An Easy Method for Interpretation of Gravity Anomalies Due to Vertical Finite Lines

A new method is introduced to determine the top and bottom depth of a vertical line using gravity anomalies. For this, gravity at a distance x from the origin and horizontal derivative at that point are utilized. A numerical value is obtained dividing the gravity at point x by horizontal derivative. Then a new equation is obtained dividing the theoretical gravity equation by the derivative equation. In that equation, assigning various values to the depth and length of vertical line, several new numerical values are obtained. Among these values, a curve is obtained for the one that is closest to the first value from attending the depth and length values. The intersection point of these curves obtained by repeating this procedure several times for different points x yield the real depth and length values of the line. The method is tested on two synthetics and field examples. Successful results are obtained in both applications.     

On Gravity Inversion for Point Mass Anomalies by Means of the Truncated Geoid

The physical meaning of the truncated geoid, which is defined by the convolution of gravity anomalies with the Stokes function on a spherical cap of specified radius, has been studied by the authors. They investigated its relation to the density distribution, generating the surface gravity, and its potential use in inversion. Some progress results for simulated studies on point mass anomalies are presented. The behavior of the truncated geoid is controlled by the radius of the integration domain, hereinafter referred to as the truncation parameter, which is treated as a free parameter. The change of the truncated geoid in response to the change of the truncation parameter was studied in the context of the simulated mass distributions. By means of such computer simulations we have managed to demonstrate the clear sensitivity of the truncated geoid to the depths, in addition to the horizontal positions, of point mass anomalies generating the synthetic surface gravity. The objective of this paper is to illustrate, with the help of computer simulation as the method of our study, the contribution of the truncated geoid to the solution of the gravimetric inverse problem. Further work towards employing the truncated geoid in gravity exploration is being conducted.     

Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.     

3D Gravity Inversion by Growing Bodies and Shaping Layers at Mt. Vesuvius (Southern Italy)

To improve our knowledge of the structural pattern of Mt. Vesuvius and its magmatic system, which represents one of the three volcanoes located in the Neapolitan area (together with Campi Flegrei and Ischia; southern Italy), we analyze here the Bouguer gravity map that is already available through its interpretation by means of 2.5-dimensional modelling. We have carried out a three-dimensional interpretation using a new and original algorithm, known as ‘Layers’, that has been especially processed for this purpose. Layers works in an automatic and non-subjective way, and allows the definition of the structural settings in terms of several layers, each representing a specific geological formation. The same data are also interpreted in terms of isolated and shallow anomalous density bodies using a well tested algorithm known as ‘Growth’. We focus our inversions on the Mt. Vesuvius volcano, while globally analyzing the entire Neapolitan area, in order to investigate the deep structures, and in particular the deep extended ‘sill’ that has been revealed by seismic tomography. The final models generally confirm the global setting of the area as outlined by previous investigations, mainly for the shape and depth of the carbonate basement below Mt. Vesuvius. The presence of lateral density contrasts inside the volcano edifice is also shown, which was only hypothesized in the 2.5-dimensional inversion. Moreover, the models allow us to note a high density body that rises from the top of the carbonate basement and further elongates above sea level. This probably represents an uprising of the same basement, which is just below the volcano and which coincides with the V_P and V_P/V_S anomalies detected under the crater. The three-dimensional results also reveal that the two inversion methods provide very similar models, where the high density isolated body in the Growth model can be associated with the rising high density anomaly in the Layers model. Taking into account the density of these modelled bodies, we would also suggest that they represent solidified magma bodies, as suggested by other studies. Finally, we did not clearly detect any deep anomalous body that can be associated with the sill that was suggested by seismic tomography.     

利用三维非均匀不稳定渗流场的数值解求解垂直井与水平井的联合开采

用差分的方法给出了三维非均匀不稳定渗流方程的离散方程组，将配斯曼（Peaceman）方程拓展成能够被用于同时求解垂直井与水平井联合开采问题的形式，利用迭代解法求解差分方程和配斯曼方程所组成的方程组，并以实际层状不均匀介质为例计算了其压强的空间分布。     

Comparative Magnetotelluric Modeling of Smooth 2D and 3D Conducting Bodies Using Rayleigh-Fourier Codes

—Recently, a method for 3D magnetotelluric modeling was developed, which is based on the application of the Rayleigh scattering theory. This method, RF-3D, is especially capable of modeling multilayered structures with smooth irregular boundaries. The formulation allows inclusion of layers with vertically anisotropic electrical conductivity.¶Using RF-3D, the response of smooth structures of practical interest is calculated and the importance of 3D effects is evaluated. Two models consisting of a 3D conductive body in the presence of a 2D shallow distortion are analyzed. In the first model, the direction of maximum elongation of the body is perpendicular to the strike direction of the 2D upper structure, and in the second one both directions coincide. In addition, the case of a small 3D shallow conductor over a regional 2D structure is also considered.¶3D effects are compared to those generated by 2D models with identical cross sections. In all the cases, the 3D responses differ from those of the 2D, especially directly over the bodies. A good agreement between the 2D transverse magnetic response and the corresponding components of the 3D response, along centrally located transverse profiles, is expected for elongate, prismatic conductors. Then, the differences obtained for the models considered in this study, particularly for the second and third models, are a consequence of the smooth geometry. They can be explained in terms of galvanic effects produced by boundary charges, which are greater near the vertical sides of a prism than on the sides of a body with smooth contours.¶Equivalent 2D models of the first and second structures are also obtained. In these models, the thickness of the conductor is underestimated, respectively, by about 30% and 24%.¶For the third model, when vertical anisotropy is analyzed, it is found that only the anisotropy of the first layer can be detected. This is because the effect of vertical anisotropy decreases strongly with depth and appears to be important only near the 3D anomaly.     

Interpretation of Gravity Data using 3D Euler Deconvolution,Tilt Angle,Horizontal Tilt Angle and Source Edge Approximation of the North-West Himalaya

The collision of the Indian plate and the Eurasian plate created shortening and imbrications with thrusting and faulting which influences northward tectonic movement. This plate movement has divided the Himalaya into four parts, viz. Outer Himalaya, Lesser Himalaya, Greater Himalaya, and Tethys Himalaya. The crystalline basement rock plays an imperative role for structural and tectonic association. The study has been carried out near Rishikesh-Badrinath neighborhood in the northwestern part of the Himalayan girdle with multifarious tectonic set up with thrusted and faulted geological setting. In this study area, 3D Euler deconvolution, horizontal gradient analysis, tilt angle (TILT) and horizontal tilt angle (TDX) analysis have been carried out using gravity data to delineate the subsurface geology and heterogeneity in the northwestern part of Himalaya. The Euler depth solutions suggest the source depth of about 12 km and various derivative analyses suggest the trend of the delineation thrust-fault boundaries along with the dip and strike direction in the study area.     

基于3DDelaunay剖分算法的重力建模与分析

地质体的重力建模是正确解释和应用重力资料的关键问题之一.针对非规则形状变密度的三度体,本文提出了基于3D Delaunay剖分算法的重力建模方法.采用3D Delaunay剖分算法将三维目标地质体分解为若干变密度四面体体元,推导了基于四面体体元的重力正演公式,建立了剩余密度值与重力异常值的线性方程组;以变密度的长方体和倾斜台阶组合体为例,比较分析了常规块体算法和3D Delaunay剖分算法应用于重力正演的有效性,并采用共轭梯度法加密度约束条件对非规则形状变密度的倾斜台阶组合体进行了密度反演.计算结果验证了本文方法的正确性和有效性.基于3D Delaunay剖分算法的重力建模可应用于存在褶皱、断层、裂缝等复杂地质体的重力正反演计算.     

基于3DDelaunay剖分算法的重力建模与分析

地质体的重力建模是正确解释和应用重力资料的关键问题之一.针对非规则形状变密度的三度体,本文提出了基于3D Delaunay剖分算法的重力建模方法.采用3D Delaunay剖分算法将三维目标地质体分解为若干变密度四面体体元,推导了基于四面体体元的重力正演公式,建立了剩余密度值与重力异常值的线性方程组;以变密度的长方体和倾斜台阶组合体为例,比较分析了常规块体算法和3D Delaunay剖分算法应用于重力正演的有效性,并采用共轭梯度法加密度约束条件对非规则形状变密度的倾斜台阶组合体进行了密度反演.计算结果验证了本文方法的正确性和有效性.基于3D Delaunay剖分算法的重力建模可应用于存在褶皱、断层、裂缝等复杂地质体的重力正反演计算.     

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.     

Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example

The Normalized Full Gradient (NFG) method which was put forward about 50 years ago has been used for downward continuation of gravity potential data, especially in the former Union of Soviet Socialist Republics. This method nullifies perturbations due to the passage of mass depth during downward continuation. The method depends on the downwards analytical continuation of normalized full gradient values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field. This method has been used in various petroleum and tectonic studies. The Trapeze method was used for the determination of Fourier coefficients during the application of this method. No other techniques for calculating these coefficients have been used. However, the Filon method was used for the determination of Fourier coefficients during the application of the NFG method in this work. This method, rather than the Trapeze method, should be preferred for indicating abnormal mass resources at the lower harmonics. In this study, the NFG method using the Filon method has been applied the first time to theoretical models of gravity profiles as example field at the Hasankale-Horasan petroleum exploration province where successful results were achieved. Hydrocarbon presence was shown on the NFG sections by the application of NFG downward continuation operations on theoretical models. Important signs of hydrocarbon structure on the NFG section for field and model data at low harmonics are obtained more effectively using this method.     

Gravity Anomalies of 2.5-D Multiple Prismatic Structures with Variable Density: A Marquardt Inversion

We present an inversion technique based on the Marquardt algorithm to estimate the depth of a 2.5-D sedimentary basin in addition to the regional gravity anomaly that is associated with the residual gravity anomaly, wherein the density contrast varies parabolically with depth. Forward modeling is carried out through a derived analytical gravity expression of a 2.5-D vertical prism. Inversion of a theoretical gravity anomaly with and without a regional gravity anomaly illustrates the procedure that it is found to be insensitive to the regional gravity effect. Furthermore, the algorithm is exemplified with the gravity anomalies of the derived density-depth model of the Godavari subbasin, India with a parabolic density profile resulting in a more consistent geological model rather than a constant density profile. The main advantage of this method is that it works well even when the profile of interpretation does not bisect the strike length of the sedimentary basin.     

Accurate and Efficient Regularized Inversion Approach for the Interpretation of Isolated Gravity Anomalies

A very fast and efficient approach for gravity data inversion based on the regularized conjugate gradient method has been developed. This approach simultaneously inverts for the depth (z), and the amplitude coefficient (A) of a buried anomalous body from the gravity data measured along a profile. The developed algorithm fits the observed data by a class of some geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, infinitely long horizontal cylinder, and sphere models using the logarithms of the model parameters [log(z) and log(|A|)] rather than the parameters themselves in its iterative minimization scheme. The presented numerical experiments have shown that the original (non-logarithmed) minimization scheme, which uses the parameters themselves (z and |A|) instead of their logarithms, encountered a variety of convergence problems. The aforementioned transformation of the objective functional subjected to minimization into the space of logarithms of z and |A| overcomes these convergence problems. The reliability and the applicability of the developed algorithm have been demonstrated on several synthetic data sets with and without noise. It is then successfully and carefully applied to seven real data examples with bodies buried in different complex geologic settings and at various depths inside the earth. The method is shown to be highly applicable for mineral exploration, and for both shallow and deep earth imaging, and is of particular value in cases where the observed gravity data is due to an isolated body embedded in the subsurface.     

Interpretation of the Gravity and Magnetic Anomalies of the Cappadocia Region,Central Turkey

The Cappadocia region, located in Central Turkey, is characterized by widespread lava flows and volcanoclastic deposits dating from Miocene to Quaternary. Gravity and aeromagnetic anomalies of the region appear to present similar high and low amplitude regions, although the aeromagnetic anomalies exhibit a rather complex pattern which is thought to be caused by remanent magnetization. The low-pass filtered aeromagnetic map shows a deep-seated magnetic anomaly which may be linked to the widespread volcanic activity at the surface. The pseudogravity transformation of the upward continued anomaly has been constructed. The pseudogravity anomaly demonstrates some form of clockwise rotation. This anomaly was modelled by means of a three-dimensional method. The top and bottom of the body are at 6.3km and 11km (including the flight height) from the ground surface, respectively. This deep body is ellipsoidal and extends along an E-W direction, which is in line with the regional stress direction deduced from GPS measurements. A new mobilistic dynamo-tectonic system appears to explain the body’s E-W elongation. The modelled body may be the source for the inferred geothermal energy of the region. Magnetic measurements were carried out on oriented rock samples collected from outcrops of ignimbrites and basalts, providing directions and intensities of remanent magnetization, susceptibilities and Koeningsberger (Q) ratios. Standard deviations of remanent directions of the Natural Remanent Magnetization (NRM) display a wide scatter implying unreliability of the surface data. Reduction to pole (RTP) transformation of magnetic anomalies was successful with the induced magnetization angle despite the complex pattern of magnetic anomalies.     

3D Gravity Inversion of Northern Sinai Peninsula: A Case Study

The Sinai Peninsula has attracted the attention of many geological and geophysical studies as it is influenced and bounded by major tectonic events. Those are (1) the Mesozoic to Early Cenozoic tectonically active opening of the Tethys, (2) the Late Cretaceous to Early Tertiary (Laramide) Syrian arc system, due to closing of the Tethys (3) the Oligo-Miocene Gulf of Suez rifted basin, and (4) the Late Miocene to Recent transform Dead Sea–Gulf of Aqaba rift. Additionally, the shear zones inside Sinai such as the Ragabet El-Naam and Minsherah-Abu Kandu Shear Zones. Each of these major tectonic events has affected dramatically the structure evolution of the northern Sinai area. The present paper estimates the 3D density contrast model using the gravity data of northern Sinai. The estimated 3D density contrast model elucidated the peculiarities of the main structural elements in the region. The estimated 3D density contrast model showed the high and low gravity anomalies that form the main mountains and main valleys in northern Sinai. The estimated low density zones are in agreement with the inferred faults resulting from the first horizontal derivative. Comparing the 3D model with the tectonic history of the region and the results of the first horizontal derivative and least square separation increased the reliability of the model.     

重力数据三维共轭梯度聚焦反演及应用

基于共轭梯度算法对欠定线性目标函数进行求解。 为改善目标函数的多解性、 消除多余构造信息影响, 引入粗糙度系数矩阵; 为克服“趋肤效应”, 更好地反映地质体的真实形态, 在模型目标函数中引入深度加权函数; 为更好的反映地质体的某些尖锐构造和边界, 本文对目标函数添加了基于最小支撑泛函的聚焦反演约束。 通过对多种模型的计算, 验证了该方法具有较好的有效性和稳定性, 并将该方法应用于实际重力资料地下密度反演中去, 得到了较好的反演结果。     

中强地震前地磁极化异常特征及其与后续地震的关系

基于国家地磁台网中心的地磁秒采样数据,采用地磁垂直强度极化法,计算了2019年1月1日至2020年7月31日全国各地磁台站的极化值,对2019年中国大陆西部(110°E以西)极化异常进行了分析,研究了2020年于田M_S6.4等中强地震前地磁极化异常变化特征及其与后续地震的关系。研究发现:(1)地磁极化异常具有空间成组特征,即空间上多个地区可以同时出现地磁极化异常;地磁极化异常一般被认为是震前震源区发生断层蠕动或岩石破裂导致的电磁辐射,这意味着震前可能会有多个地区同时发生断层蠕动或岩石破裂,这一现象似乎表明有一个"力源"在主导多区域同时发生断层蠕动或岩石破裂。(2)地磁极化异常的后续地震具有成组特征,即一个地区出现极化异常后可能发生多次地震。该现象对日常会商分析具有重要参考意义,即此类异常发生预期地震后可能还会有类似地震的发生。(3)以往的一些研究认为地磁极化异常一般在震前2—3个月出现,但本研究发现极化异常出现后10个月在异常区域仍然会发生地震,这表明电磁辐射异常可能不仅仅是短临异常,还可能具有中期指示意义,即断层蠕动或岩石破裂发生时间可能在震前近1年左右便已开始...