Extreme Points Method Research Articles

Early‐Precambrian crystalline basement beneath the Upper Yangtze Block from regional aeromagnetic anomalies: Depth from extreme points approach

AbstractAlthough the early‐Precambrian crystalline basement is now only sporadically exposed in the northern and south‐western parts of the Yangtze Block, it is supposed to have a widespread distribution beneath its Neoproterozoic and Phanerozoic covers. Here we present results of regional aeromagnetic data processing in consideration of remanent magnetization to investigate the spatial distribution of the early‐Precambrian basement buried deep under the Upper Yangtze Block and surrounding areas. The direct analytic signal amplitude of the aeromagnetic anomalies, which is less affected by the magnetization direction, reveals a broader basement below the Sichuan Basin, extending far north to the Micang Mountain. A comparison between the direct analytic signal amplitude with the reduction to the pole aeromagnetic anomalies indicates that possible remanent magnetization exists beneath the Micang Mountain near the boundary between the Qinling Orogen and Sichuan Basin. The automatic depth from extreme points transform is then performed on the direct analytic signal amplitude to estimate the depth to the early‐Precambrian crystalline basement. A synthetic model of a magnetic interface with remanent magnetization and random noise shows that the depth from extreme points method is able to resolve variable basement depths. Application of the depth from extreme points method to the direct analytic signal amplitude of the Upper Yangtze Block presents meaningful results about the early‐Precambrian crystalline basement undulations. It is shallow and uplifted beneath the Sichuan Basin, extending north to the Qinling‐Dabie Orogen, probably corresponding to the ancient Chuanzhong palaeo‐uplift. Although it gradually deepens to the east, the deepest basement is buried under the Jiangnan Orogen, which is likely associated with the collision‐induced crustal thickening between the Yangtze and Cathaysia blocks during the assembly of the Columbia supercontinent. Large gas fields around the Sichuan Basin are found at the slopes or depressions between basement uplifts, indicating that the deep marine carbonate rocks in the south and east of Sichuan Basin, particularly those located at the slopes or depressions between ancient basement uplifts, are favourable targets for further petroleum exploration.

Geophysical Characterisation and Oil–Gas Resource Analysis of the Southern Huaying Mountain Fault Zone, Sichuan Basin, China

As the west rim of an ejective fold zone, the Huaying Mountain fault zone (HMFZ) in the eastern Sichuan Basin (SB) plays an important role in the tectonic evolution of the SB. The distribution and characteristics of HMFZ are strongly associated with tectonic activities and have greatly impacted the distribution of oil and gas reservoirs. However, its distribution and characteristics have remained poorly understood due to a lack of geophysical data, especially areal gravity survey and magnetotellurics (MT) survey, which are admittedly advantageous for detecting the edges of geological structures. Therefore, we carried out the ground geophysical surveys that areal gravity survey and MT survey, and acquired 1:250,000-scale real gravity data and MT data for the first time in this area. Optimized edge-detection methods were adopted to process the areal gravity data, allowing us to characterize the planar distribution of faults more reliably and convincingly. We found that the southern HMFZ is well developed and primarily trends in NNE and NE, whereas the subordinate faults trend in N-S and W-E. Vertical information for the faults extracted using the improved depth from the extreme points method revealed that the fault dominantly dipped to the SE, which was consistent with the results of MT inversion. Based on the spatial distribution of the faults, we further discussed the gravity anomaly, fault distribution, Luzhou palaeo uplift, and the distribution and characteristics of oil-gas resources, and found the convincing evidence to analysis the distribution of oil and gas resources in this region.

Improving the Performance of an Associative Classifier in the Context of Class-Imbalanced Classification

Class imbalance remains an open problem in pattern recognition, machine learning, and related fields. Many of the state-of-the-art classification algorithms tend to classify all unbalanced dataset patterns by assigning them to a majority class, thus failing to correctly classify a minority class. Associative memories are models used for pattern recall; however, they can also be employed for pattern classification. In this paper, a novel method for improving the classification performance of a hybrid associative classifier with translation (better known by its acronym in Spanish, CHAT) is presented. The extreme center points (ECP) method modifies the CHAT algorithm by exploring alternative vectors in a hyperspace for translating the training data, which is an inherent step of the original algorithm. We demonstrate the importance of our proposal by applying it to imbalanced datasets and comparing the performance to well-known classifiers by means of the balanced accuracy. The proposed method not only enhances the performance of the original CHAT algorithm, but it also outperforms state-of-the-art classifiers in four of the twelve analyzed datasets, making it a suitable algorithm for classification in imbalanced class scenarios.

An Efficient Multi-Label SVM Classification Algorithm by Combining Approximate Extreme Points Method and Divide-and-Conquer Strategy

Excessive time complexity has severely restricted the application of support vector machine (SVM) in large-scale multi-label classification. Thus, this paper proposes an efficient multi-label SVM classification algorithm by combining approximate extreme points method and divide-and-conquer strategy (AEDC-MLSVM). The AEDC-MLSVM classification algorithm firstly uses the approximate extreme points method to obtain the representative set from the multi-label training data set. While persisting almost all the useful information of multi-label training set, representative set can effectively reduce the scale of multi-label training set. Secondly, to acquire an efficient multi-label SVM classification model, the SVM based on the improved divide-and-conquer strategy is trained on the representative set, which will further improve the training speed and classification performance. The improvement is reflected in two aspects. (1) The improved divide-and-conquer strategy is applied to divide the representative set into subsets and this can ensure that each representative subset contains a certain number of positive and negative instances. This will avoid singular problems and overcome computation load imbalance problem. (2) The different error cost (DEC) method is applied to overcome the label imbalance problem. Effective experiments have proved that the training and testing speed of AEDC-MLSVM classification algorithm can be accelerated substantially while ensuring the classification performance.

Crustal structure and lateral variations in Moho beneath the Delhi fold belt, NW India: Insight from gravity data modeling and inversion

The Proterozoic Delhi fold belt (DFB) in NW India shows a prominent NNE-SSW trending gravity high, but its northward extension beneath Gangetic alluvium lack understanding. We model the gravity anomaly using radially averaged power spectrum, depth from extreme points (DEXP) method, wavelength filtering, 3D structural inversion to constrain crustal structure of the DFB. The radially averaged power spectrum analysis suggests three interfaces and the DEXP method indicates presence of a horizontal cylindrical source below the DFB. The 3D structural inversion shows depth variation from 39 to 46 km in the study region and presence of an upwarp below the DFB and Sandmata complex. Our modeling suggests that an underplated mafic material possibly a residual plume head produces gravity high. The transverse structure of DFB is absent beneath Gangetic alluvium and show notable westward deflection in line with the NW-SE trending Delhi-Sargodha ridge. The transverse DFB attains westward deflection possibly due to NW indentation and counterclockwise rotation of Indian plate after Himalayan collision in Eocene. With continued convergence, this DFB structural element at the leading edge of Indian peninsula got involved in flexural upwarp of underthrusting Indian plate beneath the Himalaya.

Testing the value of a multi-scale gravimetric analysis in characterizing active fault 2 geometry at hypocentral depths: the 2016-2017 Central Italy seismic sequence

We report the results of a multidisciplinary investigation performed across the normal Quaternary faults that ruptured the surface during the August 24 (M w 6.0) and October 30 (M w 6.5), 2016 strong earthquakes in the Mt. Vettore-Mt. Bove areas, central Italy. Our aim is to test the effectiveness of the contribution of a multi-scale gravimetric analysis in characterizing seismogenic faults’ geometry at hypocen- tral depths on well-known outcropping faulty systems with known earthquake distribution. We adopted a multi-scale geophysical/geo- logical approach consisting in the comparison of gravity lineaments inferred by Multiscale Derivative Analysis with the Quaternary struc- tural setting mapped in the study area, the primary coseismic surface ruptures of the 2016-2017 sequence and the earthquakes’ epicentral distribution. Moreover, we performed a combined interpretation of 2D hypocentral sections of the 2016-2017 seismic sequences with im- ages resulting from the Depth from Extreme Points method, to infer the faults’ geometry at depth. Based on our results, the investigated NW-SE Mt. Vettore-Mt. Bove fault system is dipping 60°-70° westward. We also detected the splays of this primary fault and its blind an- tithetic NW-SE structure, dipping northeastward. In the Norcia basin we highlight two main faults bordering the basin with a dip of about 45°. The one edging the eastern side dips westward, whereas the fault edging the western side dips eastward. Thanks to our analysis we could identify and characterize the geometry of the Norcia and Vettore master faults, as well as other blind/buried and/or silent faults that are related to the 2016 seismogenic structure. Our results show the effectiveness of this approach in potentially high-hazard areas that are structurally poorly known.

Depth from extreme points method for gravity gradient tensor data

ABSTRACTThe ‘depth from extreme points’ method is an important tool to estimate the depth of sources of gravity and magnetic data. In order to interpret gravity gradient tensor data conveniently, formulas for the tensor data form regarding depth from the extreme points method were calculated in this paper. Then, all of the gradient tensor components were directly used to interpret the causative source. Beyond the gzz component, also the gxx and gyy components can be used to obtain depth information. In addition, the total horizontal derivative of the depth from extreme points of the gradient tensor can be used to describe the edge information of geologic sources. In this paper, we investigated the consistency of the homogeneity degree calculated by using the different components, which leads to the calculated depth being confirmed. Therefore, a more integrated interpretation can be obtained by using the gradient tensor components. Different synthetic models were used with and without noise to test the new approach, showing stability, accuracy and speed. The proposed method proved to be a useful tool for gradient tensor data interpretation. Finally, the proposed method was applied to full tensor gradient data acquired over the Vinton Salt Dome, Louisiana, USA, and the results are in agreement with those obtained in previous research studies.

Fast Extended One-Versus-Rest Multi-Label Support Vector Machine Using Approximate Extreme Points

Existing extended one-versus-rest multi-label support vector machine (OVR-ESVM) adopting non-linear kernel is seriously restricted by excessive training time when it is applied to large-scale data set. In order to overcome this problem, we improve the OVR-ESVM by introducing the principle of approximate extreme points and new approximate ranking loss to construct a novel extended OVR-ESVM using approximate extreme points (AEML-ESVM). By optimizing only on the representative set which can be acquired via adopting the approximate extreme points method, the AEML-ESVM classification algorithm can substantially shorten the training time and its classification performance is comparable to that of the OVR-ESVM classification algorithm. And it uses the new approximate ranking loss as empirical loss term to exploit label correlation of individual instance directly. Experimental study on three benchmark large-scale data sets illustrates that AEML-ESVM classification algorithm can reduce training time greatly and achieve comparable classification performance with OVR-ESVM classification algorithm. And it is also superior to the existing fast multi-label SVM classification algorithms in terms of classification performance and training time.

Inflection points of potential and polar moments of inertia of spherical celestial bodies

A simple existence criterion of inflection points of the potential in nonuniform spherical bodies is formulated. The criterion states that geometric loci of inflection points of the potential appear not only at density discontinuities but also at locations where the density ρ(r) is two-thirds of the average matter density $$\overline {\rho (r)}$$ inside a sphere of a specified radius. The criterion is universal and is fulfilled as for bodies with a continuous density distribution, and for bodies consisting of layers of finite thickness, and also in mixed models. The method of separation of extreme points method of separation of inflection points is given. The criterion is tested on many models including isothermal, polytropic, and isochronous spheres. The family of models within which there are no inflection points is specified. Testing of the method on the Earth’s model confirms its adequacy. A lower limit for the axial (polar) moment of inertia of a spherical body $$\frac{{I_{cr} }} {{M R^2 }} \approx 0.360$$ that separates planets and moons of the solar system into two groups is also obtained using the 3/2 criterion. The first and the largest group includes celestial bodies that have internal extreme points of the attraction force. The second group consists of planets and satellites that have no internal extreme points. These are the Moon, Io, Phobos, and, significantly, Mars.

Improving the local wavenumber method by automatic DEXP transformation

In this paper we present a new method for source parameter estimation, based on the local wavenumber function. We make use of the stable properties of the Depth from EXtreme Points (DEXP) method, in which the depth to the source is determined at the extreme points of the field scaled with a power-law of the altitude. Thus the method results particularly suited to deal with local wavenumber of high-order, as it is able to overcome its known instability caused by the use of high-order derivatives. The DEXP transformation enjoys a relevant feature when applied to the local wavenumber function: the scaling-law is in fact independent of the structural index. So, differently from the DEXP transformation applied directly to potential fields, the Local Wavenumber DEXP transformation is fully automatic and may be implemented as a very fast imaging method, mapping every kind of source at the correct depth. Also the simultaneous presence of sources with different homogeneity degree can be easily and correctly treated. The method was applied to synthetic and real examples from Bulgaria and Italy and the results agree well with known information about the causative sources.

A fast interpretation of self-potential data using the depth from extreme points method

We used a fast method to interpret self-potential data: the depth from extreme points (DEXP) method. This is an imaging method transforming self-potential data, or their derivatives, into a quantity proportional to the source distribution. It is based on upward continuing of the field to a number of altitudes and then multiplying the continued data with a scaling law of those altitudes. The scaling law is in the form of a power law of the altitudes, with an exponent equal to half of the structural index, a source parameter related to the type of source. The method is autoconsistent because the structural index is basically determined by analyzing the scaling function, which is defined as the derivative of the logarithm of the self-potential (or of its [Formula: see text]th derivative) with respect to the logarithm of the altitudes. So, the DEXP method does not need a priori information on the self-potential sources and yields effective information about their depth and shape/typology. Important features of the DEXP method are its high-resolution power and stability, resulting from the combined effect of a stable operator (upward continuation) and a high-order differentiation operator. We tested how to estimate the depth to the source in two ways: (1) at the positions of the extreme points in the DEXP transformed map and (2) at the intersection of the lines of the absolute values of the potential or of its derivative (geometrical method). The method was demonstrated using synthetic data of isolated sources and using a multisource model. The method is particularly suited to handle noisy data, because it is stable even using high-order derivatives of the self-potential. We discussed some real data sets: Malachite Mine, Colorado (USA), the Sariyer area (Turkey), and the Bender area (India). The estimated depths and structural indices agree well with the known information.