic Inversion Based on Electric Dipole Source Multiple Locations Excitation

In this paper, we use integral equation and damped least-squares method to invert three dimensional abnormal body's electromagnetic field through horizontal electric dipole source multiple locations excitation. Multiple groups electromagnetic field data in different excitation and receiving points to be uniform consideration in once inversion, the Jacobian matrix is obtained and divided into linear terms and nonlinear terms. At last, we use the forward simulation data fit the measured data, and gradually modify geoelectricity model parameter values, ultimately achieve optimal fitting, gain three dimensional abnormal body's resistivity. Model test shows that the inversion algorithm has a fast convergence speed, less dependents on the initial value; the inversion result is accurate and reliable. It is an effective solution to the inversion failure caused by insufficient amount of data. DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.3985 Full Text: PDF

Efficient Closed‐Form Green's Functions for Layered Stripline Structures

ABSTRACTIn this article, simple and efficient closed‐form Green's function representations for various inhomogeneously‐filled (layered) stripline structures are derived in terms of cylindrical and spherical waves for a horizontal electric dipole source. The method is based on a two‐level approximation of the spectral‐domain Green's function. After using a fast pole‐location method to extract the surface‐wave modes that are guided by the dielectric slabs and the parallel‐plate modes that are trapped by the two ground planes, we first use a method that is similar to the first step in the traditional two‐level discrete complex image method (DCIM). This step provides a good approximation to the spectral‐domain Green's function for large values of the spectral variable , thus accounting for the fields at near and intermediate distances from the source. The remainder (smaller values of ) of the spectral‐domain Green's function is approximated using a few poles and residues by using the total least squares algorithm, which requires much less computational resources as compared to the vector fitting method or DCIM. This portion of the Green's function accounts well for the fields that are further away from the source. Our proposed method provides an efficient and accurate means for representing Green's functions in layered stripline structures both near and far from the source. The results are verified by comparing with those obtained using the traditional two‐level DCIM as well as direct numerical integration of the spectral‐domain Green's function. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2261–2265, 2013

Synthesis and Characterization of YBa2Cu3O7(Y123) via Sol–Gel Method for Development of Superconducting Quantum Interference Device Magnetometer

Electromagnetic (EM) waves transmitted by Horizontal Electric Dipole (HED) source to detect contrasts in subsurface resistivity termed Seabed Logging (SBL) is now an established method for hydrocarbon exploration. However, currently used EM wave detectors for SBL have several challenges including the sensitivity and its bulk size. This work exploits the benefit of superconductor technology in developing a magnetometer termed Superconducting Quantum Interference Device (SQUID) which can potentially be used for SBL. A SQUID magnetometer was fabricated using hexagon shape-niobium wire with YBa2Cu37O, (YBCO) as a barrier. The YBa2Cu37O, samples were synthesized by sol-gel method and were sintered using a furnace and conventional microwave oven. The YBCO gel was dried at 120 degrees C in air for 72 hours. It was then ground and divided into 12 parts. Four samples were sintered at 750 degrees C, 850 degrees C, 900 degrees C, and 950 degrees C for 12 hours in a furnace to find the optimum temperature. The other eight samples were sintered in a microwave with 1100 Watt (W) with a different sintering time, 5, 15, 45 minutes, 1 hour, 1 hour 15 minutes, 1 hour 30 minutes, 1 hour 45 minutes and 2 hours. A DEWAR container was designed and fabricated using fiberglass material. It was filled with liquid nitrogen (LN2) to ensure the superconducting state of the magnetometer. XRD results showed that the optimum sintering temperature for the formation of orthorhombic Y-123 phase was at 950 degrees C with the crystallite size of 67 nm. The morphology results from Field Emission Scanning Electron Microscopy (FESEM) showed that the grains had formed a rod shape with an average diameter of 60 nm. The fabricated SQUID magnetometer was able to show an increment of approximately 249% in the intensity of the EM waves when the source receiver offset was one meter apart.

Resolution of reservoir scale electrical anisotropy from marine CSEM data

A combination of 1D and 3D forward and inverse solutions is used to quantify the sensitivity and resolution of conventional controlled source electromagnetic (CSEM) data collected using a horizontal electric dipole source to transverse electric anisotropy located in a deep-water exploration reservoir target. Because strongly anisotropic shale layers have a vertical resistivity that can be comparable to many reservoirs, we examined how CSEM can discriminate confounding shale layers through their characteristically lower horizontal resistivity. Forward modeling indicated that the sensitivity to reservoir level anisotropy is very low compared with the sensitivity to isotropic reservoirs, especially when the reservoir is deeper than about 2 km below the seabed. However, for 1D models where the number of inversion parameters can be fixed to be only a few layers, both vertical and horizontal resistivity of the reservoir can be well resolved using a stochastic inversion. We found that the resolution of horizontal resistivity increases as the horizontal resistivity decreases. This effect is explained by the presence of strong horizontal current density in anisotropic layers with low horizontal resistivity. Conversely, when the reservoir has a vertical to horizontal resistivity ratio of about 10 or less, the current density is vertically polarized and hence has little sensitivity to the horizontal resistivity. Resistivity anisotropy estimates from 3D inversion for 3D targets suggest that resolution of reservoir level anisotropy for 3D targets will require good a priori knowledge of the background sediment conductivity and structural boundaries.

Near-source response of a resistive layer to a vertical or horizontal electric dipole excitation

Frequency and time-domain analytical expressions are derived for the electromagnetic field response of a resistive layer inserted in an otherwise homogeneous whole-space as observed in the vicinity of an electric dipole source. The analysis of closed-form solutions demonstrated that at near-source-receiver offsets, the spectral and spatial distribution of the fields is better described by a superposition of images, associated with the dipolar character of the charges distributed in the boundaries, rather than the guided mode behavior dominating the response in the far offset regime. Approximate solutions of the fields in the frequency domain were derived using the saddle point method of integration. The formulas describing the fields were in good agreement with semianalytical calculations. However, a lower frequency bound was found, below which the expressions are inaccurate, and thereby they cannot be used to obtain time-domain solutions. A kernel modulation scheme was used instead, which yields an infinite series representation for the fields. The expressions thus derived produce accurate fields to very low frequencies, and thereby they were also used to obtain time-domain formulas. The analysis indicated that for a vertical electric dipole (VED) excitation, the late time response of the image field associated with the charge density induced on the upper boundary appears to cancel the direct field, thus providing the response of the layer. For a horizontal electric dipole (HED) source, the superimposed contributions of the transverse electric (TE) and transverse magnetic (TM) modes appeared to oppose the image field, resulting in the direct field dominating over the response of the layer, and thereby masking any sensitivity to the properties of the layer in this configuration.

Sensitivity of controlled-source electromagnetic fields in planarly layered media

The study of electromagnetic (EM) field sensitivities is useful for assessing the feasibility of controlled-source electromagnetic (CSEM) surveys. Sensitivity calculations are also a principal building block of EM inversion schemes. Sensitivities are formally given by the derivatives of the EM field components with respect to conductivity. For horizontally layered media, these derivatives can be evaluated analytically, offering advantages in computational efficiency and accuracy over numerical evaluation. We present a complete set of explicit analytic expressions for the EM field sensitivities in 1-D VTI-anisotropic media for horizontal and vertical electric and magnetic dipole sources, and also for finite horizontal electric sources. Since our derivations are based on a formulation for EM fields that is quite general in allowing for sources and receivers at any depth, our sensitivity expressions exhibit the same generality. We verify our expressions by comparison to numerical solutions, and finally present application examples that demonstrate the utility and versatility of these expressions for CSEM feasibility studies.

Electric field responses of different gas hydrate models excited by a horizontal electric dipole source with changing arrangements

Abstract The exploration of marine controlled source electromagnetic survey for gas hydrate generally consists of a dynamic horizontal electric dipole source towed in the sea water and a static receiver array allocated on the seafloor. In this paper, two orthogonal horizontal components of electric field excited by a horizontal electric dipole source upon one-dimensional horizontal-layered seafloor are calculated to study the effect of different arrangements and gas hydrate models on the response of electric field. There are several dominant factors determining the variation of induced field, including transmitting frequency of the source, distance between the source and the seafloor, water depth, thickness of the overburden layer, as well as physical and chemical structure of the gas hydrate model. Modeling results suggest that the amplitude of received electric fields can reach up to 10-16–10-10 V /(A·m 2 ) by adjusting transmitting frequency; keeping the source being towed several tens of meters above the seafloor can improve the survey efficiency but not decrease the quality of collected data; deep water environment and shallow thin overburden layer are favorable for the survey because of their attribution to signal-to-noise ratio; the porosity and saturation of gas hydrate have significant influence on medium resistivity-the higher resistivity the medium has, the bigger the amplitude of electric field response will be. Forward modeling can provide valuable information for the development of instruments and the design of survey to detect gas hydrate.

Development of EM Simulator for Sea Bed Logging Applications using MATLAB

This paper presents a 1D modeling of electromagnetic waves for sea bed environment developed using MATLAB software. This paper focuses on two main areas; the first is on the simulator that is able to model plane layer modeling of the sea bed environment, by setting the deep of sea water, sediments and size and location of the hydrocarbon trap. This model shall be used as a forward modeling of sea bed environment. The second focus is on the effect of electromagnetic waves called direct waves, reflected waves and refracted waves on the sea bed environment where potential hydrocarbon is present. Our work is based on Sea Bed Logging (SBL) application that uses marine controlled source electromagnetic (CSEM) sounding technique to detect and characterize hydrocarbon bearing reservoirs in deep water areas. SBL uses a mobile horizontal electric dipole (HED) source called transmitter and an array of seafloor electric field receivers. The transmitter transmits a low frequency electromagnetic signal from 30m - 40m above the sea bed into water layer and to underneath the sea bed. The array of the receivers will receive the signal in the form of direct waves, air waves, reflected waves and refracted waves and is measured in the form of amplitude and phase. These signals depend on the resistivity structure beneath the sea bed. Hydrocarbon is known to have high resistivity value of 30 – 500 Ωm in contrast to sea water layer of 0.5 – 2 Ωm and sediments of 1-2 Ωm. These signals were plotted to show the Electric Field amplitude verses offset (AVO) and comparisons were made.

Asymptotic airwave modeling for marine controlled-source electromagnetic surveying

Marine controlled-source electromagnetic (CSEM) surveying, also called seabed logging, is a technique for finding resistive layers in the subsurface, which can be hydrocarbon-saturated reservoirs. The EM signal from the horizontal electric dipole source induces an airwave along the air/sea surface that interferes with the signal from the subsurface and dominates at larger offsets. The airwave commonly denotes the energy that propagates from the source via the atmosphere to the receiver on the seabed. The airwave component is especially problematic in shallow waters, where it is less attenuated during its up-and-down propagation in the water column than for deeper waters. An asymptotically derived space-domain equation that describes the airwavecomponent in a water half-space bounded by air is well known from the EM literature. We demonstrate that by taking into account the reflections and reverberations of the airwave component in the water column between the seabed and the sea surface at both the source side and the receiver side, this equation can be generalized to a water layer. The new model we present can serve as an integrity check for other modeling schemes. Our airwave model shows how the airwave component depends on water depth, source-receiver range, frequency, and seabed resistivity. The model is verified by extensive numerical testing. Finally, we show how the source-induced airwave may affect the marine CSEM recordings and how the airwave component in principle can be suppressed by a modeling-and-subtraction approach.

Dramatic Improvements in the Matrix Solution Time for Method of Moment Problems Involving Stripline Interconnects

Method of moments (MoM) reaction matrices are typically thought of as being full matrices in most applications. However, in this paper, we demonstrate for the first time that sparse reaction matrices are produced when modeling stripline interconnects provided that a parallel-plate Green's function is employed in the analysis. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect solver (UA-FWLIS) to model stripline interconnects. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed, and the cutoff mode behavior of these electric fields is studied. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cutoff criterion for the reaction element calculations. Once the reasons for the matrix sparsity have been explained, then we test various matrix solution algorithms in order to determine their efficiencies. We found that by applying sparse matrix storage techniques and a sparse matrix solver, it is possible to dramatically improve the matrix solution time when compared with a commercial MoM-based simulator.

2D marine controlled-source electromagnetic modeling: Part 1 — An adaptive finite-element algorithm

In Part 1 of this work, we develop an adaptive finite-element algorithm for forward modeling of the frequency-domain, marine controlled-source electromagnetic (CSEM) response of a 2D conductivity structure that is excited by a horizontal electric dipole source. After transforming the governing equations for the secondary electromagnetic fields into the wavenumber domain, the coupled system of two partial differential equations for the strike-parallel electric and magnetic fields is approximated using the finite-element method. The model domain is discretized using an unstructured triangular element grid that readily accommodates arbitrarily complex structures. A numerical solution of the system of linear equations is obtained using the quasi-minimal residual (QMR) method, which requiresmuch less storagethan full matrix inversion methods. We implement an automatedadaptive grid refinement algorithm in which the finite-element solution is computed iteratively on successively refined grids. Grid refinement is guided by an a posteriori error estimator based on a recently developed gradient recovery operator. The error estimator uses the solution to a dual problem in order to bias refinement toward elements that affect the solution at the electromagnetic (EM) receiver locations and enables the computation of asymptotically exact solutions to the 2.5D partial differential equations. We validate the finite element formulation against the canonical 1D reservoir model and study the performance of the adaptive refinement algorithm. An example model study of a complex offshore structure of interest for petroleum exploration illustrates the utility of the adaptive finite-element method for CSEM modeling.