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).

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>

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.

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.

Balancing images of potential-field data

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. L17-L20 ◽  
Author(s):  
G. R. Cooper
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Large Range ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Aeromagnetic Data ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Total Gradient ◽  
Data Source

Horizontal and vertical gradients, and filters based on them (such as the analytic signal), are used routinely to enhance detail in aeromagnetic data. However, when the data contain anomalies with a large range of amplitudes, the filtered data also will contain large and small amplitude responses, making the latter hard to see. This study suggests balancing the analytic signal amplitude (sometimes called the total gradient) by the use of its orthogonal Hilbert transforms, and shows that the balanced profile curvature can be an effective method of enhancing potential-field data. Source code is available from the author on request.

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.

The monogenic signal of potential-field data: A Python implementation

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. F9-F14 ◽  
Author(s):  
Marlon C. Hidalgo-Gato ◽  
Valéria C. F. Barbosa
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Scale Space ◽  
Magnetic Data ◽  
Monogenic Signal ◽  
Potential Field Data ◽  
Source Program ◽  
Multiple Component ◽  
Ground Penetrating ◽  
Monogenic Signals

We have developed codes to calculate the local amplitude, the local phase, and the local orientation of the nonscale and the Poisson’s scale-space monogenic signals of potential-field data in version 1.0 of the open-source program Monogenic. The monogenic vector of a generic function is calculated in the wavenumber domain and then transformed back into the space domain to find the monogenic signal attributes. We compare the use of the nonscale monogenic signal with the Poisson’s scale-space monogenic signal in magnetic data. This comparison shows that the latter can produce better results as an edge detection filter. The implementation of the monogenic signal can be used to enhance other geophysical data, such as seismic, ground-penetrating radar, gravity, multiple-component gravity gradiometry, and magnetic gradient data.

Improved use of the local wavenumber in potential-field interpretation

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. L75-L85 ◽  
Author(s):  
Pierre Keating
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Thin Sheet ◽  
Homogeneous Magnetic Field ◽  
Horizontal Cylinder ◽  
Magnetic Data ◽  
Homogeneous Field ◽  
Potential Field Data ◽  
Local Wavenumber ◽  
Homogeneity Hypothesis

Fast interpretation of potential field data (magnetic data are a typical example) often uses simple geometries to describe a complex geologic reality. Many of these techniques assume that the potential field arising from the source body is homogeneous. The degree of homogeneity of a source is characteristic of its geometry. However, very few source geometries are known to generate a homogeneous field. The contact, thin sheet, horizontal cylinder, pole, and dipole all cause a homogeneous magnetic field. More complex geometries such as the thick dike or rectangular prism do not. Therefore, a major problem is to check for the validity of the homogeneity hypothesis when these types of interpretation techniques are used. The local wavenumber of a potential field calculated at a series of increasing heights above the measurement datum can be used to directly compute the depth to a source and its degree of homogeneity. In addition, the vertical derivative of the local wavenumber can provide an estimate of the depth to sources without knowledge of their degree of homogeneity. The proposed technique also allows us to test if the source is homogeneous or not, and it applies to any type of potential field data. The technique breaks down on synthetic magnetic data when anomalous sources are closer than about four times their depths. This behavior is expected from interpretation techniques that use upward continuation. The technique can be applied to profile and gridded data. Its main advantage is that it allows testing the homogeneity hypothesis and therefore the validity of the interpretation.

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