Magnetic source parameters of two‐dimensional structures using extended Euler deconvolution

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 814-823 ◽  
Author(s):  
Martin F. Mushayandebvu ◽  
P. van Driel ◽  
Alan B. Reid ◽  
James Derek Fairhead
Keyword(s):  
Homogeneous Function ◽  
A Priori ◽  
Source Parameters ◽  
Thin Sheet ◽  
Source Location ◽  
Euler Deconvolution ◽  
True Source ◽  
Susceptibility Contrast ◽  
Magnetic Profile ◽  
Constrained Solutions

The Euler homogeneity relation expresses how a homogeneous function transforms under scaling. When implemented, it helps to determine source location for particular potential field anomalies. In this paper, we introduce an additional relation that expresses the transformation of homogeneous functions under rotation. The combined implementation of the two equations, called here extended Euler deconvolution for 2-D structures, gives a more complete source parameter estimation that allows the determination of susceptibility contrast and dip in the cases of contact and thin‐sheet sources. This allows for the structural index to be correctly chosen on the basis of a priori knowledge about susceptibility and dip. The pattern of spray solutions emanating from a single source anomaly can be attributed to interfering sources, which have their greatest effect on the flanks of the anomaly. These sprays follow different paths when using either conventional Euler deconvolution or extended Euler deconvolution. The paths of these spray solutions cross and cluster close to the true source location. This intersection of spray paths is used as a discriminant between poor and well‐constrained solutions, allowing poor solutions to be eliminated. Extended Euler deconvolution has been tested successfully on 2-D model and real magnetic profile data over contacts and thin dikes.

On the application of Euler deconvolution to the analytic signal

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. L87-L93 ◽  
Author(s):  
G. Florio ◽  
M. Fedi ◽  
R. Pasteka
Keyword(s):  
Potential Field ◽  
Harmonic Functions ◽  
Horizontal Plane ◽  
Homogeneous Function ◽  
Source Parameters ◽  
Analytic Signal ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Vertical Derivative ◽  
First Vertical Derivative

Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane, according to potential-field theory. The analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function. Hence, the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent Euler deconvolution. We show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones. The consequences of this error in the structural index are equally important whether the structural index is given as input (as in standard Euler deconvolution) or represents an unknown to be solved for. The analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions. We suggest computing the first vertical derivative of the analytic signal modulus, taking into account its nonharmonicity, by using a simple finite-difference algorithm. When the vertical derivative of the analytic signal is computed by finite differences, the depth to source and the structural index consistent with known source parameters are, in fact, obtained.

Automatic conversion of magnetic data to depth, dip, and susceptibility contrast using the SPI (TM) method

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 807-813 ◽  
Author(s):  
Jeffrey B. Thurston ◽  
Richard S. Smith
Keyword(s):  
Remanent Magnetization ◽  
Source Parameters ◽  
Thin Sheet ◽  
Source Parameter ◽  
Magnetic Data ◽  
Magmatic Arc ◽  
Peace River ◽  
Magnetic Inclination ◽  
Susceptibility Contrast ◽  
Peace River Arch

The Source Parameter Imaging (SPI™) method computes source parameters from gridded magnetic data. The method assumes either a 2-D sloping contact or a 2-D dipping thin‐sheet model and is based on the complex analytic signal. Solution grids show the edge locations, depths, dips, and susceptibility contrasts. The estimate of the depth is independent of the magnetic inclination, declination, dip, strike and any remanent magnetization; however, the dip and the susceptibility estimates do assume that there is no remanent magnetization. Image processing of the source‐parameter grids enhances detail and provides maps that facilitate interpretation by nonspecialists. The SPI method tests successfully on synthetic profile and gridded data. SPI maps derived from aeromagnetic data acquired over the Peace River Arch area of northwestern Canada correlate well with known basement structure and furthermore show that the Ksituan Magmatic Arc can be divided into several susceptibility subdomains.

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.

Magnetic curve fit for a thin dike: Calculator program (TI 59)

Geophysics ◽  
1980 ◽  
Vol 45 (3) ◽  
pp. 447-455 ◽  
Author(s):  
Edwin J. Ballantyne
Keyword(s):  
Massive Sulfide ◽  
Sulfide Deposits ◽  
Curve Fit ◽  
Magnetic Curve ◽  
Original Field ◽  
Susceptibility Contrast ◽  
Magnetic Profile ◽  
Depth Of Burial ◽  
Minimum Points ◽  
Interpretation Problem

In the exploration for massive sulfide deposits, many of the sources of magnetic anomalies are long tabular dike‐like bodies which are thin in relation to the depth of burial. That is, the width of the dike is less than the depth of burial. A program is presented to aid in the inverse solution of this interpretation problem. Demagnetization effects are ignored, and the program will not function for symmetrical anomalies. Given field‐observed amplitudes and coordinates of maximum and minimum points on a total‐ or vertical‐field magnetic profile, this program fits the corresponding theoretical profile for a thin dipping magnetic dike. Coordinate and depth of the top of dike, dip of dike, and width‐susceptibility contrast of the dike are calculated. A theoretical anomaly profile may also be calculated for comparison with the original field curve. Successive iterations may be used to refine estimates of the calculated parameters.

3-D Gravity Inversion with Euler Deconvolution as a Priori Information

2005 ◽  
Author(s):  
H. Rim ◽  
Y.-S. Park ◽  
M. Lim ◽  
S.B. Koo ◽  
B.D. Kwon
Keyword(s):  
A Priori ◽  
Gravity Inversion ◽  
A Priori Information ◽  
Euler Deconvolution ◽  
Priori Information

Self-potential Data Interpretation for Two Co-axial Structures Utilizing the RMS Parameter

2020 ◽  
Vol 25 (1) ◽  
pp. 15-23
Author(s):  
Khalid S. Essa ◽  
Zein E. Diab ◽  
Mahmoud Elhussein
Keyword(s):  
A Priori ◽  
Source Parameters ◽  
Data Interpretation ◽  
The Body ◽  
Inversion Method ◽  
Model Parameters ◽  
Polarization Angle ◽  
Potential Field Data ◽  
Rms Error ◽  
Self Potential

We have developed an algorithm to obtain the model parameters for two co-axial structures from self-potential data. The method uses the first numerical horizontal derivatives calculated from the observed self-potential anomaly employing filters of sequential window lengths (s-values) so as to gauge the model constraints for the shallow and deep structures. In addition, this algorithm uses a standard inversion method for solving a non-linear equation based on the lowest root-mean-square (RMS) error of the estimated model parameters. The body constraints are the depth, polarization angle and electric dipole moment of each structure. Our approach models the self-potential dataset as an aggregation of spheres, horizontal cylinders, and vertical cylinders. These simple bodies are used to approximate, without a priori expectations, the furthermost plausible position and/or area of intersection. In other words, the bodies are used to estimate the true values of the source parameters for the two-co-axial bodies at different s-values. Minimizing the RMS error has the advantage of optimizing all model factors. The proposed technique is tested using a numerical model with and without noise and on self-potential field data acquired at a site in Germany. In all cases, the assessed body parameters are reasonable approximations of the known values.

Perceived Loudness and Visually-Determined Auditory Distance

Perception ◽  
1981 ◽  
Vol 10 (5) ◽  
pp. 531-543 ◽  
Author(s):  
Donald H Mershon ◽  
Douglas H Desaulniers ◽  
Stephan A Kiefer ◽  
Thomas L Amerson ◽  
Jeanne T Mills
Keyword(s):  
Apparent Distance ◽  
Source Location ◽  
Sound Level ◽  
Visual Capture ◽  
Noise Stimulus ◽  
Auditory Distance ◽  
Sound Levels ◽  
Apparent Source ◽  
True Source ◽  
Physical Changes

Three experiments were conducted to determine whether variations in the perceived distance to a test sound could influence its loudness in the absence of physical changes in sound-level. The phenomenon of visual capture provided the means for manipulating apparent distance. A ‘dummy’ loudspeaker was used to vary the apparent source location of a short noise stimulus while the true source of this sound remained fixed (and hidden) with respect to the observer. Sound-levels from 40 to 75 dB(A) were presented to independent groups of observers in either anechoic or semi-reverberant acoustical environments. In general, reported loudness increased with perceived distance. This finding has implications for conceptualizing the phenomenon of loudness constancy.

scholarly journals Sensitivity maps for time-reverse imaging: an accuracy study for the Los Humeros Geothermal Field (Mexico)

2020 ◽  
Vol 222 (1) ◽  
pp. 231-246
Author(s):  
C Finger ◽  
E H Saenger
Keyword(s):  
A Priori ◽  
Velocity Model ◽  
Source Location ◽  
Geothermal Field ◽  
Location Accuracy ◽  
Accurate Localization ◽  
Localization Scheme ◽  
Priori Information ◽  
Initial Source ◽  
Sensitivity Maps

SUMMARY The estimation of the source–location accuracy of microseismic events in reservoirs is of significant importance. Time-reverse imaging (TRI) provides a highly accurate localization scheme to locate events by time-reversing the recorded full wavefield and back propagating it through a velocity model. So far, the influence of the station geometry and the velocity model on the source–location accuracy is not well known. Therefore, sensitivity maps are developed using the geothermal site of Los Humeros in Mexico to evaluate the spatial variability of the source–location accuracy. Sensitivity maps are created with an assumed gradient velocity model with a constant vp–vs ratio and with a realistic velocity model for the region of Los Humeros. The positions of 27 stations deployed in Los Humeros from September 2017 to September 2018 are used as surface receivers. An automatic localization scheme is proposed that does not rely on any a priori information about the sources and thus negates any user bias in the source locations. The sensitivity maps are created by simulating numerous uniformly distributed sources simultaneously and locating these sources using TRI. The found source locations are compared to the initial source locations to estimate the achieved accuracy. The resulting sensitivity maps show that the station geometry introduces complex patterns in the spatial variation of accuracy. Furthermore, the influence of the station geometry on the source–location accuracy is larger than the influence of the velocity model. Finally, a microearthquake recorded at the geothermal site of Los Humeros is located to demonstrate the usability of the derived sensitivity maps. This study stresses the importance of optimizing station networks to enhance the accuracy when locating seismic events using TRI.

3D Euler deconvolution: Theoretical basis for automatically selecting good solutions

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1962-1968 ◽  
Author(s):  
João B. C. Silva ◽  
Valéria C. F. Barbosa
Keyword(s):  
Magnetic Anomaly ◽  
Theoretical Basis ◽  
Source Location ◽  
The Other ◽  
Euler Deconvolution ◽  
Data Window ◽  
Other Hand ◽  
3D Euler Deconvolution ◽  
Structural Indices ◽  
Derivatives Of

We derive the analytical estimators for the horizontal and vertical source positions in 3D Euler deconvolution as a function of the x‐, y‐, and z‐derivatives of the magnetic anomaly within a data window. From these expressions we show that, in the case of noise‐corrupted data, the x‐, y‐, and z‐coordinate estimates computed at the anomaly borders are biased toward the respective horizontal coordinate of the data window center regardless of the true or presumed structural indices and regardless of the magnetization inclination and declination. On the other hand, in the central part of the anomaly, the x‐ and y‐coordinate estimates are very close to the respective source horizontal coordinates regardless of the true or presumed structural indices and regardless of the magnetization inclination and declination. This contrasting behavior of the horizontal coordinate estimates may be used to automatically delineate the region associated with the best solutions. Applying the Euler deconvolution operator inside this region would decrease the dispersion of all position estimates, improving source location precision.

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