scholarly journals Reframing the magnetotelluric phase tensor for monitoring applications: improved accuracy and precision in strike determinations

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Ana G. Bravo-Osuna ◽  
Enrique Gómez-Treviño ◽  
Olaf J. Cortés-Arroyo ◽  
Nestor F. Delgadillo-Jauregui ◽  
Rocío F. Arellano-Castro
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Electrical Current ◽  
Numerical Approach ◽  
Geothermal Field ◽  
Analytic Formula ◽  
Phase Tensor ◽  
The Matrix ◽  
Electrical Current Flow ◽  
Cerro Prieto

AbstractThe magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar datasets. One of the issues is that the noise complicates the distribution of estimates between the four quadrants. This can be handled by sending all values to the same quadrant by adding or subtracting the appropriate amount. This is justified by showing that the analytic formula is also a least squares solution. This is equivalent to define penalty functions for the matrix of eigenvalues and then select the minima numerically. Contrary to the analytic formula, this numerical approach can be generalized to compute strikes using windows of any number of periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.

scholarly journals Reframing the magnetotelluric phase tensor for monitoring applications: improved accuracy and precision in strike determinations

2020 ◽  
Author(s):  
Ana Gabriela Bravo-Osuna ◽  
Enrique Gómez-Treviño ◽  
Olaf Josafat Cortés-Arroyo ◽  
Néstor Fernando Delgadillo-Jáuregui ◽  
Rocío Fabiola Arellano-Castro
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Electrical Current ◽  
Numerical Approach ◽  
Geothermal Field ◽  
Analytic Formula ◽  
Similar Data ◽  
Phase Tensor ◽  
Electrical Current Flow ◽  
Cerro Prieto

Abstract The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. One of the issues is that the noise complicates the distribution of estimates between the four quadrants. This can be handled by sending all values to the same quadrant by adding or subtracting the appropriate amount. This is justified by showing that the analytic formula is also a least squares solution. This is equivalent to define penalty functions for the matrix of eigenvalues and then select the minima numerically. Contrary to the analytic formula this numerical approach can be generalized to compute strikes using windows of any number of periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.

scholarly journals Reframing the magnetotelluric phase tensor for monitoring applications: improved accuracy and precision in strike determinations.

2021 ◽  
Author(s):  
Ana Gabriela Bravo-Osuna ◽  
Enrique Gómez-Treviño ◽  
Olaf Josafat Cortés-Arroyo ◽  
Néstor Fernando Delgadillo-Jáuregui ◽  
Rocío Fabiola Arellano-Castro
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Electrical Current ◽  
Numerical Approach ◽  
Geothermal Field ◽  
Analytic Formula ◽  
Similar Data ◽  
Phase Tensor ◽  
Electrical Current Flow ◽  
Cerro Prieto

Abstract The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. One of the issues is that the noise complicates the distribution of estimates between the four quadrants. This can be handled by sending all values to the same quadrant by adding or subtracting the appropriate amount. This is justified by showing that the analytic formula is also a least squares solution. This is equivalent to define penalty functions for the matrix of eigenvalues and then select the minima numerically. Contrary to the analytic formula this numerical approach can be generalized to compute strikes using windows of any number of periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.

scholarly journals Reframing the magnetotelluric phase tensor for monitoring applications: improved accuracy and precision in strike determinations

2020 ◽  
Author(s):  
Ana Gabriela Bravo-Osuna ◽  
Enrique Gómez-Treviño ◽  
Olaf Josafat Cortés-Arroyo ◽  
Néstor Fernando Delgadillo-Jáuregui ◽  
Rocío Fabiola Arellano-Castro
Keyword(s):  
Analytical Formula ◽  
Synthetic Data ◽  
Noisy Data ◽  
Real Data ◽  
Electrical Current ◽  
Geothermal Field ◽  
Similar Data ◽  
Phase Tensor ◽  
Electrical Current Flow ◽  
Cerro Prieto

Abstract The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. On the other hand, the classical Swift’s approach for strike is very stable for noisy data but it is severely affected by galvanic distortions. In this paper we impose the criterion of Swift’s approach to the phase tensor. Rather than developing an analytical formula we optimize numerically the same criterion. This stabilizes the estimation of strike by relaxing an exact condition to an optimal condition in the presence of noise. This has the added benefit that it can be applied to windows of several periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.

scholarly journals Reframing the magnetotelluric phase tensor for monitoring applications: improved accuracy and precision in strike determinations

2020 ◽  
Author(s):  
Ana Gabriela Bravo-Osuna ◽  
Enrique Gómez-Treviño ◽  
Olaf Josafat Cortés-Arroyo ◽  
Néstor Fernando Delgadillo-Jáuregui ◽  
Rocío Fabiola Arellano-Castro
Keyword(s):  
Analytical Formula ◽  
Synthetic Data ◽  
Noisy Data ◽  
Real Data ◽  
Electrical Current ◽  
Geothermal Field ◽  
Similar Data ◽  
Phase Tensor ◽  
Electrical Current Flow ◽  
Cerro Prieto

Abstract The magnetotelluric method is increasingly being used to monitor electrical resistivity changes in the subsurface. One of the preferred parameters derived from the surface impedance is the strike direction, which is very sensitive to changes in the direction of the subsurface electrical current flow. The preferred method for estimating the strike changes is that provided by the phase tensor because it is immune to galvanic distortions. However, it is also a fact that the associated analytic formula is unstable for noisy data, something that limits its applicability for monitoring purposes, because in general this involves comparison of two or more very similar data sets. On the other hand, the classical Swift’s approach for strike is very stable for noisy data but it is severely affected by galvanic distortions. In this paper we impose the criterion of Swift’s approach to the phase tensor. Rather than developing an analytical formula we optimize numerically the same criterion. This stabilizes the estimation of strike by relaxing an exact condition to an optimal condition in the presence of noise. This has the added benefit that it can be applied to windows of several periods, thus providing tradeoffs between variance and resolution. The performance of the proposed approach is illustrated by its application to synthetic data and to real data from a monitoring array in the Cerro Prieto geothermal field, México.

scholarly journals Bayesian inversion of magnetotelluric data considering dimensionality discrepancies

2020 ◽  
Vol 223 (3) ◽  
pp. 1565-1583
Author(s):  
Hoël Seillé ◽  
Gerhard Visser
Keyword(s):  
Learning Algorithm ◽  
Synthetic Data ◽  
Real Data ◽  
Error Model ◽  
Bayesian Inversion ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Likelihood Functions ◽  
Training Images ◽  
Phase Tensor

SUMMARY Bayesian inversion of magnetotelluric (MT) data is a powerful but computationally expensive approach to estimate the subsurface electrical conductivity distribution and associated uncertainty. Approximating the Earth subsurface with 1-D physics considerably speeds-up calculation of the forward problem, making the Bayesian approach tractable, but can lead to biased results when the assumption is violated. We propose a methodology to quantitatively compensate for the bias caused by the 1-D Earth assumption within a 1-D trans-dimensional Markov chain Monte Carlo sampler. Our approach determines site-specific likelihood functions which are calculated using a dimensionality discrepancy error model derived by a machine learning algorithm trained on a set of synthetic 3-D conductivity training images. This is achieved by exploiting known geometrical dimensional properties of the MT phase tensor. A complex synthetic model which mimics a sedimentary basin environment is used to illustrate the ability of our workflow to reliably estimate uncertainty in the inversion results, even in presence of strong 2-D and 3-D effects. Using this dimensionality discrepancy error model we demonstrate that on this synthetic data set the use of our workflow performs better in 80 per cent of the cases compared to the existing practice of using constant errors. Finally, our workflow is benchmarked against real data acquired in Queensland, Australia, and shows its ability to detect the depth to basement accurately.

scholarly journals High-Resolution Seismic Data Deconvolution by A0 Algorithm

Geosciences ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 497
Author(s):  
Fedor Krasnov ◽  
Alexander Butorin
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Resolving Power ◽  
New Information ◽  
Geological Information ◽  
The Matrix ◽  
Complex Models ◽  
Practical Development

Sparse spikes deconvolution is one of the oldest inverse problems, which is a stylized version of recovery in seismic imaging. The goal of sparse spike deconvolution is to recover an approximation of a given noisy measurement T = W ∗ r + W 0 . Since the convolution destroys many low and high frequencies, this requires some prior information to regularize the inverse problem. In this paper, the authors continue to study the problem of searching for positions and amplitudes of the reflection coefficients of the medium (SP&ARCM). In previous research, the authors proposed a practical algorithm for solving the inverse problem of obtaining geological information from the seismic trace, which was named A 0 . In the current paper, the authors improved the method of the A 0 algorithm and applied it to the real (non-synthetic) data. Firstly, the authors considered the matrix approach and Differential Evolution approach to the SP&ARCM problem and showed that their efficiency is limited in the case. Secondly, the authors showed that the course to improve the A 0 lays in the direction of optimization with sequential regularization. The authors presented calculations for the accuracy of the A 0 for that case and experimental results of the convergence. The authors also considered different initialization parameters of the optimization process from the point of the acceleration of the convergence. Finally, the authors carried out successful approbation of the algorithm A 0 on synthetic and real data. Further practical development of the algorithm A 0 will be aimed at increasing the robustness of its operation, as well as in application in more complex models of real seismic data. The practical value of the research is to increase the resolving power of the wave field by reducing the contribution of interference, which gives new information for seismic-geological modeling.

scholarly journals Focal mechanism of seismic events with a dipolar component

1995 ◽  
Vol 38 (3-4) ◽  
Author(s):  
F. Batini ◽  
M. Caputo ◽  
R. Console
Keyword(s):  
Synthetic Data ◽  
High Standard ◽  
Seismic Source ◽  
Real Data ◽  
Computer Code ◽  
Geothermal Field ◽  
Observation Data ◽  
Amplitude Data ◽  
Double Couple ◽  
Fault Mechanism

In this paper we model the geometry of a seismic source as a dislocation occurring on an elemental flat fault in an arbitrary direction with respect to the fault plane. This implies the use of a fourth parameter in addition to the three usual ones describing a simple double couple mechanism. We applied the radiation pattern obtained from the theory to a computer code written for the inversion of the observation data (amplitudes and polarities of the first onsets recorded by a network of stations). It allows the determination of the fault mechanism gener- alized in the above mentioned way. The computer code was verified on synthetic data and then applied to real data recorded by the seismic network operated by the Ente Nazionale per l'Energia Elettrica (ENEL), monitoring the geothermal field of Larderello. The experimental data show that for some events the source mechanism exhibits a significant dipolar component. However, due to the high standard deviation of the amplitude data, F-test applied to the results of the analysis shows that only for two events the confidence level for the general- ized model exceeds 90%.

Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. W15-W30 ◽  
Author(s):  
Gary F. Margrave ◽  
Michael P. Lamoureux ◽  
David C. Henley
Keyword(s):  
Fourier Transform ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Numerical Approach ◽  
Gabor Transform ◽  
Minimum Phase ◽  
Approximate Factorization ◽  
Time Frequency ◽  
Complex Valued

We have extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes. As in the stationary case, we have assumed a statistically white reflectivity and a minimum-phase source and attenuation process. This extension is based on a nonstationary convolutional model, which we have developed and related to the stationary convolutional model. To facilitate our method, we have devised a simple numerical approach to calculate the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary convolutional model. This factorization serves as a guide to develop a smoothing process that, when applied to the Gabor transform of the nonstationary seismic trace, estimates the magnitude of the time-frequency attenuation function and the source wavelet. By assuming that both are minimum-phase processes, their phases can be determined. Gabor deconvolution is accomplished by spectral division in the time-frequency domain. The complex-valued Gabor transform of the seismic trace is divided by the complex-valued estimates of attenuation and source wavelet to estimate the Gabor transform of the reflectivity. An inverse Gabor transform recovers the time-domain reflectivity. The technique has applications to synthetic data and real data.

Detection and measure of the shear‐wave birefringence from vertical seismic data: Theory and applications

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1463-1481 ◽  
Author(s):  
Frédéric Lefeuvre ◽  
Laurence Nicoletis ◽  
Valérie Ansel ◽  
Christian Cliet
Keyword(s):  
Shear Wave ◽  
Least Squares Method ◽  
Synthetic Data ◽  
Real Data ◽  
Original Method ◽  
Depth Interval ◽  
Seismic Profiles ◽  
Data Set ◽  
Vertical Seismic Profiles ◽  
The Matrix

An original method is presented that allows us to measure the local shear‐wave birefringence properties over any depth interval. It requires the acquisition of two shear‐wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths [Formula: see text] and [Formula: see text], the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least‐squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polarizations at a depth [Formula: see text] for two linear and mutually perpendicular polarizations at depth [Formula: see text]. This allows for the measurement of the birefringence properties in all azimuthal directions to determine the directions for which a linearly polarized shear‐wave propagates. In addition, the method can be applied to perform the deconvolution of the upgoing wavefield by the downgoing wavefield to obtain a reflection matrix. Then the matrix can be interpreted in terms of anisotropy below the receiver depths (particularly below the well bottom) and in terms of anisotropy of the reflector itself. The proposed method is validated on synthetic data and is applied to real data from the Paris basin. For this particular data set, the birefringence is located in two layers; the first layer consists of unproductive sands and clays while the second one corresponds to a carbonate oil reservoir from the Dogger formation. The natural directions in both layers are very close to the main directions known for the regional stress field. The presence of fractures in the reservoir layer can explain the strong birefringence ratio (>6 percent).

Method of determination of the text direction on the image with the use of convolutional neural network

2020 ◽  
pp. 96-99
Author(s):  
P.L. Nikolaev
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Deep Neural Network ◽  
Binary Classification ◽  
Synthetic Data ◽  
Real Data ◽  
Method Of Determination ◽  
Classification Of Images

This article deals with method of binary classification of images with small text on them Classification is based on the fact that the text can have 2 directions – it can be positioned horizontally and read from left to right or it can be turned 180 degrees so the image must be rotated to read the sign. This type of text can be found on the covers of a variety of books, so in case of recognizing the covers, it is necessary first to determine the direction of the text before we will directly recognize it. The article suggests the development of a deep neural network for determination of the text position in the context of book covers recognizing. The results of training and testing of a convolutional neural network on synthetic data as well as the examples of the network functioning on the real data are presented.

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