Inversion of magnetic anomalies due to isolated thin dike-like sources using artificial neural networks

A new approach is proposed to interpret magnetic anomalies caused by isolated thin dike-like causative targets. The approach is essentially based on utilizing artificial neural network (ANN) inversion for estimating the problem parameters. Particularly, the modular neural network (MNN) is used for the inversion process in order to quantitatively interpret the magnetic anomalies. The MNN inversion has been first tested on a synthetic data with and without random white Gaussian noise. The effect of random noise has been clearly investigated where it showed that the approach provided satisfactory results. Furthermore, three field examples have been inverted in order to investigate the applicability of the proposed approach. The results showed good agreement with the techniques that have been stated in the literatures.     

Interpretation of some magnetic bodies using neural networks inversion

Magnetic surveys have been used for mineral exploration where different data processing techniques were used to derive the parameters of causative targets. In this respect, the neural network (NN) technique was used to estimate the magnetic causative target parameters. Examples of NN inversion have been tested on synthetic examples where the NN was trained well using forward models of the vertical magnetic effect of a vertical sheet and a horizontal circular cylinder. Specifically, modular neural network (MNN) inversion has been used for the parameter estimation of the causative targets, where the sigmoid function was used as the activation function. The effect of random noise and the error estimation of the horizontal location have been analyzed. When NN is applied to real data, it estimates successfully the parameters of the causative targets such as burial depths, magnetic constants, and angle of polarization. Hilbert transform has been used to locate the source origin, which is important for the NN inversion. This approach has more advantages than the conventional data inversions in terms of its efficiency and flexibility. It also gives fast solutions. The MNN approach has been applied to the Kursk and Manjampalli anomalies, where the results were shown to be in good agreement with the other techniques published in the literature.     

Artificial neural network inversion of magnetic anomalies caused by 2D fault structures

A new approach is proposed to interpret magnetic anomalies caused by 2D fault structures. This approach is based on the artificial neural network inversion, utilizing particularly modular neural network algorithm. The inversion process is implemented to estimate the parameters of 2D fault structures where it has been verified first on synthetic models. The results of the inversion show that the parameters derived from the inversion agree well with the true ones. The analysis of noise has been studied in order to investigate the stability of the approach where it has been tested for contaminated anomalies with 5 and 10 % of white Gaussian noise. The results of the inversion provide satisfactory results even with contaminated signals.The validity of the approach has been demonstrated through real data taken from New South Wales, Australia. A comparable and satisfactory agreement is shown between the inversion results of the neural network and those from techniques published in literatures.     

Two-dimensional interpretation of gravity anomalies over sedimentary basins with an exponential decrease of density contrast with depth

The decrease of density contrast with depth in sedimentary basins is approximated by an exponential function. The anomaly equation, in frequency domain, of a prismatic model with an exponential density function is derived. The method has been extended to derive the Fourier transforms of the gravity anomalies of the sedimentary basin, wherein the basin is viewed as vertical prisms placed in juxtaposition. The gravity anomalies of the sedimentary basin are obtained by taking the inverse Fourier transforms. Filon’s method has been extended for calculating accurate inverse Fourier transforms. The accuracy of the method has been tested using a synthetic example. A combination of space and frequency domain methods have been developed for inversion of gravity anomalies over the sedimentary basin. The method has been applied to interpret one synthetic profile and one field profile over the Godavari basin. The method developed in this paper to calculate the inverse Fourier transforms yields continuous spectrum with accurate values. The maximum depth deduced from the gravity anomalies is of the same order as the depth encountered to the basement at the Aswaraopeta borewell.     

Gravity anomaly interpretation of 2D fault morphologies by means of nonplanar fault planes and exponential density contrast model: a space domain technique

Boundary faults associated with thick sedimentary basins are more often curved in cross section rather than planar. We develop a space domain-based automatic gravity inversion technique to quantify such listric fault sources from a set of observed gravity anomalies. The density contrast within the hanging wall of fault morphology is presumed to be known according to a prescribed exponential law. Furthermore, the fault plane is described by a polynomial function of arbitrary but specific degree, whose coefficients become the unknown parameters to be estimated from a set of observed gravity anomalies in addition to the thickness of the fault structure. Using a set of characteristic anomalies, the present inversion identifies approximate parameters pertaining to the origin of fault plane and depth to decollement horizon. Based on the errors between the observed and model gravity anomalies of the structure, the algorithm constructs and solves a system of normal equations to estimate the improvements in depth and coefficients of the polynomial in an iterative approach until one of the specified convergence criteria is fulfilled. The efficacy of the algorithm is shown with the analysis of gravity anomalies attributable to a synthetic model of a listric fault source in the presence of pseudorandom noise. Application of the proposed inversion technique on the observed gravity anomalies of the Ahri-Cherla master fault of the Godavari subbasin in India using the derived exponential density contrast model has yielded an interpretation that is consistent with the available/reported information.     

GUI based inversion code for automatic quantification of strike limited listric fault sources and regional gravity background from observed Bouguer gravity anomalies

A method coupled with a GUI based code in JAVA is developed in the space domain to simultaneously estimate the structures of strike limited listric fault sources and regional gravity background from a set of observed Bouguer gravity anomalies. The density contrast within the hanging wall of the structure is assumed to be varying continuously with depth based on a parabolic equation. The limiting surface of the fault plane is described with an exponential function. This method is automatic in the sense that it initializes both parameters of a strike limited listric fault source and regional gravity background from a set of observed Bouguer gravity anomalies and improves them iteratively until the modeled gravity anomalies fit the observed anomalies within the specified convergence criteria. The advantage of the code is that besides generating output in both ASCII and graphical forms it displays the animated versions of (i) the changes in model geometry, (ii) variation of each model parameter and misfit with iteration number, (iii) improvements in modeled gravity anomalies, and (iv) variation of density contrast with depth. The applicability of the code is demonstrated on both synthetic and real field gravity anomalies. In case of synthetic example pseudorandom noise is added to the residual gravity anomalies of the structure prior to inversion. The noisy anomalies are then inverted for the unknown parameters presuming (i) an ideal listric fault structure bounded by an exponential limiting surface with perfect flat top and bottom surfaces, (ii) non-ideal structure with uneven top and bottom surfaces with imperfect exponential limiting surface. Further, the robustness of the algorithm is exemplified by adding both regional gravity background and pseudorandom noise to the anomalies of the structure before inversion. In all cases, the interpreted parameters of the structure closely mimic the assumed parameters. The interpretation of gravity anomalies across the master fault of the Chintalpudi sub-basin in India has yielded information that is consistent with both DSS results and drilling information. The highlight of the code is that it can be used to interpret the gravity anomalies of listric fault sources even when the profile along which the interpretation is intended fails to bisect the strike length of the structure.     

规则体重力异常余弦变换谱特征及反演

提出利用余弦变换,研究规则体重力异常谱特征及反演方法。推导出球体、无限长水平圆柱体、无限和有限延伸垂直台阶的重力异常余弦变换谱及反演表达式。球体与无限长水平圆柱体的余弦变换谱相似,无限延伸垂直台阶的变化很尖锐,有限台阶的表现为上、下有规律的跳跃。在模型反演算例中,选择了适当的采样间隔和“趋势镶边”法,反演的圆柱体线密度和轴心深度误差分别为0.25%和3.8%。     

Mathematical analysis of gravity anomalies due to an infinite sheet-like structure

Gravity anomalies caused by a thin infinite sheet are interpreted quantitatively based on an integral transform approach which is elegant and simple. The proposed technique depends on the modified Hilbert transform which is called “Sundararajan transform.” The amplitudes of the well-known Hilbert transform and Sundararajan transform are exactly the same but with a phase difference of 270° between them. The interpretation of gravity anomalies due to a thin infinite sheet has been implemented using the Sundararajan transform rather than the well-known Hilbert transform, yielding a straightforward solution. Parameters such as the depth to the top of the sheet (z), the inclination angle (θ), and the amplitude coefficient (K) have been analytically determined using simple mathematical equations. The origin of the causative target can be determined by the intersection point between Hilbert and Sundararajan transforms as well as the intersection point of the amplitudes of the analytic signal of the two transforms. The proposed technique has been first applied to synthetic data where the procedures are clearly illustrated. The effect of noise on the interpretation procedures of the proposed technique has been investigated, showing in general satisfactory results especially depth estimation. However, the most sensitive parameter to noise is the dipping angle, which can be misleading in high level of noise, whereas the least sensitive parameter is the depth. Strictly speaking, the noise does not significantly distort the depth estimation obtained with this proposed technique. Finally, the interpretation of the gravity anomaly across the Mobrun ore body, Noranda, Quebec, Canada, has been carried out using the proposed technique where the parameters are estimated and compared to the results that have been published in literatures using different techniques.     

MATLAB programs for the synthetic models

The separation of residual gravity anomaly from regional gravity has considerably been studied for many years in gravity explorations. In addition, it is considered as a critical step in gravity data inversion. Some techniques have been developed for regional–residual anomaly separation both in space and frequency domains. One of these techniques for computing the regional anomaly is nonlinear filtering. In this paper, some techniques such as low-pass filtering, Butterworth, upward continuation, and nonlinear filtering are used to on synthetic gravity data in present of random noise and noise free for the purpose of residual–regional anomaly separation. The obtained results of techniques are compared with each other. The results have shown that separation methods are so efficient where synthetic models are located in shallow depth. Moreover, it is found that in comparison with other separation techniques, nonlinear filtering is more efficient in residual–regional anomaly separation and upward continuation technique is more efficient than Butterworth filter and low-pass filter. In addition, all of the obtained results have shown that Butterworth and low-pass filters are the same.     

计算重力异常垂向二阶导数的DCT法——模型实验

基于离散余弦变换（DCT）的重力异常垂询二阶导数的计算方法是笔者提出的新方法。以无限长水平圆柱体为例研究了DCT法的计算规律：模型实验证实,该法计算的无限长水平圆柱体重力异常垂向二阶导数的精度与采样闻隔、剩余密度及圆柱体半径大小无关。与圆柱体轴心埋藏深度成正比。通过分析给出了基于DCT的合适的线性滤波方式,滤波后的重力异常垂向二阶导数与理论二阶导数拟合效果好,具有较高的计算精度。     

Gravity Anomalies and Crustal Thickness Variations over the Western Ghats

The Western Ghats (WG), a topographic scarp facing towards the west coast of India and extending over diverse geological terranes – Deccan Volcanic Province (DVP), Dharwar Craton (DC) and Southern Granulite Terrain (SGT), is an enigmatic geomorphic feature. WG is characterized by low gravity anomalies. In order to decipher the sources of gravity anomalies, we have decomposed the gravity anomalies using wavelength filter and have obtained estimates of the depth to crust-mantle boundary (CMB) under WG and surrounding regions from the inversion of gravity data, which is compared with seismically determined CMB estimates. Overall, the CMB depth varies from 33 to 50 km, which is consistent with seismically determined values, except in the region of shear zones between DC and SGT probably indicating a different density contrast at CMB. The major source of gravity low is found to be the deepening of CMB under the WG compared to adjacent regions regardless of surface lithology. The CMB depths under WG and surrounding region generally approximate the CMB depths estimated for low strength flexural isostatic models, which suggests that flexural compensation of uplifted topography, later modified by tectonic and denudation processes, is a likely development model for the Western Ghats.     

三维密度界面反演的一个近似方法

在区域地球物理研究工作中,应用重力资料反演密度界面,尤其是计算莫氏面的深度,已被广大学者所重视。目前某些计算方法,如线性公式法、压缩质面法等已被应用。我们认为,在利用小比例尺区域重力资料反演密度界面时,现有的一些方法各有其一定的局限性。     

利用Radon变换进行三度体重磁异常反演

从Ｒａｄｏｎ变换角度分析解释了重磁三度体异常和二度体异常之间的等价关系，提出了利用Ｒａｄｏｎ正变换将三度体异常转化为二度体异常，对二度体异常做一维反演，然后将反演结果通过反Ｒａｄｏｎ变换实现三维场源图象重建的思想，并付诸实施，在微机上通过模型检验，证明该方法实用、可行。     

Three-dimensional P-wave velocity image under the Carpathian arc

An inversion of P-wave travel time residuals from selected earthquakes in the distance range 30°–98° to two seismic station networks was used to model P-wave velocity anomalies down to 250 km depth. In the first inversion experiment a region between 43.5°–47.5°N and 21°–29°E was modelled, using 35 seismic stations, while in the second one a region between 44°–47°N and 25°–29°E was modelled, using 19 seismic stations. The 4-layer block model of the first inversion offers 19% reduction in residual variance, while the 5-layer block model of the second one offers 26% reduction, the rest being explained by noise and smaller scale heterogeneities. The obtained velocity anomalies correlate remarkably well with the gravity anomalies and with the tectonic model for the Vrancea region of Fuchs et al. (1979).     

南海重力异常特征及其显著的构造意义

在南海地区地震测深数据有限的情况下,利用重力异常可以研究南海大范围的深部地壳结构及地质构造展布特征。基于空间重力异常,结合最新的地形、沉积物厚度及地震测深等数据,分别从地震约束的莫霍面反演和无约束的三维相关成像两个视角研究南海的地壳结构,利用壳幔界面起伏、地壳厚度及三维等效密度分布来探讨地壳结构的纵横向变化。同时,联合采用延拓、水平梯度及线性构造增强滤波方法聚焦重力异常中的区域线性特征,突出显示了反映地壳横向变化的深断裂、洋陆转换边界、海盆扩张轴等线性构造的展布。重力解释与贯穿南海南北的广州-巴拉望地学断面对比表明,重力异常反演及异常的区域线性特征,较好地揭示了南海海域大范围的地壳结构与区域构造展布。     

不同深度岩溶管道的高密度电阻率法反演特征

高密度电法在岩溶区找水具有很好的效果,岩溶山区岩溶管道深度各异,为了探寻岩溶管道深度变化下高密度电阻率的响应规律,本文以高密度电阻率法原理为基础,采用高密度电阻率法微测系统,利用铜柱体模型,模拟均匀介质下不同深度岩溶管道的高密度电阻率响应特征。结果表明:当岩溶管道深度大于15倍电极距时,矩形AMN装置和滚动MNB装置未能探测到该深度的岩溶管道;当岩溶管道深度小于10~11倍电极距时,矩形AMN和滚动MNB装置联合能较精准地定位岩溶管道在平面上的投影位置;岩溶管道反演异常的横向宽度始终大于真实异常横向宽度,反演异常顶部埋深小于或等于真实异常顶部埋深,且岩溶管道深度越浅,反演异常体的形态、大小、埋深越接近真实异常;随岩溶管道深度的增加,岩溶管道的矩形AMN装置和滚动MNB装置异常反演形态由椭圆向半椭圆、弓形变化,直至消失。      

重力密度反演的自适应异常权函数法及其对东海钓北凹陷地层结构划分

重力密度反演通过将地下剖分为多个网格,计算每个网格密度的方式来实现,现今方法计算结果分辨率较低。本文提出自适应权函数三维密度反演方法,通过上半空间不同高度异常凸显不同埋深地质体的特征,建立相应的空间异常权函数进行迭代反演,从而提升结果的收敛性和分辨率。模型试验表明,自适应异常权函数密度反演方法相对已有方法能有效提升分辨率和精度,且具有良好的抗噪声干扰能力。利用所提出的反演方法重建东海陆架盆地东部坳陷带空间密度结构,分析东部坳陷带中生界残留分布特征。结果表明,东部坳陷带内中生界分布南北差异明显,南部钓北凹陷中生界广泛分布,厚度较大,约4 km,颠覆了以往盆地北部西湖凹陷中生界较薄、两个凹陷中生界特征一致的认识。因此钓北凹陷中生界为陆缘坳陷型盆地,盆地范围局限于现今盆地中南部。     

重磁异常的人机联作校正－迭代反演

本文提出了三度体重磁异常的人机联作校正－迭代反演方法。该方法用二度半组合多边形棱柱体来逼近三度体，从而把三度体重磁异常反演问题转化为二度半体的反演问题；为了消除组合体迭加场的影响，该方法采用了一种校正－迭代技术。理论模型反演计算表明，该方法实际可行。     

重磁异常的人机联作校正－迭代反演

本文提出了三度体重磁异常的人机联作校正－迭代反演方法。该方法用二度半组合多边形棱柱体来逼近三度体，从而把三度体重磁异常反演问题转化为二度半体的反演问题；为了消除组合体迭加场的影响，该方法采用了一种校正－迭代技术。理论模型反演计算表明，该方法实际可行。     

Density structure of the Northeast German basin: 3D modelling along the DEKORP line BASIN96

The key for understanding the dynamics of the Northeast German basin is the knowledge of its present-day structures. Our studies are focused on the complex geometry and evolution of this basin by the aid of numerical models. To support this task, it was necessary to consider and integrate all available geoscientific information. Based on borehole data, depth maps and on results of isostatic modelling we derived a 3D model of the basin structure. A smoothed map of the regional gravity field (after Grosse and Conrad, 1990) completed the data base. By means of 3D gravity modelling, the initial model structure was modified to fit in the geophysical data set.An important characteristic of the Northeast German Basin is the presence of Upper Permian Zechstein salt. The salt domes and walls related to the postdepositional mobilisation of the salt layer cause pronounced negative gravity anomalies. This effect is considered as a central problem in this study. In order to investigate possible causes of gravimetric anomalies, we studied the influence of different crustal depth levels. We applied a 3D gravity stripping approach to eliminate the gravimetric effects caused by sedimentary fill of the basin and to separate density anomalies within the sedimentary fill from the influence of deeper levels in the crystalline crust. Complementary, we calculated the downward continuation of the gravimetric field to the basin floor and compared the outcome with the results obtained by 3D stripping. The good fit between the calculated gravity anomalies and the measured anomalies confirms the applicability of the approach. Additionally, we interpreted the Bouguer anomalies in terms of crustal density distribution and discuss the model concerning its consistency with other geophysical data considering the first results of the seismic reflection experiment DEKORP BASIN96.