Depth estimation from downward continuation: An entropy-based approach to normalized full gradient

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. J33-J42
Author(s):  
Giovanni Florio ◽  
Maurizio Fedi
Keyword(s):  
Synthetic Data ◽  
Depth Estimation ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Depth Estimate ◽  
Ordnance Survey ◽  
Normalized Full Gradient ◽  
Gradient Based ◽  
Specific Source ◽  
Source Level

The normalized full gradient is based on the noticeable stability of the modulus of the analytic signal of downward potential fields. We have developed a new approach to the study of the normalized full gradient, based on assessing the entropy of the normalized modulus of the analytic signal at each level of continuation. The increased disorder of progressively downward continued fields implies an increase of the computed entropy. However, a local decrease of the entropy is expected at the source level, where the field gets singular, as entropy decreases when the information is concentrated. Thus, our method is based on a simple search for a minimum of the computed entropy versus depth curve, and the estimated depth will be that at which the minimum is attained. The method is sensitive to interference and other types of noise, and specific strategies to deal with these limitations are defined and tested on synthetic data. The depth estimate is obtained without the assumption of a specific source shape. The depth could correspond to the top or center in case of a simple, one-point source, or it may be related to an intermediate depth between the source top and its center in case of a finite, general source. We applied this method to real magnetic data from an unexploded ordnance survey, and it could verify a rather accurate depth-to-source estimate when compared with excavation results.

Functional approach to the search for quasi-optimal value of regularization parameter in downward continuation of potential field

Geophysics ◽  
2021 ◽  
pp. 1-34
Author(s):  
Roland Karcol ◽  
Roman Pašteka
Keyword(s):  
Regularization Parameter ◽  
Gravity Data ◽  
Synthetic Data ◽  
Downward Continuation ◽  
Magnetic Data ◽  
Problem Solution ◽  
Ordnance Survey ◽  
Boundary Estimation ◽  
Optimal Value ◽  
Regional Gravity

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.

Automatic 3-D interpretation of potential field data using analytic signal derivatives

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Nicole Debeglia ◽  
Jacques Corpel
Keyword(s):  
Signal Amplitude ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Practical Implementation ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Second Derivatives ◽  
Gravity And Magnetic Data ◽  
Derivatives Of

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.

scholarly journals Estimating Effectiveness of Some Methods for Detecting Edge of Potential Field Sources

2020 ◽  
Vol 36 (4) ◽  
Author(s):  
Pham Thanh Luan ◽  
Le Thi Sang ◽  
Vu Duc Minh ◽  
Ngo Thi To Nhu ◽  
Do Duc Thanh ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Tilt Angle ◽  
Northeast China ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Detection Methods ◽  
Magnetic Data ◽  
Horizontal Gradient ◽  
North Vietnam ◽  
Gradient Amplitude

This paper presents a comparative study of effectiveness of edge detection methods such as total horizontal gradient, analytic signal amplitude, tilt angle, gradient amplitude of tilt angle, theta map, horizontal tilt angle, tilt angle of total horizontal gradient, tilt angle of analytic signal, improved theta map, and total horizontal gradient of improved tilt angle. The effectiveness of each method was estimated on synthetic magnetic data and synthetic gravity anomaly data with and without noise. The obtained results show that the tilt angle of gradient amplitude can detect all the edges more clearly and precisely. The applicability of each method is demonstrated on the aeromagnetic anomaly data from the Zhurihe region of Northeast China, and Bouguer gravity anomaly data from a region of North Vietnam. The results computed by the tilt angle of horizontal gradient were also in accord with the geologic structures of the areas.

The Use of Euler Deconvolution Technique in the Estimation of Depth to Magnetic Source Bodies around the Schist Belt Parts of Kano State, Nigeria

2021 ◽  
Vol 14 (1) ◽  
pp. 19-23
Keyword(s):  
Depth Estimation ◽  
Magnetic Survey ◽  
Schist Belt ◽  
Euler Deconvolution ◽  
Depth Estimate ◽  
Paper Detail ◽  
Magnetic Source ◽  
Deconvolution Technique ◽  
Proton Precession Magnetometer ◽  
Ground Magnetic

Abstract: Depth estimation of magnetic source bodies in parts of the Schist Belt of Kano, using Euler Deconvolution is presented in this paper. Detail ground magnetic survey was carried out using SCINTREX proton precession magnetometer to produce the Total Magnetic Intensity (TMI) map and consequently the residual map. The TMI ranges from 34,261 nT to 34,365 nT, while the residual field ranges from -160 nT to 115 nT. The depth estimate for contacts ranges from 6.5 m to 39.8 m, while that of dyke ranges from 8.9 m to 51.3 m. The depth estimation presented in this work is compared with the results of aeromagnetic study carried out in the same area and found to agree fairly well. Further, this also ensures the validity of aeromagnetic investigation in such applications. Keywords: Contacts, Dykes, Euler Deconvolution, Schist Belt. PACS: 91.25.F and 91.25.Rt.

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.

Developing a Novel Stereovision Scheme for Improving Accuracy of Depth Estimation in Robotic Vision Systems

2015 ◽  
Vol 764-765 ◽  
pp. 1227-1233
Author(s):  
Kuan Yu Chen ◽  
Chien Hung Chen ◽  
Cheng Chin Chien
Keyword(s):  
Focal Length ◽  
Rapid Development ◽  
Three Dimensional ◽  
Depth Estimation ◽  
Depth Interval ◽  
Stereo Images ◽  
Depth Estimate ◽  
Parameter Matching ◽  
Improving Accuracy ◽  
Deformation Coefficient

Acquiring three-dimensional data from a pair of stereo images is called stereovision that has been studied by researchers for decades. However, most of the previous studies on this topic focused on establishment of stereovision parameter matching and made conclusions on the premise of fixed focus. With the rapid development of multimedia technology, varifocal digital cameras have been widely used in many robotic applications recently. In general, error in the depth estimate becomes bigger when the focus and aperture is unknown or not fixed. For that reason, a three-stage framework is proposed in this paper to modify the conventional stereovision model for improving accuracy of depth estimation. The first stage is to modify the computational model of conventional stereovision for varifocal cameras. Then, the spacing of depth interval in non-uniform spacing of discrete depth levels can be altered, in particular, it is unaffected by changes in focal length. Finally, with considering the affine transformation, we add the deformation coefficient into the modified stereovision model for correcting three-dimensional affine deformations. Experimental results demonstrated that the depth estimation from stereo images using the proposed scheme was more accurate than conventional method.

2.5‐D inversion of frequency‐domain electromagnetic data generated by a grounded‐wire source

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1753-1768 ◽  
Author(s):  
Yuji Mitsuhata ◽  
Toshihiro Uchida ◽  
Hiroshi Amano
Keyword(s):  
Frequency Domain ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Statistical Criterion ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Gas Field ◽  
Data Set ◽  
Transient Electromagnetic

Interpretation of controlled‐source electromagnetic (CSEM) data is usually based on 1‐D inversions, whereas data of direct current (dc) resistivity and magnetotelluric (MT) measurements are commonly interpreted by 2‐D inversions. We have developed an algorithm to invert frequency‐Domain vertical magnetic data generated by a grounded‐wire source for a 2‐D model of the earth—a so‐called 2.5‐D inversion. To stabilize the inversion, we adopt a smoothness constraint for the model parameters and adjust the regularization parameter objectively using a statistical criterion. A test using synthetic data from a realistic model reveals the insufficiency of only one source to recover an acceptable result. In contrast, the joint use of data generated by a left‐side source and a right‐side source dramatically improves the inversion result. We applied our inversion algorithm to a field data set, which was transformed from long‐offset transient electromagnetic (LOTEM) data acquired in a Japanese oil and gas field. As demonstrated by the synthetic data set, the inversion of the joint data set automatically converged and provided a better resultant model than that of the data generated by each source. In addition, our 2.5‐D inversion accounted for the reversals in the LOTEM measurements, which is impossible using 1‐D inversions. The shallow parts (above about 1 km depth) of the final model obtained by our 2.5‐D inversion agree well with those of a 2‐D inversion of MT data.

First-arrival traveltime tomography based on the adjoint-state method

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCB1-WCB10 ◽  
Author(s):  
Cédric Taillandier ◽  
Mark Noble ◽  
Hervé Chauris ◽  
Henri Calandra
Keyword(s):  
Synthetic Data ◽  
Point Of View ◽  
Data Set ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Adjoint State ◽  
Gradient Based ◽  
First Arrival ◽  
State Method ◽  
Adjoint State Method

Classical algorithms used for traveltime tomography are not necessarily well suited for handling very large seismic data sets or for taking advantage of current supercomputers. The classical approach of first-arrival traveltime tomography was revisited with the proposal of a simple gradient-based approach that avoids ray tracing and estimation of the Fréchet derivative matrix. The key point becomes the derivation of the gradient of the misfit function obtained by the adjoint-state technique. The adjoint-state method is very attractive from a numerical point of view because the associated cost is equivalent to the solution of the forward-modeling problem, whatever the size of the input data and the number of unknown velocity parameters. An application on a 2D synthetic data set demonstrated the ability of the algorithm to image near-surface velocities with strong vertical and lateral variations and revealed the potential of the method.

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