A comparative performance of least-square method and very fast simulated annealing global optimization method for interpretation of self-potential anomaly over 2-D inclined sheet type structure

Inversion of self-potential anomaly for 2-D inclined sheets of infinite horizontal extent has been studied. Least-square inversion and very fast simulated annealing global optimization has been used to model the five parameters of self potential anomaly. The method of least square and very fast simulated annealing global optimization method is compared and analyzed. Very fast simulated annealing can model the noisy and field data of self potential anomaly very precisely than linear inversion technique. However, time taken by very fast simulated annealing inversion is larger than linearized inversion. The comparative analysis has been done on synthetic data (noise free and noisy) and two field data from Bavarian woods anomaly, Germany and Surda anomaly, India to show the efficacy of both the methods. The estimated parameters were compared with those from previous studies using various global optimization algorithms, mainly neural network, genetic algorithm and particle swarm optimization on the same field data sets. It can be concluded that the global optimization algorithms considered in this study were able to yield compatible solutions with those from least-square methods. The present global optimization method is in good agreement with the other global optimization methods in terms of results and computation time.     

复杂条件二维重力场及重力张量场空间波数域正演方法

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。     

Forward and inverse self-potential modeling: a new approach

Software has been designed for forward and inverse modeling of natural self-potential (SP) fields which allows simulating the geoelectric patterns simultaneously for up to 29 sheet-like and prismatic electrostatically polarized conductors. The cross sections for a number of ore fields obtained by inversion with the new SPI-SV code (self-potential inversion, Siberian version) have been corroborated by later drilling and are consistent with reference geologic sections used in algorithm testing. SPI-SV simulation can provide high-quality assessment of mineral deposits and, furthermore, allows approaching global-scale investigation into the natural self potential of crust and mantle.     

一种基于磁异常梯度测深的电性分析方法

通过收集某地区地磁台记录的磁场,和当天另一地区地磁日变场数据,以某地的地磁台记录磁场作为参考地磁场,以另一地当天地磁日变场作为主要地磁场,采用傅立叶变换对时变地磁异常进行频谱分析。计算出二地的地磁场水平导数和某地磁响应参数及视电阻率,并对其进行了一维电磁测深反演,与在同一测深剖面施测的可控源音频大地电磁测深（CSAMT）反演结果对比分析,效果基本一致。采取这种计算方法,可有效地提取磁异常深部信息,为危机矿山深部找矿增加一种新的解释手段。     

A new approach to analysis of landslide slope stability

This paper is based on data from engineering-geological research on the landslide slopes of the Moscow River valley from the site of a proposed bridge crossing reconstruction. A method for delineating the slippage surface is suggested, which allows a more reliable evaluation of landslide stability and pressure for planning and decision-making purposes during the reconstruction of the bridge crossing, and an appropriate mitigation strategy.     

First-order analysis of deformation of a thrust sheet moving over a ramp

John L. Rich introduced the revolutionary concept that many folds in the Appalachian Mountains can be explained as superficial structures formed by passive translation of thrust blocks over ramps in detachment surfaces. The amount of layer-parallel shortening can be negligible in the formation of these folds. Rich primarily was concerned with an explanation for the Powell Valley anticline, in the southern Appalachians, but the essential kinematic features of his model of folding have been verified in other folds in the Appalachians, in the Canadian Rockies, in the Idaho-Wyoming thrust belt, and in the Pyrenees. In this paper we solve the boundary-value problem for an idealized thrust block moving over a detachment surface and ramp with zero drag, and produce theoretical fold forms in the thrust block that closely resemble those in Rich's idealized model. The anticline is narrow and rounded if the translation is small, and broad and flat-topped if the translation is large. The limbs of the anticline are symmetric. We also incorporate drag along the ramp part of the detachment surface in order to derive a possible explanation for the asymmetry of dips of the two limbs of the Powell Valley anticline. We show that drag can explain the asymmetry, particularly if drag between relatively competent rocks in opposition at the ramp caused an initial anticline to form as the thrust block began to move, and then drag reduced markedly as relatively soft shales at the base of the block were thrust over competent rocks in the ramp. The existence of the initial anticline should be reflected in asymmetry of the two limbs and in a bulge at the distal edge of the broad anticline.     

Model of the MAGSAT magnetic anomaly field over Europe using spherical cap harmonic analysis

Based on the MAGSAT magnetic anomaly fields over Europe and the adjacent areas spherical cap models have been derived. The method of spherical cap harmonic analysis, due to Haines (1985), has been applied for the modelling of the MAGSAT magnetic anomalies. The data set used in the analysis included the 1 ° × 1 ° gridded values of the MAGSAT anomaly fields between latitudes ϑ = 6 ° to 60 °N and longitudes λ = 19 °W to 70 °E. The pole of the cap is at ϑ = 33 °N and λ = 26 °E and its half-angle is 40 ° . The maximum index (K_m) of the model is 18 and the total number of model coefficients is 361. A minimum wavelength corresponding to this index at the Earth's surface is ~ 1000 km. The RMS deviations between the calculated and observed values are ~ 4 nT for δX, ~ 3 nT for ΔY and 3,5 nT for ΔZ respectively. The spherical cap harmonic model was used for the construction of magnetic anomaly maps for all components and at different altitudes.     

一种求地球化学异常下限的新方法——含量排列法

地球化学异常下限的确定,在矿产勘查和资源预测中占有十分重要的地位。传统计算地球化学异常下限的方法,要求数据服从正态分布或对数正态分布,而且存在计算依据不充分的问题。这里在研究背景和异常关系的基础上,提出了一种求地球化学异常下限的新方法,即含量排列法。该方法不要求数据服从正态分布或对数正态分布,直接用原始数据求异常下限,方法简便。用此方法对广东始兴地区化探数据进行处理,取得了较好的效果。     

A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd.     

CURVGRAV-GUI: a graphical user interface to interpret gravity data using curvature technique

CURVGRAV-GUI is an open source software that was developed to interpret gridded gravity data by using curvature technique. It was developed using C# language with Microsoft.NET Framework 4.0. This program calculates the critical and extreme points, and estimates the depths of source bodies at this points. Besides, CURVGRAV-GUI processes gravity data by using minimum curvature, one of the attributes of curvature, and detects the subsurface lineaments. It is a user-friendly application that can display obtained solutions and gravity data thanks to image and scatter maps. CURVGRAV-GUI was designed to develop both synthetic and field applications. Additionally, the β constant, a parameter related to the source geometry, was examined for different source types such as sphere, horizontal and vertical cylinder and thin vertical fault. This program was tested by using two synthetic model applications. In the first synthetic model application, it was used a complex synthetic model consisting of three sphere and a horizontal cylinder located at the different depths. In the second synthetic model application, a graben model consisting of two thin vertical fault was used. Finally, the performance of the CURVGRAV-GUI was tested with using a real gravity data belonging to Kozakli-Central Anatolia region, Turkey. Very successful results were obtained for both synthetic and field data. Earth scientist can use CURVGRAV-GUI for educational experiments.     

Drought characterization using a new copula-based trivariate approach

Meteorological drought is a natural climatic phenomenon that occurs over various time scales and may cause significant economic, environmental and social damages. Three drought characteristics, namely duration, average severity and peak intensity, are important variables in water resources planning and decision making. This study presents a new method for construction of three-dimensional copulas to describe the joint distribution function of meteorological drought characteristics. Using the inference function for margins, the parameters for six types of copulas were tested to select the best-fitted copulas. According to the values of the log-likelihood function, Galambos, Frank and Clayton were the selected copula models to describe the dependence structure for pairs of duration–severity, severity–peak and duration–peak, respectively. Trivariate cumulative probability, conditional probability and drought return period were also investigated based on the derived copula-based joint distributions. The proposed model was evaluated over the observed data of a Qazvin synoptic station, and the results were compared with the empirical probabilities. For measuring the model accuracy, R ², root mean square error (RMSE) and the Nash–Sutcliffe efficiency (NSE) criteria were used. Results indicated that R ², RMSE and NSE were equal to 0.91, 0.098 and 0.668, respectively, which demonstrate sufficient accuracy of the proposed model. Drought probabilistic characteristics can provide useful information for water resource planning and management.     

An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters

A very fast and efficient approach to self-potential (SP) data inversion for ore exploration has been developed. This approach is based on Tikhonov regularization and the conjugate gradient method, and simultaneously inverts for the depth (z), electric dipole moment (k), and angle of polarization (θ) of a buried anomalous body from SP data measured along a profile. This inversion algorithm works iteratively, and solves for z and k in the logarithmic-space (log(z) and log(k)), and solves for θ in the linear-space (non-logarithmic). It is found that the original inversion formulation that uses the model parameters themselves (z, k and θ) is unstable and divergent. It is also found that the inversion formulation that uses the logarithm of the model parameters (log(z), log(k) and log(θ)) is unstable and divergent. Rather, the new inversion scheme that is based on the aforementioned mixed log-linear combination of the model parameters (log(z), log(k), and θ) overcomes and eliminates the mentioned instability and divergence problems. The sensitivity analysis and numerical experiments investigated have indicated that the new approach has a far better and far more optimized minimization search direction. This proposed technique fits the observed data by some geometrically simple body in the restricted class of vertical cylinder, horizontal cylinder, and sphere models. The applicability of the algorithm has been demonstrated on various reliable synthetic data sets with and without noise. The algorithm has been carefully and successfully applied to six real data examples, with ore bodies buried in different complex geologic settings and at various depths in the subsurface. The method is shown to be highly applicable for mineral exploration, and is of particular value in cases where the SP observed data is due to ore body embedded in the subsurface. On average, it took about 40 s of computation (not CPU) time on a 1 GHz PC.     

边坡可靠度分析的一种新的优化求解方法

介绍了Low & Tang提出的一种新的可靠度优化求解方法,并将之用于边坡可靠度分析中：该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,直接在变量的原始空间内搜索边坡的最小可靠指标和概率临界滑面,可采用任何合适的约束优化方法进行求解,方法清晰简洁。边坡可靠度分析常用的滑面有2个：最小安全系数（变量均值处）对应的确定性临界滑面和最小可靠指标对应的概率临界滑面,但这2个滑面在有些情况下差别较大,Hassan & Wolff提出了一种简化方法可以方便地获得概率临界滑面,但由于方法简单,受到质疑。通过一系列算例分析,优化求解方法得到的概率临界滑面和Hassan & Wolff的简化方法滑面非常接近,显示了简化方法的有效性,值得在工程实践中推广。     

A new approach to time-load-deformation-stress hypersurface of rocks to stability analysis of underground openings

The most important developments in rock engineering are about time-dependent deformation behavior of rocks under different loads. Many studies have been done for the purpose of identifying mathematically time-load-deformation (TLD) characteristics of the rocks. These studies have made an important contribution to the research on the stability of constructions built in rock masses, and rock material is the main part of the rock mass in which the engineering constructions. When considered from this point of view, the time-dependent deformation behavior of the rocks under different loads is important to determine unstable conditions of the rock constructions in the long term. Researches in rock masses use surfaces based on TLD data. On the other hand, the strength of the rock is also part of these analyzes. The new model developed in this study has four variables such as time, load, deformation, and strength. Therefore, TLD surfaces developed for time-load-deformation has been associated with another variable and three-component (TLD) surfaces eventually transformed into four-component (time-load-deformation-strength; TLDS) hypersurfaces. Hypersurfaces, which illustrate new TLDS behaviors of the rocks, developed in underground openings in different rock constructions in different areas. It is thought that the TLDS hypersurfaces will especially be contributed to the numerical modeling studies of rock construction analysis.     

A new approach to the three-dimensional quantification of angularity using image analysis of the size and form of coarse aggregates

This paper describes a system for the acquisition and analysis of 3D data from the surfaces of coarse aggregate particles. The technique uses laser triangulation to acquire data from the upper hemispheres of particles passing along a conveyor belt. Methods of determining particle size and form in three dimensions are described and a new approach to the quantification of angularity is presented. The algorithm uses mathematical morphology to provide a geometrically meaningful interpretation of particle shape. The relative advantages of 2D and 3D analysis of aggregate particles are discussed, and results are presented which demonstrate the validity of this approach.     

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

In this paper we report the results of a study using small angle and ultra-small angle neutron scattering techniques (SANS and USANS) to examine the evolution of carbonates during contact metamorphism. Data were obtained from samples collected along two transects in the metamorphosed Hueco limestone at the Marble Canyon, Texas, contact aureole. These samples were collected from the igneous contact out to ∼1700 m. Scattering curves obtained from these samples show mass fractal behavior at low scattering vectors, and surface fractal behavior at high scattering vectors. Significant changes are observed in the surface and mass fractal dimensions as well as the correlation lengths (pore and grain sizes), surface area to volume ratio and surface Gibbs Free energy as a function of distance, including regions of the aureole outside the range of classic metamorphic petrology. A change from mass-fractal to non-fractal behavior is observed at larger scales near the outer boundary of the aureole that implies significant reorganization of pore distributions early in the metamorphic history. Surface fractal results suggest significant smoothing of grain boundaries, coupled with changes in pore sizes. A section of the scattering curve with a slope less than −4 appears at low-Q in metamorphosed samples, which is not present in unmetamorphosed samples. A strong spike in the surface area to volume ratio is observed in rocks near the mapped metamorphic limit, which is associated with reaction of small amounts of organic material to graphite. It may also represent an increase in pore volume or permeability, suggesting that a high permeability zone forms at the boundary of the aureole and moves outwards as metamorphism progresses. Neutron scattering data also correlate well with transmission electron microscopic (TEM) observations, which show formation of micro- and nanopores and microfractures during metamorphism. The scattering data are, however, quantifiable for a bulk rock in a manner that is difficult to achieve using high-resolution imaging (e.g. TEM). Thus, neutron scattering techniques provide a new approach to the analysis and study of metamorphism.     

A geometric approach to two-dimensional finite strain compatibility: interpretation and review

The purpose of this paper is to collect, clarify, augment and modify the authors' previous work on the subject of finite strain compatibility. The derivations of the fundamental equations are reviewed so that the geometric meaning of each step can be explained. Besides providing a basis for the geological interpretations of the equations, these derivations also lead to a useful new form of the strain compatibility equations.We begin by showing that compatibility is a geometric property of continuous and smooth coordinate grids, and we derive and explain the coordinate grid compatibility equations. We then use the fact that every finite deformation may be described by two coordinate grids to derive finite strain compatibility equations in principal coordinates and Cartesian coordinates. The resulting strain compatibility equations are not easily solved for general strain fields in any coordinate system. Nonetheless, we show that many common geological strain patterns have simple geometries for which the compatibility equations can be interpreted. For example, if a deformation has constant strain in one direction, as most shear zones do, then compatibility provides an iterative method for determining the strain throughout the deformed region if the strain is initially known at any one point. Some of the other strain geometries to which we apply compatibility in this paper include simple shear, inhomogeneous pure shear, parallel and similar folding.     

A new probabilistic approach to analysis of compressive strength test data of rock specimens

In this paper, a new probabilistic approach has been proposed for dealing with the wide scatter in laboratory values of compressive strength test (uni-axial and tri-axial compressive strength tests) data of rock specimens. This wide scatter is essentially due to randomness in number as well as orientation of micro-cracks. In the proposed methodology, Stanley's approach, which uses Weibull's theory based on the weakest link model, has been modified to analyse the compressive strength test data. Stanley's approach is applicable to poly-axial tensile stress conditions. Design of all underground excavations requires, as input data, uni-axial compressive strength and the strength under poly-axial stress conditions. Data from compressive strength tests have been analysed using Weibull's theory and the proposed approach. Corresponding cumulative distribution functions of the state variable, i.e., the applied stress level, have been obtained and goodness-of-fit tests performed to check the fitness of test data to these statistical distributions. These cumulative distribution functions have been subsequently invoked to correlate the applied stress level at failure and the associated risk of failure. The analysis finds its application in specifying the design strength of rocks or rock masses for a permissible probability of failure.