Higher derivatives analysis of 2-D magnetic data

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 205-212 ◽  
Author(s):  
E. M. Abdelrahman ◽  
E. R. Abo‐Ezz
Keyword(s):  
Theoretical Data ◽  
Horizontal Cylinder ◽  
Magnetic Data ◽  
Random Errors ◽  
New Approach ◽  
Depth Determination ◽  
Higher Derivatives ◽  
Optimum Order ◽  
Fourth Derivative ◽  
Actual Depth

This paper presents a new approach for determining the depth of a buried structure from numerical second‐, third‐, and fourth‐horizontal‐derivative anomalies obtained from 2-D magnetic data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form z = f(z). Formulas have been derived for a horizontal cylinder and a dike. The depths obtained from the second‐, third‐, and fourth‐derivative anomaly values can be used to determine simultaneously the actual depth to the buried structure and the optimum order of the regional magnetic field along the profile. This powerful technique can solve two major potential field problems: regional residual separation and depth determination. The method is applied to theoretical data with and without random errors and is tested on a field example from Arizona.

A new approach to depth determination from magnetic anomalies

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1524-1531 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby ◽  
Tarek M. El‐Araby ◽  
Khalid S. Essa
Keyword(s):  
Synthetic Data ◽  
Vertical Component ◽  
Horizontal Cylinder ◽  
Magnetic Data ◽  
New Approach ◽  
Data Points ◽  
Symmetric Points ◽  
Surface Geology ◽  
Effective Intensity ◽  
Shallow Structure

We have developed a semiautomatic method to determine the depth to shallow and deep‐seated structures from a magnetic anomaly profile. It involves using a relationship between the depths to two coaxial sources obtained by combining observations at symmetric points with respect to the coordinate of the sources center. For five established, fixed data points, the depth to the shallow structure is determined for each preassigned depth of the deep‐seated structure. The computed depths to the shallow structure are plotted against the computed depths to the deep‐seated structure, yielding a continuous, monotonically increasing depth curve. The spacing between the observations is then modified, producing several curves. The accepted estimates for the depths to both structures are read at the common intersection of these curves. The effective intensity and the angle of magnetization of both structures are also estimated. The proposed method was tested both on noisy synthetic and real magnetic data. In the case of synthetic data, the depth curves method determined the correct depths of both coaxial and laterally offset sources. In the case of practical data (vertical component anomaly over a chromite body in the Guleman concession, Turkey), the method suggested the shape of the buried shallow structure resembles a horizontal cylinder model buried at a depth of 31 m and the shape of the buried deep seated structure resembles a dike model buried at a depth of 62 m. The estimated shape and depth of the shallow structure are in very good agreement with the results obtained from drilling and surface geology. The area appears to still hold promise for chromite exploration from the deeper structure.

New methods for shape and depth determinations from SP data

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1202-1210 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby ◽  
Abdel‐Rady G. Hassaneen ◽  
Mahfooz A. Hafez
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Least Squares Method ◽  
Random Noise ◽  
Theoretical Data ◽  
Derivative Analysis ◽  
Higher Derivatives ◽  
Optimum Order ◽  
Simple Linear Equation ◽  
Sp Anomaly

We have extended our earlier derivative analysis method to higher derivatives to estimate the depth and shape (shape factor) of a buried structure from self‐potential (SP) data. We show that numerical second, third, and fourth horizontal‐derivative anomalies obtained from SP data using filters of successive window lengths can be used to simultaneously determine the depth and the shape of a buried structure. The depths and shapes obtained from the higher derivatives anomaly values can be used to determine simultaneously the actual depth and shape of the buried structure and the optimum order of the regional SP anomaly along the profile. The method is semi‐automatic and it can be applied to residuals as well as to observed SP data. We have also developed a method (based on a least‐squares minimization approach) to determine, successively, the depth and the shape of a buried structure from the residual SP anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin, the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of form f(z) = 0. Knowing the depth and applying the least‐squares method, the shape factor is determined using a simple linear equation. Finally, we apply these methods to theoretical data with and without random noise and on a known field example from Germany. In all cases, the depth and shape solutions obtained are in good agreement with the actual ones.

Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Oluwaseun Adeyeye ◽  
Ali Aldalbahi ◽  
Jawad Raza ◽  
Zurni Omar ◽  
Mostafizur Rahaman ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Block Method ◽  
Wide Range ◽  
Higher Derivatives ◽  
Fourth Derivative ◽  
Improved Accuracy

AbstractThe processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating solutions, the adoption of block methods is yet to be investigated. Hence, this article introduces a new two-step third–fourth-derivative block method as a numerical approach to solve the reaction–diffusion equation. In order to ensure improved accuracy, the method introduces the concept of nonlinearity in the solution of the linear model through the presence of higher derivatives. The method obtained accurate solutions for the model at varying values of the dimensionless diffusion parameter and saturation parameter. Furthermore, the solutions are also in good agreement with previous solutions by existing authors.

scholarly journals Analytic Signal Depth from High Resolution Aeromagnetic Data over the Gongola Basin Upper Benue Trough Northeastern Nigeria

2021 ◽  
Vol 25 (4) ◽  
pp. 585-590
Author(s):  
H. Musa ◽  
N.E. Bassey ◽  
R. Bello
Keyword(s):  
High Resolution ◽  
Magnetic Structure ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Aeromagnetic Data ◽  
Polynomial Fitting ◽  
Benue Trough ◽  
Local Maxima ◽  
Depth Determination ◽  
Programming Software

The study of high-resolution aeromagnetic data was carried out over the Gongola basin, upper Benue trough, northeastern Nigeria, for analytic signal depth determination. Total intensity magnetic map obtained from the data using the Oasis Montaj TM programming software was used to get the residual map by polynomial fitting, from where the analytic signal was obtained with the use of anomaly width at half the amplitude (X1/2). This was used to carry out depth estimations over the study area. The results showed that it peaks over the magnetic structure with local maxima over its edges (boundaries or contact), and the amplitude is simply related to magnetization, likewise results also showed that the depth estimates were in the range of 1.2 to 5.9 km and were calculated for contact, dyke/sill and horizontal cylinder respectively. The lowest values are from DD profiles, while the highs are from AA profiles. This work is important in identifying dykes, contacts and intrusives over an area.

scholarly journals Gravitational waves and perspectives for quantum gravity

2014 ◽  
Vol 29 (30) ◽  
pp. 1430034 ◽  
Author(s):  
Ilya L. Shapiro ◽  
Ana M. Pelinson ◽  
Filipe de O. Salles
Keyword(s):  
Quantum Gravity ◽  
Gravitational Waves ◽  
Classical Solutions ◽  
Quantum Level ◽  
Quantum Matter ◽  
Higher Derivatives ◽  
Fourth Derivative ◽  
Matter Fields ◽  
Classical Background

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.

Imaging depth, structure, and susceptibility from magnetic data: The advanced source-parameter imaging method

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. L31-L38 ◽  
Author(s):  
Richard S. Smith ◽  
Ahmed Salem
Keyword(s):  
Source Parameters ◽  
Thin Sheet ◽  
Signal Amplitude ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Imaging Method ◽  
Structural Index ◽  
Synthetic Test ◽  
Vertical Contact

An important problem in the interpretation of magnetic data is quantifying the source parameters that describe the anomalous structure. We present a new method that uses various combinations of the local wavenumbers for estimating the depth and shape (structural index) of the structure. Because the estimates are derived from third derivatives of the magnetic data, they are noisy. However, there are multiple ways of calculating the depth and index, and these solutions can be averaged to give a stable estimate. Even so, a synthetic test shows that the results are erratic away from the locations where the analytic-signal amplitude is large. Hence, when we generate images of the depth and structural index, we make the results most visible where the analytic-signal amplitude is large and less visible where the signal is small. The advantage of the method is that estimates can be obtained at all locations on a profile and used to generate continuous profiles or images of the source parameters. This can be used to help identify the locations where interference might be corrupting the results. The structural index image can be used to determine the most appropriate type of model for an area. Assuming this model, it is possible to calculate the depth that would be consistent with the model and the data. Knowing both the depth and model, the analytic-signal amplitude can be converted to apparent susceptibility. If a vertical-contact model is assumed, the susceptibility contrast across the contact can be imaged. For the thin-sheet and horizontal-cylinder models, we can image the susceptibility-thickness and susceptibility-area products, respectively.

THE INTERPRETATION OF AEROMAGNETIC SURVEYS FOR HYDROCARBON EXPLORATION

1999 ◽  
Vol 39 (1) ◽  
pp. 494
Author(s):  
I. Kivior ◽  
D. Boyd
Keyword(s):  
Spectral Analysis ◽  
Sedimentary Basins ◽  
Hydrocarbon Exploration ◽  
Petroleum Exploration ◽  
Magnetic Data ◽  
Curve Matching ◽  
Aeromagnetic Data ◽  
Profile Data ◽  
Aeromagnetic Survey ◽  
New Approach

Aeromagnetic surveys have been generally regarded in petroleum exploration as a reconnaissance tool for major structures. They were used commonly in the early stages of exploration to delineate the shape and depth of the sedimentary basin by detecting the strong magnetic contrast between the sediments and the underlying metamorphic basement. Recent developments in the application of computer technology to the study of the earth's magnetic field have significantly extended the scope of aeromagnetic surveys as a tool in the exploration for hydrocarbons. In this paper the two principal methods used in the analysis and interpretation of aeromagnetic data over sedimentary basins are: 1) energy spectral analysis applied to gridded data; and, 2) automatic curve matching applied to profile data. It is important to establish the magnetic character of sedimentary and basement rocks, and to determine the regional magnetic character of the area by applying energy spectral analysis. Application of automatic curve matching to profile data can provide results from the sedimentary section and deeper parts of a basin. High quality magnetic data from an experimental aeromagnetic survey flown over part of the Eromanga/Cooper Basin has recently been interpreted using this new approach. From this survey it is possible to detect major structures such as highs and troughs in the weakly magnetic basement, as well as pick out faults, and magnetic layers in the sedimentary section. The results are consistent with interpretation from seismic and demonstrate that aeromagnetic data can be used to assist seismic interpretation, for example to interpolate between widely spaced seismic lines and sometimes to locate structures which can not be detected from seismic surveys. This new approach to the interpretation of aeromagnetic data can provide a complementary tool for hydrocarbon exploration, which is ideal for logistically difficult terrain and environmentally sensitive areas.

New approach for interpretation of scattered ground magnetic data in a part of Delhi Fold Belt-NW Indian shield

2013 ◽  
Vol 7 (7) ◽  
pp. 2633-2639 ◽  
Author(s):  
Prabhakara Prasad P. ◽  
Satish Kumar K. ◽  
Seshunarayana T. ◽  
Rama Rao Ch.
Keyword(s):  
Magnetic Data ◽  
Fold Belt ◽  
Indian Shield ◽  
New Approach ◽  
Ground Magnetic

ACCURATE DEPTH DETERMINATION OF THE VELOCITY SURVEY WELL PHONE

Geophysics ◽  
1961 ◽  
Vol 26 (1) ◽  
pp. 100-100
Author(s):  
R. P. Nolting
Keyword(s):  
The Other ◽  
Log Data ◽  
Survey Report ◽  
Depth Determination ◽  
Depth Curve ◽  
Actual Depth ◽  
Check Level ◽  
Made In

Many velocity surveys have been shot in which the actual depth of the well phone was in question at one or more of the levels shot in the borehole. The computed time to the questioned level would not fit the other data obtained from the velocity survey, i.e., the data from the questioned level would not fit the time‐depth curve within reason or, more recently, it could not properly be fitted to the corrected continuous velocity log data. If the “first break” of the questioned level could not be repicked to conform to the other data, a notation was made in the velocity survey report that the depth of the well phone was probably in error. Although this assumption was correct in many cases, there are various other reasons why data from one check level should not fit the rest of the data.

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