Functional approach to the search for quasi-optimal value of regularization parameter in downward continuation of potential field

Geophysics ◽  
2021 ◽  
pp. 1-34
Author(s):  
Roland Karcol ◽  
Roman Pašteka
Keyword(s):  
Regularization Parameter ◽  
Gravity Data ◽  
Synthetic Data ◽  
Downward Continuation ◽  
Magnetic Data ◽  
Problem Solution ◽  
Ordnance Survey ◽  
Boundary Estimation ◽  
Optimal Value ◽  
Regional Gravity

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.

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.

scholarly journals Improving the use of the randomized singular value decomposition for the inversion of gravity and magnetic data

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. G93-G107
Author(s):  
Saeed Vatankhah ◽  
Shuang Liu ◽  
Rosemary Anne Renaut ◽  
Xiangyun Hu ◽  
Jamaledin Baniamerian
Keyword(s):  
Singular Value Decomposition ◽  
Spectral Properties ◽  
Regularization Parameter ◽  
Gravity Data ◽  
Singular Value ◽  
Magnetic Data ◽  
Gravity And Magnetic ◽  
Magnetic Inversion ◽  
Model Matrix ◽  
Value Decomposition

The focusing inversion of gravity and magnetic potential-field data using the randomized singular value decomposition (RSVD) method is considered. This approach facilitates tackling the computational challenge that arises in the solution of the inversion problem that uses the standard and accurate approximation of the integral equation kernel. We have developed a comprehensive comparison of the developed methodology for the inversion of magnetic and gravity data. The results verify that there is an important difference between the application of the methodology for gravity and magnetic inversion problems. Specifically, RSVD is dependent on the generation of a rank [Formula: see text] approximation to the underlying model matrix, and the results demonstrate that [Formula: see text] needs to be larger, for equivalent problem sizes, for the magnetic problem compared to the gravity problem. Without a relatively large [Formula: see text], the dominant singular values of the magnetic model matrix are not well approximated. We determine that this is due to the spectral properties of the matrix. The comparison also shows us how the use of the power iteration embedded within the randomized algorithm improves the quality of the resulting dominant subspace approximation, especially in magnetic inversion, yielding acceptable approximations for smaller choices of [Formula: see text]. Further, we evaluate how the differences in spectral properties of the magnetic and gravity input matrices also affect the values that are automatically estimated for the regularization parameter. The algorithm is applied and verified for the inversion of magnetic data obtained over a portion of the Wuskwatim Lake region in Manitoba, Canada.

Depth estimation from downward continuation: An entropy-based approach to normalized full gradient

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. J33-J42
Author(s):  
Giovanni Florio ◽  
Maurizio Fedi
Keyword(s):  
Synthetic Data ◽  
Depth Estimation ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Depth Estimate ◽  
Ordnance Survey ◽  
Normalized Full Gradient ◽  
Gradient Based ◽  
Specific Source ◽  
Source Level

The normalized full gradient is based on the noticeable stability of the modulus of the analytic signal of downward potential fields. We have developed a new approach to the study of the normalized full gradient, based on assessing the entropy of the normalized modulus of the analytic signal at each level of continuation. The increased disorder of progressively downward continued fields implies an increase of the computed entropy. However, a local decrease of the entropy is expected at the source level, where the field gets singular, as entropy decreases when the information is concentrated. Thus, our method is based on a simple search for a minimum of the computed entropy versus depth curve, and the estimated depth will be that at which the minimum is attained. The method is sensitive to interference and other types of noise, and specific strategies to deal with these limitations are defined and tested on synthetic data. The depth estimate is obtained without the assumption of a specific source shape. The depth could correspond to the top or center in case of a simple, one-point source, or it may be related to an intermediate depth between the source top and its center in case of a finite, general source. We applied this method to real magnetic data from an unexploded ordnance survey, and it could verify a rather accurate depth-to-source estimate when compared with excavation results.

scholarly journals Penerapan Persamaan Trend Surface Analysis untuk Pemisahan Anomali Residual dan Regional pada Data Gayaberat

2021 ◽  
pp. 102-115
Author(s):  
Purwaditya Nugraha ◽  
Nono Agus Santoso
Keyword(s):  
Surface Analysis ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Anomalies ◽  
Analysis Method ◽  
Trend Surface Analysis ◽  
Microsoft Excel ◽  
Trend Surface ◽  
Surface Analysis Method ◽  
Regional Gravity

The separation of regional anomalies and residual anomalies in gravity data is an important part in interpreting gravity data. This process aims to obtain gravity anomalies that have been associated with exploration targets. The Trend Surface Analysis method is a mathematical approach to the earth field that can be used to separate maps into regional components and local components. The application of this method into gravity data can be used to separate regional anomalies and residual anomalies. The process of processing the trend surface analysis method can be done using Microsoft Excel. This method is tested first on synthetic gravity data, the purpose of this test is to determine the performance of the trend surface analysis method in performing anomaly separation. Based on the test results of the trend surface analysis method on synthetic gravity data, it was found that this method was quite good at separating regional anomalies and residual anomalies. This is evidenced by the anomalous pattern that is already the same between the regional gravity anomaly resulting from the separation of the anomaly using the trend surface analysis method and the regional anomaly resulting from synthetic data. The same anomaly pattern can also be seen in the residual anomaly resulting from the separation of the anomaly using the trend surface analysis method with the residual anomaly resulting from synthetic data. The application of the trend surface analysis method to field data has been carried out by producing regional anomalies and residual anomalies. This method is very good at separating regional anomalies and residual anomalies, especially in regional anomalies located at deep depths.Pemisahan anomali regional dan anomali residual pada data gayaberat merupakan bagian penting dalam melakukan interpretasi data gayaberat. Proses ini bertujuan untuk mendapatkan anomali gayaberat yang sudah berasosiasi dengan target eksplorasi. Metode Trend Surface Analysis merupakan teknik pendekatan matematika pada bidang kebumian yang dapat digunakan untuk memisahkan peta kedalam komponen regional dan komponen lokal. Penerapan metode ini ke dalam data gayaberat dapat digunakan untuk memisahkan anomali regional dan anomali residual. Proses pengolahan metode trend surface analysis dapat dilakukan dengan menggunakan microsoft excel. Metode ini diuji terlebih dahulu pada data gayaberat sintetis, tujuan pengujian ini adalah untuk mengetahui performa metode trend surface analysis dalam melakukan pemisahan anomali. Berdasarkan hasil pengujian metode trend surface analysis pada data gayaberat sintetis didapatkan bahwa metode ini cukup baik dalam memisahkan anomali regional dan anomali residual. Hal ini dibuktikan pada pola anomali yang sudah sama antara anomali gayaberat regional hasil pemisahan anomali metode trend surface analysis dengan anomali regional hasil data sintetis. Pola anomali yang sama juga dapat dilihat pada anomali residual hasil pemisahan anomali metode trend surface analysis dengan anomali residual hasil data sintetis. Penerapan metode trend surface analysis pada data lapangan telah dilakukan dengan menghasilkan anomali regional dan anomali residual. Metode ini sangat baik dalam memisahkan anomali regional dan anomali residual terutama pada anomali regional yang berada pada kedalaman dalam

Interpreting potential field anomaly of an isolated source of regular geometry revisited

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. IM41-IM48 ◽  
Author(s):  
Indrajit G. Roy
Keyword(s):  
Potential Field ◽  
Regularization Parameter ◽  
A Priori ◽  
Synthetic Data ◽  
Practical Method ◽  
Regularization Technique ◽  
First Order ◽  
Gravity And Magnetic ◽  
Optimal Value ◽  
Gravity And Magnetic Anomaly

I have developed an improved practical method for interpreting a symmetrical-shaped potential field anomaly due to an isolated source body of regular geometric configuration. The method uses the first-order horizontal derivative of the logarithmically transformed absolute value of the anomaly in estimating the source-body parameters, such as the location, depth of burial, and shape factor. To tackle noise in data, a regularization technique is designed, which ensures a robust estimate of the first-order derivative of logarithmically transformed data. The regularization technique uses an optimal value of regularization parameter that, although noise dependent, requires no a priori knowledge of the noise level in the data. A graphical method is designed to determine an optimal value of the regularization parameter from the position of the local minimum of a specially defined functional with respect to the regularization parameters. Numerical tests have been conducted on the noise-contaminated synthetic data to validate the proposed method. The successful application of the method on published field data for the gravity and magnetic anomaly suggests the applicability of the method.

Study on Elliptic Filters in Airborne Gravity Data Processing

2013 ◽  
Vol 341-342 ◽  
pp. 999-1004
Author(s):  
Wei Zhou ◽  
Ti Jing Cai
Keyword(s):  
Data Processing ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Optimal Parameters ◽  
Evaluation Indicator ◽  
Filter Order ◽  
Upper Limit ◽  
Optimal Value ◽  
Low Pass ◽  
Stopband Attenuation

For low-pass filtering of airborne gravity data processing, elliptic low-pass digital filters were designed and filtering influences of the elliptic filter order, upper limit passband frequency, maximal passband attenuation and minimal stopband attenuation were studied. The results show that the upper limit passband frequency has the greatest effect on filtering among four parameters; the filter order and the maximal passband attenuation have some influence, but instability will increase with larger order; the effect of the minimal stopband attenuation is not obvious when reaching a certain value, which requires a combination of evaluation indicator accuracy to determine the optimal value. The standard deviations of discrepancies between the elliptic filtered gravity anomaly with optimal parameters and the commercial software result are within 1mGal, and the internal accord accuracy along four survey lines after level adjusting is about 0.620mGal.

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.

scholarly journals A Subspace Preconditioned LSQR Gauss-Newton Method with a Constrained Line Search Path Applied to 3D Biomedical Microwave Imaging

2015 ◽  
Vol 2015 ◽  
pp. 1-21
Author(s):  
Jürgen De Zaeytijd ◽  
Ann Franchois
Keyword(s):  
Complex Permittivity ◽  
Line Search ◽  
Synthetic Data ◽  
Iterative Solution ◽  
Initial Guess ◽  
Microwave Imaging ◽  
Single Frequency ◽  
Problem Solution ◽  
Source Position ◽  
Search Path

Three contributions that can improve the performance of a Newton-type iterative quantitative microwave imaging algorithm in a biomedical context are proposed. (i) To speed up the iterative forward problem solution, we extrapolate the initial guess of the field from a few field solutions corresponding to previous source positions for the same complex permittivity (i.e., “marching on in source position”) as well as from a Born-type approximation that is computed from a field solution corresponding to one previous complex permittivity profile for the same source position. (ii) The regularized Gauss-Newton update system can be ill-conditioned; hence we propose to employ a two-level preconditioned iterative solution method. We apply the subspace preconditioned LSQR algorithm from Jacobsen et al. (2003) and we employ a 3D cosine basis. (iii) We propose a new constrained line search path in the Gauss-Newton optimization, which incorporates in a smooth manner lower and upper bounds on the object permittivity, such that these bounds never can be violated along the search path. Single-frequency reconstructions from bipolarized synthetic data are shown for various three-dimensional numerical biological phantoms, including a realistic breast phantom from the University of Wisconsin-Madison (UWCEM) online repository.

Application of gravity and magnetic methods to assess geological hazards and natural resource potential in the Mosida Hills, Utah County, Utah

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1514-1526 ◽  
Author(s):  
Alvin K. Benson ◽  
Andrew R. Floyd
Keyword(s):  
Gravity Data ◽  
Magnetic Data ◽  
Geological Hazards ◽  
Mafic Lava ◽  
Subsurface Geology ◽  
Gravity And Magnetic ◽  
Geophysical Surveys ◽  
Utah County ◽  
Gravity And Magnetic Data ◽  
Hills Area

Gravity and magnetic data were collected in the Mosida Hills, Utah County, Utah, at over 1100 stations covering an area of approximately 58 km2 (150 mi2) in order to help define the subsurface geology and assess potential geological hazards for urban planning in an area where the population is rapidly increasing. In addition, potential hydrocarbon traps and mineral ore bodies may be associated with some of the interpreted subsurface structures. Standard processing techniques were applied to the data to remove known variations unrelated to the geology of the area. The residual data were used to generate gravity and magnetic contour maps, isometric projections, profiles, and subsurface models. Ambiguities in the geological models were reduced by (1) incorporating data from previous geophysical surveys, surface mapping, and aeromagnetic data, (2) integrating the gravity and magnetic data from our survey, and (3) correlating the modeled cross sections. Gravity highs and coincident magnetic highs delineate mafic lava flows, gravity lows and magnetic highs reflect tuffs, and gravity highs and magnetic lows spatially correlate with carbonates. These correlations help identify the subsurface geology and lead to new insights about the formation of the associated valleys. At least eight new faults (or fault segments) were identified from the gravity data, whereas the magnetic data indicate the existence of at least three concealed and/or poorly exposed igneous bodies, as well as a large ash‐flow tuff. The presence of low‐angle faults suggests that folding or downwarping, in addition to faulting, played a role in the formation of the valleys in the Mosida Hills area. The interpreted location and nature of concealed faults and volcanic flows in the Mosida Hills area are being used by policy makers to help develop mitigation procedures to protect life and property.

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