Relationship of the self‐potential Green’s function to solutions of controlled source direct‐current potential problems

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1879-1881 ◽  
Author(s):  
David V. Fitterman
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Direct Current ◽  
Streaming Potential ◽  
The Self ◽  
Simple Relationship ◽  
Controlled Source ◽  
Source Mechanisms ◽  
Vertical Contact ◽  
Self Potential

This note presents a simple relationship between the self‐potential (SP) Green’s function and the solution of the controlled‐source direct‐current (dc) potential problem which allows a simplified means of determining the SP Green’s function. An example of its application to the vertical contact problem will be presented. The case of a streaming potential source mechanism will be considered, although any of the SP source mechanisms described by Nourbehecht (1963) could be substituted.

scholarly journals Parallel Simulation of Audio- and Radio-Magnetotelluric Data

Minerals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 42 ◽  
Author(s):  
Nikolay Yavich ◽  
Mikhail Malovichko ◽  
Arseny Shlykov
Keyword(s):  
Numerical Modeling ◽  
Green’S Function ◽  
Green's Function ◽  
Mineral Exploration ◽  
Iterative Solvers ◽  
Contraction Operator ◽  
Magnetotelluric Data ◽  
Controlled Source ◽  
Em Simulation ◽  
Preconditioned Iterative

This paper presents a novel numerical method for simulation controlled-source audio-magnetotellurics (CSAMT) and radio-magnetotellurics (CSRMT) data. These methods are widely used in mineral exploration. Interpretation of the CSAMT and CSRMT data collected over an area with the complex geology requires application of effective methods of numerical modeling capable to represent the geoelectrical model of a deposit well. In this paper, we considered an approach to 3D electromagnetic (EM) modeling based on new types of preconditioned iterative solvers for finite-difference (FD) EM simulation. The first preconditioner used fast direct inversion of the layered Earth FD matrix (Green’s function preconditioner). The other combined the first with a contraction operator transformation. To illustrate the effectiveness of the developed numerical modeling methods, a 3D resistivity model of Aleksandrovka study area in Kaluga Region, Russia, was prepared based on drilling data, AMT, and a detailed CSRMT survey. We conducted parallel EM simulation of the full CSRMT survey. Our results indicated that the developed methods can be effectively used for modeling EM responses over a realistic complex geoelectrical model for a controlled source EM survey with hundreds of receiver stations. The contraction-operator preconditioner outperformed the Green’s function preconditioner by factor of 7–10, both with respect to run-time and iteration count, and even more at higher frequencies.

scholarly journals Monitoring of induced distributed double-couple sources using Marchenko-based virtual receivers

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1301-1319 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, for which the full wave field without artifacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality to the monopole responses. If the source signal is not symmetric in time, our technique based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artifacts. The duration of these artifacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as is the source location of the signal. These artifacts do not occur in another method that creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, and similar results to the ones on synthetic data are achieved, which shows the potential for application on real data signals.

Calculations of self‐potential anomalies near vertical contacts

Geophysics ◽  
1979 ◽  
Vol 44 (2) ◽  
pp. 195-205 ◽  
Author(s):  
David V. Fitterman
Keyword(s):  
Physical Mechanism ◽  
Chemical Potential ◽  
Source Region ◽  
Streaming Potential ◽  
Source Mechanism ◽  
Constant Intensity ◽  
Potential Gradients ◽  
Vertical Contact ◽  
Chemical Potential Gradients ◽  
Self Potential

The self‐potential anomalies due to streaming potential effects in the vicinity of a vertical contact are analyzed. This approach is different from most previous studies in that the source is tied to a specific physical mechanism instead of arbitrarily selected charge distributions or current sources. The analysis is valid for any source mechanism that can be thought of in terms of crosscoupled flows, e.g., the thermoelectric effect or chemical potential gradients. The anomalies tend to be antisymmetric across the contact with the magnitude of the anomaly being larger on the more resistive side of the contact. An analytic expression for the case of a constant intensity, rectangular source is derived from the general solution. The anomalies for this simple case are computable with a handheld calculator and can be used to estimate the location, extent, and magnitude of the anomaly source region. With this information it is possible to determine the most probable crosscoupling source mechanism.

scholarly journals Monitoring induced distributed double-couple sources using Marchenko-based virtual receivers

2019 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, where the full wavefield without artefacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality as the monopole responses. If the source signal is not symmetric in time, our technique that is based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artefacts. The duration of these artefacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as well as the source location of the signal. These aretefacts do not occur in another method which creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, where similar results to synthetic data are achieved, which shows the potential for the application on real data signals.

3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

2020 ◽  
Vol 25 (3) ◽  
pp. 381-390
Author(s):  
Jing Xie ◽  
Yi-an Cui ◽  
Lijuan Zhang ◽  
Changying Ma ◽  
Bing Yang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Streaming Potential ◽  
Forward Modeling ◽  
The Self ◽  
Coupling Method ◽  
Infinite Element ◽  
Coupled Method ◽  
Complex Models ◽  
Self Potential

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.

Modeling of self‐potential anomalies near vertical dikes

Geophysics ◽  
1983 ◽  
Vol 48 (2) ◽  
pp. 171-180 ◽  
Author(s):  
David V. Fitterman
Keyword(s):  
Field Data ◽  
Source Region ◽  
The Self ◽  
Model Parameters ◽  
Dc Resistivity ◽  
Constant Intensity ◽  
Source Regions ◽  
Source Mechanisms ◽  
Self Potential ◽  
Sp Anomaly

The self‐potential (SP) Green’s function for an outcropping vertical dike is derived from solutions for the dc resistivity problem for the same geometry. The Green’s functions are numerically integrated over rectangular source regions on the contacts between the dike and the surrounding material to obtain the SP anomaly. The analysis is valid for thermoelectrical source mechanisms. Two types of anomalies can be produced by this geometry. When the two source planes are polarized in opposite directions, a monopolar anomaly is produced. This corresponds to the thermoelectrical properties of the dike being in contrast with the surrounding material. When the thermoelectric coefficients change monotonically across the dike, a dipolar anomaly is produced. In either case positive and negative anomalies are possible, and the greatest variation in potential will occur in the most resistive regions. Examples of the effect of changing different model parameters are given for sources that have constant intensity throughout the rectangular source regions. For these patch models the depth to the top of the source region is approximately equal to the distance between the minimum (or maximum) of the anomaly outside of the dike and the edge of the dike. Field data collected over a hot intrusive fissure are presented which have been modeled by the technique described.

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