Stability analysis and improvement of structural index estimation in Euler deconvolution

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 48-60 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Stability Analysis ◽  
Vertical Position ◽  
Horizontal Position ◽  
Total Field ◽  
Source Position ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Data Window ◽  
Base Level ◽  
New Criterion

Euler deconvolution has been widely used in automatic aeromagnetic interpretations because it requires no prior knowledge of the source magnetization direction and assumes no particular interpretation model, provided the structural index defining the anomaly falloff rate related to the nature of the magnetic source, is determined in advance. Estimating the correct structural index and electing optimum criteria for selecting candidate solutions are two fundamental requirements for a successful application of this method. We present a new criterion for determining the structural index. This criterion is based on the correlation between the total‐field anomaly and the estimates of an unknown base level. These estimates are obtained for each position of a moving data window along the observed profile and for several tentative values for the structural index. The tentative value for the structural index producing the smallest correlation is the best estimate of the correct structural index. We also propose a new criterion to select the best solutions from a set of previously computed candidate solutions, each one associated with a particular position of the moving data window. A current criterion is to select only those candidates producing a standard deviation for the vertical position of the source smaller than a threshold value. We propose that in addition to this criterion, only those candidates producing the best fit to the known quantities (combinations of anomaly and its gradients) be selected. The proposed modifications to Euler deconvolution can be implemented easily in an automated algorithm for locating the source position. The above results are grounded on a theoretical uniqueness and stability analysis, also presented in this paper, for the joint estimation of the source position, the base level, and the structural index in Euler deconvolution. This analysis also reveals that the vertical position and the structural index of the source cannot be estimated simultaneously because they are linearly dependent; the horizontal position and the structural index, on the other hand, are linearly independent. For a known structural index, estimates of both horizontal and vertical positions are unique and stable regardless of the value of the structural index. If this value is not too small, estimates of the base level for the total field are stable as well. The proposed modifications to Euler deconvolution were tested both on synthetic and real magnetic data. In the case of synthetic data, the proposed criterion always detected the correct structural index and good estimates of the source position were obtained, suggesting the present theoretical analysis may lead to a substantial enhancement in practical applications of Euler deconvolution. In the case of practical data (vertical component anomaly over an iron deposit in the Kursk district, Russia), the estimated structural index (corresponding to a vertical prism) was in accordance with the known geology of the deposit, and the estimates of the depth and horizontal position of the source compared favorably with results reported in the literature.

Scattering, symmetry, and bias analysis of source‐position estimates in Euler deconvolution and its practical implications

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1149-1156 ◽  
Author(s):  
J. B. C. Silva ◽  
V. C. F. Barbosa ◽  
W. E. Medeiros
Keyword(s):  
Vertical Position ◽  
Lower Sensitivity ◽  
Horizontal Position ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Bias Analysis ◽  
Data Noise ◽  
Data Window ◽  
Symmetry Properties ◽  
Window Position

Despite being widely used, Euler deconvolution has received little attention in its theoretical aspects. We obtain analytical estimators [Formula: see text] and [Formula: see text] for the horizontal [Formula: see text] and the vertical [Formula: see text] source positions, which are the parameters to be estimated when the structural index is assigned a tentative value. By analyzing the estimators’ properties, we show two things. (1) Scattering of the alternative solutions associated with different data window positions has two components: data noise and the use of a wrong tentative value for the structural index, (2) The differences [Formula: see text] and [Formula: see text], as a function of the data window position, exhibit antisymmetric and symmetric behaviors, respectively, about [Formula: see text] when the magnetization and the geomagnetic field inclinations are 90°, 0°, or 45°. For intermediate inclinations there is a moderate departure from the symmetry properties. This analysis shows that the criterion for determining the structural index as the tentative value producing the smallest solution scattering is theoretically sound but occasionally fails in practice because data noise also contributes to solution scattering. In addition, the lower sensitivity of the averages of estimates of the horizontal position (as compared with the vertical position) occurs because [Formula: see text] displays an antisymmetric behavior with respect to the true horizontal position while the estimates of the vertical position display a symmetric behavior with respect to the same point.

Correct structural index in Euler deconvolution via base-level estimates

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. J87-J98 ◽  
Author(s):  
Felipe F. Melo ◽  
Valéria C. F. Barbosa
Keyword(s):  
Standard Deviation ◽  
Field Measurements ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
Total Field ◽  
Minimum Standard ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Base Level

In most applications, the Euler deconvolution aims to define the nature (type) of the geologic source (i.e., the structural index [SI]) and its depth position. However, Euler deconvolution also estimates the horizontal positions of the sources and the base level of the magnetic anomaly. To determine the correct SI, most authors take advantage of the clustering of depth estimates. We have analyzed Euler’s equation to indicate that random variables contaminating the magnetic observations and its gradients affect the base-level estimates if, and only if, the SI is not assumed correctly. Grounded on this theoretical analysis and assuming a set of tentative SIs, we have developed a new criterion for determining the correct SI by means of the minimum standard deviation of base-level estimates. We performed synthetic tests simulating multiple magnetic sources with different SIs. To produce mid and strongly interfering synthetic magnetic anomalies, we added constant and nonlinear backgrounds to the anomalies and approximated the simulated sources laterally. If the magnetic anomalies are weakly interfering, the minima standard deviations either of the depth or base-level estimates can be used to determine the correct SI. However, if the magnetic anomalies are strongly interfering, only the minimum standard deviation of the base-level estimates can determine the SI correctly. These tests also show that Euler deconvolution does not require that the magnetic data be corrected for the regional fields (e.g., International Geomagnetic Reference Field [IGRF]). Tests on real data from part of the Goiás Alkaline Province, Brazil, confirm the potential of the minimum standard deviation of base-level estimates in determining the SIs of the sources by applying Euler deconvolution either to total-field measurements or to total-field anomaly (corrected for IGRF). Our result suggests three plug intrusions giving rise to the Diorama anomaly and dipole-like sources yielding Arenópolis and Montes Claros de Goiás anomalies.

Estimating the nature and the horizontal and vertical positions of 3D magnetic sources using Euler deconvolution

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. J87-J98 ◽  
Author(s):  
Felipe F. Melo ◽  
Valeria C. F. Barbosa ◽  
Leonardo Uieda ◽  
Vanderlei C. Oliveira Jr. ◽  
João B. C. Silva
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Angular Coefficient ◽  
Coefficient Estimates ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Vertical Coordinate ◽  
Base Level ◽  
The One ◽  
Inclined Planes

We have developed a new method that drastically reduces the number of the source location estimates in Euler deconvolution to only one per anomaly. Our method employs the analytical estimators of the base level and of the horizontal and vertical source positions in Euler deconvolution as a function of the [Formula: see text]- and [Formula: see text]-coordinates of the observations. By assuming any tentative structural index (defining the geometry of the sources), our method automatically locates plateaus, on the maps of the horizontal coordinate estimates, indicating consistent estimates that are very close to the true corresponding coordinates. These plateaus are located in the neighborhood of the highest values of the anomaly and show a contrasting behavior with those estimates that form inclined planes at the anomaly borders. The plateaus are automatically located on the maps of the horizontal coordinate estimates by fitting a first-degree polynomial to these estimates in a moving-window scheme spanning all estimates. The positions where the angular coefficient estimates are closest to zero identify the plateaus of the horizontal coordinate estimates. The sample means of these horizontal coordinate estimates are the best horizontal location estimates. After mapping each plateau, our method takes as the best structural index the one that yields the minimum correlation between the total-field anomaly and the estimated base level over each plateau. By using the estimated structural index for each plateau, our approach extracts the vertical coordinate estimates over the corresponding plateau. The sample means of these estimates are the best depth location estimates in our method. When applied to synthetic data, our method yielded good results if the bodies produce weak- and mid-interfering anomalies. A test on real data over intrusions in the Goiás Alkaline Province, Brazil, retrieved sphere-like sources suggesting 3D bodies.

Correct structural index defined by base level estimates in Euler deconvolution

2017 ◽  
Author(s):  
Felipe Ferreira de Melo ◽  
Valeria Cristina Ferreira Barbosa
Keyword(s):  
Euler Deconvolution ◽  
Structural Index ◽  
Base Level

New criterion for selecting the structural index in Euler deconvolution

1997 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Euler Deconvolution ◽  
Structural Index ◽  
New Criterion

Peripheral representation of antennal orientation by the scapal hair plate of the cockroach Periplaneta americana

2001 ◽  
Vol 204 (24) ◽  
pp. 4301-4309 ◽  
Author(s):  
J. Okada ◽  
Y. Toh
Keyword(s):  
Single Unit ◽  
Periplaneta Americana ◽  
Vertical Component ◽  
Horizontal Component ◽  
Vertical Position ◽  
Horizontal Position ◽  
Joint Movement ◽  
Basal Segment ◽  
Dynamic Phase ◽  
Hair Sensilla

SUMMARY Arthropods have hair plates that are clusters of mechanosensitive hairs, usually positioned close to joints, which function as proprioceptors for joint movement. We investigated how angular movements of the antenna of the cockroach (Periplaneta americana) are coded by antennal hair plates. A particular hair plate on the basal segment of the antenna, the scapal hair plate, can be divided into three subgroups: dorsal, lateral and medial. The dorsal group is adapted to encode the vertical component of antennal direction, while the lateral and medial groups are specialized for encoding the horizontal component. Of the three subgroups of hair sensilla, those of the lateral scapal hair plate may provide the most reliable information about the horizontal position of the antenna, irrespective of its vertical position. Extracellular recordings from representative sensilla of each scapal hair plate subgroup revealed the form of the single-unit impulses in response to hair deflection. The mechanoreceptors were characterized as typically phasic-tonic. The tonic discharge was sustained indefinitely (>20 min) as long as the hair was kept deflected. The spike frequency in the transient (dynamic) phase was both velocity- and displacement-dependent, while that in the sustained (steady) phase was displacement-dependent.

3. On the Figures of Equilibrium of Liquid Films

1869 ◽  
Vol 6 ◽  
pp. 76-78
Author(s):  
David Brewster
Keyword(s):  
Soap Solution ◽  
Liquid Films ◽  
Vertical Position ◽  
Soap Bubble ◽  
Horizontal Position ◽  
Soap Films ◽  
Figures Of Equilibrium ◽  
New Phenomena

In repeating some of the experiments of Professor Plateau, described in seven interesting memoirs published in “The Transactions of the Belgian Academy,” and in prosecuting his own experiments on the colours of the soap-bubble, the author of this paper observed several new phenomena which may have escaped the notice of the Belgian philosopher.Professor Plateau has described and drawn the beautiful systems of soap-films, obtained by lifting from a soap solution a cube made of wires about one and a half inch long. This system is a polyhedron, composed of twelve similar films stretching from the wires, and united to a plane quadrangular film in the centre. When this vertical film was blown upon, M. Von Rees observed that it was reduced to a line, and then reproduced in a horizontal position, from which it could be blown again into a vertical position.

Tip-Over Stability Analysis for a Wheeled Mobile Manipulator

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Shuai Guo ◽  
Tao Song ◽  
Fengfeng (Jeff) Xi ◽  
Richard Phillip Mohamed
Keyword(s):  
Stability Analysis ◽  
Path Planning ◽  
Static Load ◽  
System Stability ◽  
Mobile Manipulator ◽  
Inertial Forces ◽  
Horizontal Position ◽  
Reaction Forces ◽  
Simulation Results

A method is presented for tip-over stability analysis of a wheeled mobile manipulator. A wheeled mobile manipulator may tip over resulting from its operation. In this study, first a Newton–Euler formulation is applied to formulate the manipulator’s reaction forces and moments exerted onto the mobile platform. Tip-over criterion is derived to judge the system stability. Three load and motion analyses are carried on. The first static load deals with links and payload to show the effect of the horizontal position of the system’s center of gravity (CG). The second and third are the inertial forces resulting from joint speeds and accelerations, respectively. Case study is path planning with tip-over criterion result which can make the system stable along the path. The simulation results demonstrate the effectiveness of the proposed method.

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