scholarly journals 3D Convolution Conjugate Gradient Inversion of Potential Fields in Acoculco Geothermal Prospect, Mexico

2022 ◽  
Vol 9 ◽  
Author(s):  
José P. Calderón ◽  
Luis A. Gallardo
Keyword(s):  
Conjugate Gradient ◽  
Potential Field ◽  
Field Data ◽  
Large Scale ◽  
Three Dimensional ◽  
Potential Fields ◽  
Magnetic Data ◽  
Geothermal System ◽  
Potential Field Data ◽  
Model Compression

Potential field data have long been used in geophysical exploration for archeological, mineral, and reservoir targets. For all these targets, the increased search of highly detailed three-dimensional subsurface volumes has also promoted the recollection of high-density contrast data sets. While there are several approaches to handle these large-scale inverse problems, most of them rely on either the extensive use of high-performance computing architectures or data-model compression strategies that may sacrifice some level of model resolution. We posit that the superposition and convolutional properties of the potential fields can be easily used to compress the information needed for data inversion and also to reduce significantly redundant mathematical computations. For this, we developed a convolution-based conjugate gradient 3D inversion algorithm for the most common types of potential field data. We demonstrate the performance of the algorithm using a resolution test and a synthetic experiment. We then apply our algorithm to gravity and magnetic data for a geothermal prospect in the Acoculco caldera in Mexico. The resulting three-dimensional model meaningfully determined the distribution of the existent volcanic infill in the caldera as well as the interrelation of various intrusions in the basement of the area. We propose that these intrusive bodies play an important role either as a low-permeability host of the heated fluid or as the heat source for the potential development of an enhanced geothermal system.

Three-dimensional depth-to-basement modelling based on seismic and potential field data – basement configuration in the westernmost Polish Outer Carpathians

2020 ◽  
Author(s):  
Mateusz Mikołajczak ◽  
Jan Barmuta ◽  
Małgorzata Ponikowska ◽  
Stanislaw Mazur ◽  
Krzysztof Starzec
Keyword(s):  
Qualitative Analysis ◽  
Cross Sections ◽  
Potential Field ◽  
Field Data ◽  
Gravity Data ◽  
Three Dimensional ◽  
Magnetic Data ◽  
Gravity Inversion ◽  
Potential Field Data ◽  
Outer Carpathians

<p>The Silesian Nappe in the westernmost part of the Polish Outer Carpathians Fold and Thrust Belt exhibits simple, almost homoclinal character. Based on the field observations, a total stratigraphic thickness of this sequence equals to at least 5400 m. On the other hand, the published maps of the sub-Carpathian basement show its top at depths no greater than 3000 m b.s.l. or even 2000 m b.s.l. in the southern part of the Silesian Nappe. Assuming no drastic thickness variations within the sedimentary sequence of the Silesian Nappe, such estimates of the basement depth are inconsistent with the known thickness of the Silesian sedimentary succession. The rationale behind our work was to resolve this inconsistency and verify the actual depth and structure of the sub-Carpathian crystalline basement along two regional cross-sections. In order to achieve this goal, a joint 2D quantitative interpretation of gravity and magnetic data was performed along these regional cross-sections. The interpretation was supported by the qualitative analysis of magnetic and gravity maps and their derivatives to recognize structural features in the sub-Carpathian basement. The study was concluded with the 3D residual gravity inversion for the top of basement. The cross-sections along with the borehole data available from the area were applied to calibrate the inversion.</p><p>In the westernmost part of the Polish Outer Carpathians, the sub-Carpathian basement comprises part of the Brunovistulian Terrane. Because of great depths, the basement structure was investigated mainly by geophysical, usually non-seismic, methods. However, some deep boreholes managed to penetrate the basement that is composed of Neoproterozoic metamorphic and igneous rocks. The study area is located within the Upper Silesian block along the border between Poland and Czechia. There is a basement uplift as known mainly from boreholes, but the boundaries and architecture of this uplift are poorly recognized. Farther to the south, the top of the Neoproterozoic is buried under a thick cover of lower Palaeozoic sediments and Carpathian nappes.</p><p>Our integrative study allowed to construct a three-dimensional map for the top of basement the depth of which increases from about 1000 m to over 7000 m b.s.l. in the north and south of the study area, respectively. Qualitative analysis of magnetic and gravity data revealed the presence of some  basement-rooted faults delimiting the extent of the uplifted basement. The interpreted faults are oriented mainly towards NW-SE and NE-SW. Potential field data also document the correlation between the main basement steps and important thrust faults.</p><p> </p><p>This work has been funded by the Polish National Science Centre grant no UMO-2017/25/B/ST10/01348</p>

Noniterative three‐dimensional inversion of magnetic data

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 782-785 ◽  
Author(s):  
A. M. Pustisek
Keyword(s):  
Inverse Problem ◽  
Potential Field ◽  
Field Data ◽  
Three Dimensional ◽  
Magnetic Data ◽  
Aeromagnetic Data ◽  
Nonlinear Inverse Problem ◽  
Potential Field Data

The interpretation of magnetic or aeromagnetic data often requires the inverse problem’s solution of the structure of the magnetization interface. This nonlinear inverse problem of mapping the basement topography from potential field data was first discussed by Peters (1949).

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

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.

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

Large-scale 3D inversion of potential field data

2012 ◽  
Vol 60 (6) ◽  
pp. 1186-1199 ◽  
Author(s):  
Martin Čuma ◽  
Glenn A. Wilson ◽  
Michael S. Zhdanov
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Large Scale ◽  
3D Inversion ◽  
Potential Field Data

Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 780-786 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Field Data ◽  
Three Dimensional ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Automatic Interpretation ◽  
The Hilbert Transform

The paper extends to three dimensions (3-D) the two‐dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy‐Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case. Finally, the previously developed concept of analytic signal in 2-D can be extended to 3-D as a first step toward the development of an automatic interpretation technique for potential field data.

DESIGN OF SMALL OPERATORS FOR THE CONTINUATION OF POTENTIAL FIELD DATA

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 488-506 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Grid Point ◽  
Frequency Characteristics ◽  
Potential Fields ◽  
Two Dimensional ◽  
Potential Field Data ◽  
Computational Work ◽  
Considerable Loss ◽  
Equivalent Operators

Two‐dimensional continuation of potential fields is commonly achieved by employing a continuation operator which consists of a number of coefficients operating upon uniformly gridded field data. To obtain accurate results, the size of the operator has to be quite large. This not only requires a lot of computational work, but also causes a considerable loss of information due to the reduced size of the field obtained after continuation. Small‐size “equivalent” operators were designed which are free from these drawbacks but yield accurate results. In order to demonstrate the efficiency of these operators, a potential field was continued upward by using 31×31 Tsuboi coefficients. This required 961 multiplications for computing the continued field at each grid point. When procedure was repeated using the equivalent operator, the number of multiplications required for each grid point was reduced to 15, the size of the resulting map was much larger, but the results in both cases were practically identical in accuracy. Frequency characteristics of the equivalent operators and the continuation of data very close to the boundary of the field map are discussed.

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