Sundararajan transform—an application to geophysical data analysis

An integral transform, called in this study as Sundararajan transform, has been used to estimate the parameters of vertical magnetic effect of a fault structure. It differs from the well-known Hilbert transform in the property of phase shift as it yields a phase shift of 270° unlike the Hilbert transform, which is a 90° phase shifter. Other properties of the Sundararajan transform remain almost the same as the Hilbert transform. The transform has been tested on synthetic data and a field example of Lachlan Foldbelts, New South Wales, Australia. The results of this technique agree with the one published in the literature. The noise analysis has been examined and showed that it still provides acceptable results. The application of this transform to geophysical interpretation illustrates its potentiality, and it may be widely applied in various disciplines mainly in the field of communication engineering, signal, and image processing. An interesting property of this transform is that two successive transforms of a function return it to its original form unlike the Hilbert transform, which returns it to the negative of the original form. The procedure discussed may be automated.     

Interpretation of gravity anomalies due to some two-dimensional structures: A Hilbert transform technique

An interpretation procedure is formulated using the Hilbert transform for analysing the gravity effect of (a) two-dimensional horizontal circular cylinder, (b) semi-infinite thin fault block, and (c) a geologic contact. In all three cases the abscissa of the point of intersection of the gravity anomaly curve or the horizontal derivative curve and its Hilbert transform yields directly the depth of the body. The proposed method is tested on theoretical models. Also, the method is applied to the field data of a geologic contact taken over the Himalayan foothills across the Brahmaputra valley.     

Potential field transformation on the basis of a continuous wavelet transform

The possibility of applying the continuous wavelet analysis on the basis of a Poissonian core for the processing and interpretation of gravity and magnetic survey data is considered. Based on the wavelet spectrum, W(x,h), reconstruction of the initial signal, g(x), is possible. Additionally, based on this wavelet spectrum, the equivalent distributions of mass and magnetization that produce the initial field, g(x), can be reconstructed. These possibilities allow the wavelet transform to be used for solving such classical problems as the filtering of initial signals, continuation of the field, calculation of higher field derivatives in the upper and lower half-spaces, and reduction of magnetic anomalies to the pole.     

Analysis of gravity gradients over a thin infinite sheet

A simple method to interpret gravity gradients over a thin infinite dipping sheet is discussed. The Hilbert transform is used to compute the vertical gradient from the horizontal gradient of the gravity field. The method is illustrated with a theoretical example.     

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%。     

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.     

Inversion of residual gravity anomalies using neural network

A new approach is presented in order to interpret residual gravity anomalies from simple geometrically shaped bodies such as horizontal cylinder, vertical cylinder, and sphere. This approach is mainly based on using modular neural network (MNN) inversion for estimating the shape factor, the depth, and the amplitude coefficient. The sigmoid function has been used as an activation function in the MNN inversion. The new approach has been tested first on synthetic data from different models using only one well-trained network. The results of this approach show that the parameter values estimated by the modular inversion are almost identical to the true parameters. Furthermore, the noise analysis has been examined where the results of the inversion produce satisfactory results up to 10% of white Gaussian noise. The reliability of this approach is demonstrated through two published real gravity field anomalies taken over a chromite deposit in Camaguey province, Cuba and over sulfide ore body, Nornada, Quebec, Canada. A comparable and acceptable agreement is obtained between the results derived by the MNN inversion method and those deduced by other interpretation methods. Furthermore, the depth obtained by the proposed technique is found to be very close to that obtained by drilling information.     

VSP wavefield separation using the gray-scale Hough transform: synthetic data

The principal objective in Vertical Seismic Profile (VSP) processing is the separation of the downgoing and upgoing wavefields. Several methods have been suggested in this area. This paper presents a new approach based on the gray-scale Hough transform (GSHT) which is an extension of the conventional Hough transform used to detect straight lines and other curves. The technique, we suggest here, directly maps the gray-scale VSP image, including the downgoing and upgoing linear events, in image coordinate space (x,t,g) to the gray Hough parameter counting space (θ,ρ,g), where θ and ρ are the polar parameters and g is the gray-scale value. In this new space, the downgoing events appear in the negative angles θ quadrant and the upgoing in the positive quadrant, owning to their opposite apparent velocities. The inverse GSHT algorithm, we developed in this study, is performed for extracting separately these two wavefields by considering the straight lines that satisfy the corresponding filtering conditions. The experimental results on synthetic VSP datasets are convincing. The wave separation is well performed, even in the presence of loud noise levels, with signal to noise ratio improvement and amplitude preservation, in contrast to median filtering.     

Identification of pre-seismic anomalies of soil radon-222 signal using Hilbert–Huang transform

Concentration of Rn-222 in soil has been monitored continuously at Ravangla in the Sikkim Himalayan Region of eastern India for about 7 months from October 2015 to May 2016 to detect earthquake-induced anomalies. The recorded data clearly show that various physical and meteorological parameters influence the soil radon concentration, leading to very complex soil Rn-222 time series. The components due to such external influences have been removed from the present time series, and Hilbert–Huang transform (HHT) applied for analysis of the data. Two radon anomalies caused due to earthquakes of magnitude M _b = 5.0 that occurred on 19 November 2015 and 5 April 2016 within an epicentral distance of 500 km from the monitoring station have been identified on the soil Rn-222 time series. These two precursory anomalies occurred 9 and 10 days, respectively, before the occurrence of the earthquakes. The absence of spurious signals or missing anomalies demonstrates that HHT is advantageous for analysis of nonlinear non-stationary data, and hence, it is a promising technique to analyse soil radon behaviour for predicting the possibility of occurrence of earthquakes.     

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。     

Common features of the tectonosphere deep structure in the Western Pacific Margins (Northeast Asia Region and Australia)

This paper analyses the spatial distributions of gravity sources and density contrast of geological media between the centers of mass of density heterogeneities and surfaces of some layers, which is reflected by the values of parameter μ_z, in the Northeast Asia Region and Australia. Statistical images of complex distributions of density heterogeneities are generally consistent with the shallowest tectonic structures, wave velocity, and electric anomalies. The correlation of μ_z minimums with high heat flow suggests melted magmas beneath the crust base and in the asthenosphere. In the lower crust layer, large μ_z maximums correlate with major continental megaelements, which are divided by extended linear μ_z minimums, high conductivity anomalies, and Vp/Vs maximums marking zones of lower viscosity. Deep boundaries and a thickness of lithospheric plates and asthenosphere lenses have been defined in the Northeast Asia Region. In Australia, two roughly NS-striking low-viscosity zones crossing the continent reflect the deep setting of the Lasseter (in the west) and the Tasman (in the east) lines. These zones are displayed in a wide depth range (15–120 km) and are confined to the Archean–Proterozoic and Proterozoic–Phanerozoic boundaries in the Australian lithosphere. Statistical gravity models derived without external (relatively to gravity) geological and geophysical information prove the multilayered tectonosphere structure of both continents and the similar deep structure features of their margins.     

Geodynamics and underlying bedrock of the magnetically active crust layer of the Lut block,Eastern Iran

The Curie point depth map of Eastern Iran was constituted from spectral analysis of the aeromagnetic data. The reduction to pole (RTP) was applied to the magnetic anomaly data. The Curie point depth values from 165 overlapping blocks, 100 × 100 km in size, have been estimated. The Curie point depth method provides a relationship between the 2-D FFT power spectrum of the magnetic anomalies and the depth of magnetic sources by transforming the spatial data into the frequency domain. The centroid and top depth of the magnetic sources (respectively Z₀ and Z_t) is calculated from radially averaged log power spectrum for each block. Finally, the Curie point depth of Eastern Iran is obtained by Z_b = 2Z₀–Z_t. The highest value of 24 km is located in eastern and western boundaries of the Lut block, and the lowest value of 12 km is located at north of study area. The shallow depths in the Curie-point depth map are well correlated with the young volcanic areas and geothermal potential fields. Geothermal gradient ranging from 24 to 45°C/km. The deduced thermal structure in eastern Iran has a relationship with orogenic collapse associated with delamination of thickened lithospheric root between the Lut and Afghan continental blocks.     

小波变换在位场资料去噪和位场分离中的应用

根据小波变换的原理,研究了小波阙值去噪方法和位场分离方法在某实测布格重力异常的应用及效果。多矩形棱柱体模型试验表明:选取合适的小波基和小波参数,可以更好地提取出重力异常中的有用信息,为下一步在实测重力数据中的应用提供理论基础。实测布格重力资料处理结果表明:基于小波变换的去噪方法和位场分离方法,能够较好地去除随机噪声,更好地区别出局部异常和区域异常,提高数据处理与解释中有用信号识别的精度。     

基于位场分离方法的极地冰盖重力异常剥离：以模型试验为例

为了提高极地重力数据处理的质量,降低巨厚冰层对重力数据解释的影响,将极地大陆冰盖引起的重力异常从叠加异常中剥离出来成为极地重力数据处理的重要步骤之一。针对该问题,本文建立两个极地大陆冰层构造模型,对不同模型进行正演获得对应布格重力异常,再尝试利用三种位场分离方法,包括趋势分析法、向上延拓法和优化滤波法,对冰层引起的重力异常进行剥离试验,基于模型试验结果对比分析不同位场分离方法对极地冰层重力效应剥离的应用效果。模型试验结果显示,趋势分析法在冰层界面起伏较平缓情况下效果较好,但当冰层界面起伏复杂时难以用数学表达式精确拟合区域场,因此易在结果中引入虚假异常;向上延拓法在局部场源较浅的异常分离中效果较好,但由于极地模型冰盖深度较深及延拓高度选取不合理,在试验中出现了分离不足的情况;优化滤波法在相对复杂模型中分离效果相对好,但由于频段选取的主观性,使得该方法也易出现分离不足或过度情况。综合上述模型试验表明,在剥离极地冰盖引起的重力异常时,由于极地冰盖厚度起伏等地质情况复杂多变,应结合实际地质情况及其他可获得的地球物理资料进行综合分析,选择适用于具体情况的分离方法。     

梯度法解释复杂二维断裂重力异常

对以往的二维断裂重力异常的梯度解释方法作了几点改进:①采用最小二乘拟合方法求取台阶倾角α;②直接利用台阶倾角与台阶的水平边界位置来计算台阶的埋深;③将重力二维梯度解释方法推广到复杂断裂模型的解释。文中详细论述了这种方法的原理, 给出了其具体实现步骤。该方法比起以往重力梯度解释方法, 应用更加简便而且解释结果更加稳定。用该法成功地解释了某油气盆地的实测重力资料。     

A condition for the existence of quasi-periodic nonlinear internal waves in the ocean shelf zone

Free internal gravity waves, which are typical of the shelf ocean zone are studied. A necessary condition for the existence of nonlinear wave disturbances quasi-periodic in time in a continuously stratified sea with variable depth H is found in the quasistatic and the “hard cap” approximation with respect to dissipative factors and latitudinal variation in the Coriolis parameter. The obtained assessment is equivalent to the condition obtained within the framework of linear theory for the case of the f-plane and a constant depth H.     

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.     

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.     

Estimation of Pullout Capacity of Vertical Plate Anchors in Cohesionless Soil Using MARS

Vertical plate anchors provide an economical solution to safely resist the large horizontal forces experienced by the foundation of different structures such as bulkheads, sheet piles, retaining walls and so forth. This paper develops a multivariate adaptive regression spline (MARS) model-based approach for the determination of horizontal pullout capacity (P _u ) of vertical plate anchors buried in cohesionless soil by utilizing experimental results reported by different researchers. Based on the collection of forty different pullout experimental test results reported in the literature for anchors buried in loose to dense cohesionless soil with an embedment ratio ranges from 1 to 5, a predictive approach for P _u of vertical plate anchors has been developed in terms of non-dimensional pullout coefficient (M _γq ). The capability of the proposed MARS model for estimating the values of M _γq is examined by comparing the results obtained in the present study with those methods available in the literature. Using different statistical error measure criteria, this study indicates that the present approach is efficient in estimating the horizontal pullout capacity of vertical plate anchors as compared to other methods. The sensitivity analysis indicates that the embedment ratio (H/h, where H = embedment depth of anchor, and h = height of anchor) and internal friction angle (?) of soil mass are the two most important parameters for the evaluation of non-dimensional pullout coefficient (M _γq ) using the proposed MARS model.     

利用DCT法计算重力归一化总梯度

利用重力归一化总梯度方法可以寻找场源位置,通过“两高夹一低”的典型场特征可以检测油气构造,传统的方法主要采用的是别列兹金法（即傅立叶级数法）和傅立叶变换法。利用DCT法计算重力归一化总梯度是最新研究方法。从理论上给出了基于DCT的重力异常转换公式,进而研究了无限长水平圆柱体、三度体非含油气球冠以及储油球冠模型G_H场特征。模型实验证实：随着地质体埋深的增大,谐波数会逐渐减小,G_H场奇点极大值向下移动,且呈现线性衰减的特征;储油球冠G_H场等值线表现出明显的“两高夹一低”的储油气藏典型标志;用DCT法计算的G_H场具有优良的稳定性,而且能够增加向下延拓的计算深度。