NORMALIZED VERTICAL DERIVATIVES IN THE EDGE ENHANCEMENT OF MAXIMUM-EDGE-RECOGNITION METHODS IN POTENTIAL FIELDS

Geophysics ◽  
2021 ◽  
pp. 1-88
Author(s):  
Yingjie Zhu ◽  
wanyin wang ◽  
Colin Farquharson ◽  
Jinming Huang ◽  
Minghua Zhang ◽  
...  
Keyword(s):  
Extreme Values ◽  
Order Derivative ◽  
Magnetic Data ◽  
Recognition Method ◽  
Potential Field Data ◽  
First Order ◽  
Horizontal Derivative ◽  
Total Horizontal Derivative ◽  
Edge Recognition ◽  
Derivatives Of

Gravity and magnetic data have unique advantages for studying the lateral extents of geological bodies. There is a class of methods for edge recognition called the maximum-edge-recognition methods that use their extreme values to locate the edges of geological bodies. These methods include the total horizontal derivative, the analytic signal amplitude, the theta map, and the normalized standard deviation. These are all first-order derivative-based techniques. There are also higher-order derivative-based methods that are derived from the first-order filters, for example, the total horizontal derivative of the tilt angle. We present an edge recognition filter that is based on the idea of the normalized vertical derivatives of existing methods. For each maximum-edge-recognition method, we first calculate its nth-order vertical derivative and then use thresholding to locate its peaks. The peak values are subsequently normalized by the values of the original maximum-edge-recognition method. Testing on synthetic and real data shows that the normalized vertical derivatives of the maximum-edge-recognition methods have higher accuracy, better lateral resolution and are more interpretable than existing techniques, and thus are a worthwhile addition to the set of edge-detection tools for potential-field data.

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.

NAV-Edge: Edge detection of potential-field sources using normalized anisotropy variance

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. J43-J53 ◽  
Author(s):  
Heng Lei Zhang ◽  
Dhananjay Ravat ◽  
Yára R. Marangoni ◽  
Xiang Yun Hu
Keyword(s):  
Edge Detection ◽  
Potential Field ◽  
Field Data ◽  
Gaussian Function ◽  
Magnetic Data ◽  
Horizontal Gradient ◽  
Potential Field Data ◽  
Variance Method ◽  
Detection Algorithms ◽  
Total Horizontal Derivative

Most existing edge-detection algorithms are based on the derivatives of potential-field data, and thus, enhance high wavenumber information and are sensitive to noise. The normalized anisotropy variance method (NAV-Edge) was proposed for detecting edges of potential-field anomaly sources based on the idea of normalized standard deviation (NSTD). The main improvement over the balanced, windowed normalized variance method (i.e., NSTD) used for similar purposes was the application of an anisotropic Gaussian function designed to detect directional edges and reduce sensitivity to noise. NAV-Edge did not directly use higher-order derivatives and was less sensitive to noise than the traditional methods that use derivatives in their calculation. The utility of NAV-Edge was demonstrated using synthetic potential-field data and real magnetic data. Compared with several existing methods (i.e., the curvature of horizontal gradient amplitude, tilt angle and its total-horizontal derivative, theta map, and NSTD), NAV-Edge produced superior results by locating edges closer to the true edges, resulting in better interpretive images.

scholarly journals Simultaneous Determination of Prasugrel and Aspirin by Second Order and Ratio First Order Derivative Ultraviolet Spectrophotometry

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shahabuddin N. Alvi ◽  
Mehul N. Patel ◽  
Prakash B. Kathiriya ◽  
Bhavna A. Patel ◽  
Shraddha J. Parmar
Keyword(s):  
Simultaneous Determination ◽  
Second Order ◽  
Order Derivative ◽  
Zero Crossing ◽  
First Order ◽  
Spectrophotometric Methods ◽  
Relative Standard ◽  
Derivative Method ◽  
Derivatives Of

Two simple, accurate, and precise UV derivative spectrophotometric methods for the simultaneous determination of Prasugrel and Aspirin in synthetic mixture form have been developed. The first method involves measurement of second order derivative spectra of Prasugrel and Aspirin. The zero crossing wavelengths 267.62 nm and 252.40 nm were selected for estimation of Prasugrel and Aspirin, respectively. In the second method, the first order derivatives of ratio spectra were calculated and used for the determination of Prasugrel and Aspirin by measuring the peak intensity at 268 nm and 290 nm, respectively. The methods were validated as per the ICH guideline Q2 (R1). Beer’s law is followed in the range of 5–45 μg/mL for Prasugrel and 25–150 μg/mL for Aspirin by second order derivative method and 6–22 μg/mL for Prasugrel and 45–165 μg/mL for Aspirin by ratio first order derivative method. The recovery studies confirmed the accuracy of the methods. Relative standard deviations for repeatability and inter- and intraday assays were less than 2%. Hence, the described derivative spectrophotometric methods are simple, accurate, precise, and excellent alternatives to sophisticated chromatographic techniques and can be potentially used for the simultaneous determination of Prasugrel and Aspirin in combined dosage form.

scholarly journals The Spatial Different Order Derivative Method of Gravity and Magnetic Anomalies for Source Distribution Inversion

2021 ◽  
Vol 13 (5) ◽  
pp. 964
Author(s):  
Yanbo Ming ◽  
Guoqing Ma ◽  
Lili Li ◽  
Jiangtao Han ◽  
Taihan Wang
Keyword(s):  
Magnetic Measurements ◽  
Magnetic Anomalies ◽  
Source Distribution ◽  
Order Derivative ◽  
Potential Field Data ◽  
Characteristic Value ◽  
Gravity And Magnetic ◽  
Derivative Method ◽  
Derivatives Of ◽  
Different Order

Gravity and magnetic measurements are common remote sensing strategies to obtain the property change of observed targets. Nowadays, the characteristic value of the derivatives of gravity and magnetic anomalies is commonly used to detect the source horizontal edge. We found that the horizontal coordinates of the characteristic value of different-order derivatives are not directly corresponding to the edge of the source, which varies with the depth and size of the source. The spatial different-order derivative (SDD) method of gravity and magnetic anomalies was developed, and we proved that the spatial intersection of different-order derivatives is corresponding to the location of the source, and used this feature to obtain horizontal location and depth of the source simultaneously. The model tests proved that the SDD method has high accuracy and strong anti-noisy. According to the corresponding relationship between the potential field data and lithology, we used the SDD method to delineate the potential metalorganic area in the survey region, which provides the basis for subsequent exploration.

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

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.

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