Quantitative Interpretation of Self-Potential Anomalies of Some Simple Geometric Bodies

We have developed a new numerical method to determine the shape (shape factor), depth, polarization angle, and electric dipole moment of a buried structure from residual self-potential (SP) anomalies. The method is based on defining the anomaly value at the origin and four characteristic points and their corresponding distances on the anomaly profile. The problem of shape determination from residual SP anomaly has been transformed into the problem of finding a solution to a nonlinear equation of the form q = f (q). Knowing the shape, the depth, polarization angle and the electric dipole moment are determined individually using three linear equations. Formulas have been derived for spheres and cylinders. By using all possible combinations of the four characteristic points and their corresponding distances, a procedure is developed for automated determination of the best-fit-model parameters of the buried structure from SP anomalies. The method was applied to synthetic data with 5% random errors and tested on a field example from Colorado. In both cases, the model parameters obtained by the present method, particularly the shape and depth of the buried structures are found in good agreement with the actual ones. The present method has the capability of avoiding highly noisy data points and enforcing the incorporation of points of the least random errors to enhance the interpretation results.     

An Automatic Method of Direct Interpretation of Residual Gravity Anomaly Profiles due to Spheres and Cylinders

We have developed a least-squares minimization approach to determine the depth and the amplitude coefficient of a buried structure from residual gravity anomaly profile. This approach is basically based on application of Werner deconvolution method to gravity formulas due to spheres and cylinders, and solving a set of algebraic linear equations to estimate the two-model parameters. The validity of this new method is demonstrated through studying and analyzing two synthetic gravity anomalies, using simulated data generated from a known model with different random error components and a known statistical distribution. After being theoretically proven, this approach was applied on two real field gravity anomalies from Cuba and Sweden. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by the proposed approach is found to be in very good agreement with that obtained from drilling information.     

Self-potential data interpretation using standard deviations of depths computed from moving-average residual anomalies

We have developed a least‐squares minimization approach to determine simultaneously the shape (shape factor) and the depth of a buried structure from self‐potential (SP) data. The method is based on computing the standard deviation of the depths determined from all moving‐average residual anomalies obtained from SP data, using filters of successive window lengths for each shape factor. The standard deviation may generally be considered a criterion for determining the correct depth and shape factor of the buried structure. When the correct shape factor is used, the standard deviation of the depths is less than the standard deviations computed using incorrect shape factors. This method is applied to synthetic data with and without random errors, complicated regionals and interference from neighbouring sources, and is tested on a known field example from Turkey. In all cases, the shape and depth solutions obtained are in a good agreement with the actual values.     

A new least-squares minimization approach to depth and shape determination from magnetic data

We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.     

A gradient‐ratio method for the semi‐automatic interpretation of gravity map data sets

The application of semi‐automatic interpretation techniques to potential field data can be of significant assistance to a geophysicist. This paper generalizes the magnetic vertical contact model tilt‐depth method to gravity data using a vertical cylinder and buried sphere models. The method computes the ratio of the vertical to the total horizontal derivative of data and then identifies circular contours within it. Given the radius of the contour and the contour value itself, the depth to the source can be determined. The method is applied both to synthetic and gravity data from South Africa. The Matlab source code can be obtained from the author upon request.     

A Numerical Approach to Depth Determination from Residual Gravity Anomaly Due to Two Structures

—The residual anomaly expression due to two simple geologic structures can be represented by the sum of fields produced by two known source bodies whose depths are to be determined. For a few fixed characteristic points and distances along the residual anomaly profile, the depth to the upper structure is determined iteratively using a simple formula for each depth of the lower structure. The computed depths to the lower structure are plotted against the depths to the upper structure representing a depth curve. The solution for the depths to both structures is read at the common intersection of the depth curves. Procedures are also formulated to estimate the radii of the two buried structures. The method is a powerful technique for separating the composite residual anomaly into two residual components due to two structures. The method is applied to theoretical data with and without random errors and tested on a field example from U.S.A.     

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.     

THE DEPTH OF MOHO INTERFACE AND CRUSTAL THICKNESS IN SICHUAN-YUNNAN REGION,CHINA

By using moving average method to separate Bouguer gravity anomaly field in Sichuan-Yunnan region, we got the low-frequency Bouguer gravity anomaly field which reflects the undulating of Moho interface. The initial model is obtained after seismic model transformation and elevation correction. Then, we used Parker method to invert the low-frequency Bouguer gravity anomaly field to obtain the depth of Moho interface and crustal thickness in the area. The results show that the Qinghai-Tibet block in the northwest of the study area deepens and thickens from the edge to the interior, with the depth of Moho interface and the crust thickness of about 52~62km and 54~66km, respectively. The depth of Moho interface in Sichuan Basin is about 38~42km. In Sichuan-Yunnan block, the depth of Moho interface is about 42~62km from southeast to northwest. Beneath the West Yunnan block, west of the Red River fault zone, the Moho depth is about 34~52km from south to north. The Longmen Mountains and Red River fault zone are the gradient zone of the Moho depth change. Along the Red River fault zone, the depth difference of Moho interface is increasing gradually from north to south. No obvious uplift is found on the Moho interface of Panzhihua rift valley. The depth of Moho interface distribution in Sichuan and Yunnan is obviously restricted by the collision between the Indian plate and the Eurasian plate and the lateral subduction of the Indo-China peninsula. The mean square error of the depth of Moho interface is less than 1.7km between the result of divisional density interface inversion and artificial seismic exploration. At the same time, we compared the integral with divisional inversion result. It shows that:in areas where there is obvious difference between the crust velocity and density structure in different tectonic blocks, the use of high resolution seismic exploration data as the constraints to the divisional density interface inversion can effectively improve the reliability of inversion results.     

A Versatile Nonlinear Inversion to Interpret Gravity Anomaly Caused by a Simple Geometrical Structure

A geophysical interpretative method is proposed to depth, amplitude coefficient and geometrical shape factor determination of a buried structure from an observed gravity anomaly related to a cylinder or a sphere-like structure.The method is based on nonlinearly constrained mathematical modelling and also on stochastic optimization approaches. The proposed interpretative method first has been tested on theoretical synthetic models with different random errors at a certain depth, where a very close agreement has been observed between assumed and evaluated parameters. Subsequent field data have been considered for which the interpreted results by other methods are available for comparison. The agreement between the obtained results by the proposed technique and by other geophysical methods is good. A statistical analysis has been also carried out to demonstrate the accuracy and the precision of the suggested interpretative method.     

A Least-squares Approach to Shape Determination from Residual Self-potential Anomalies

—We have developed a least-squares minimization approach to determine the shape (shape-factor) of a buried polarized body from a residual self-potential anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin on the profile, the problem of the shape-factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0. Procedures are also formulated to estimate the depth of polarization angle, and the electric dipole moment. The method is applied to synthetic data with and without random noise. The obtained shape-factor agrees very well with the model shape-factor when using synthetic data. After adding ± 2 percent random error in the synthetic data, the shape factor obtained is within ± 4 percent. Finally the validity of the method is tested on a field example from the Ergani copper district, Turkey.     

硬夹层埋深对场地地震动参数的影响

选取某重要工程场地A3钻孔的厚度、剪切波速、密度等实际勘探数据,通过改变硬夹层的埋深,分析硬夹层不同埋深、不同地震时程对场地地震动参数的影响。研究结果表明:在硬夹层厚度不变和模型总厚度不变的情况下,地表水平向的峰值加速度随硬夹层埋深的增大而增大,但增幅逐渐减小;硬夹层埋深到达一定深度时不再影响地表水平峰值加速度;随着硬夹层埋深的增加,整个反应谱的谱值普遍增大。     

Depth Estimates for Slingram Electromagnetic Anomalies from Dipping Sheet-like Bodies by the Normalized Full Gradient Method

The Normalized Full Gradient (NFG) method was proposed in the mid–1960s and was generally used for the downward continuation of the potential field data. The method eliminates the side oscillations which appeared on the continuation curves when passing through anomalous body depth. In this study, the NFG method was applied to Slingram electromagnetic anomalies to obtain the depth of the anomalous body. Some experiments were performed on the theoretical Slingram model anomalies in a free space environment using a perfectly conductive thin tabular conductor with an infinite depth extent. The theoretical Slingram responses were obtained for different depths, dip angles and coil separations, and it was observed from NFG fields of the theoretical anomalies that the NFG sections yield the depth information of top of the conductor at low harmonic numbers. The NFG sections consisted of two main local maxima located at both sides of the central negative Slingram anomalies. It is concluded that these two maxima also locate the maximum anomaly gradient points, which indicates the depth of the anomaly target directly. For both theoretical and field data, the depth of the maximum value on the NFG sections corresponds to the depth of the upper edge of the anomalous conductor. The NFG method was applied to the in-phase component and correct depth estimates were obtained even for the horizontal tabular conductor. Depth values could be estimated with a relatively small error percentage when the conductive model was near-vertical and/or the conductor depth was larger.     

埋深对地铁车站地震反应的影响分析

关于埋深对地下结构地震反应的影响的研究对象多见于地下隧道,对地铁车站地震反应受埋深影响变化规律缺乏深入研究。本文基于ANSYS有限元软件,采用改进的简化方法建立三种不同埋深的地铁车站结构有限元模型,以两种基岩波的水平向和竖向地震动作为激励,求解各模型中地铁车站结构重要部位的地震反应。分析不同埋深时地铁车站结构惯性作用、侧面土体和上部土体三个因素对地铁车站地震反应的影响情况。分析结果表明:在双向地震作用下,地铁车站侧壁弯矩、剪力、轴力和中柱轴力随埋深的增加而增加,中柱剪力和弯矩随埋深增加而减少。埋深越深,侧面土体对地铁车站地震反应影响越大;上部土体使中柱轴力不断增加;结构自身的惯性作用对其地震反应的贡献逐渐减小。     

新疆境内部分地质年代数据反映的现代构造运动

由地质样品的年代及其埋深，得到样品所在地的沉降速率。一般情况下，一个剖面上只有一个数据，可得到一个地区的沉降速率。昆仑山的沉降速率最大，阿尔泰山次之，天山最小，但特克斯是个例外。少数剖面上有2—3个数据，由同一剖面上的不同数据，可得到阶段性的沉降速率。阶段速率图(the picture of phase rate—PPR图)清楚地表示了晚更新世至全新世4不同阶段不一样的沉降速率。     

中国海—西太平洋莫霍面深度分布特征及其地质意义

中国海—西太平洋位于欧亚板块、印澳板块和太平洋板块的交汇处,构造运动剧烈,地质情况复杂,是认识板块运动、洋陆相互作用、物质交换和能量传递不可多得的窗口,而莫霍面深度对于研究壳幔结构以及深部动力过程有着重要的意义.本文使用最新的覆盖全球的重力和地形数据,收集了深地震测深、多道地震测深等剖面183条,数字化得到2982个控制点,使用带控制点的三维界面反演方法来约束反演过程,得到中国海—西太平洋莫霍面深度,由莫霍面形态分析可知大洋板块的俯冲和印澳板块与欧亚板块的碰撞对西太平洋边缘海的形成演化有着重要作用.结合地热、岩石圈厚度、地震活动等地质地球物理资料,分析得知研究区内各个海域莫霍深度和地壳性质的变化是处于不同构造演化阶段的表现.并在马里亚纳沟弧盆拟合一条重力2.5维剖面,结果表明热物质上涌导致了马里亚纳海槽处地幔密度减小,马里亚纳海槽以及帕里西维拉海盆到西马里亚纳海岭的下地壳高密度异常是由残留的岩浆岩引起的.     

Mean Free-Air Gravity Anomalies in the Mountains

Mean free-air gravity anomalies are often needed in geodesy for gravity field modelling. Two possible ways of compiling the mean free-air gravity anomalies are discussed. One way is via simple Bouguer gravity anomalies and the second and more time consuming way is via refined Bouguer gravity anomalies. In flat areas the differences between using any of the two ways should not be significant. In the mountains however, every effect introducing a high dependency, such as e.g. terrain effect, can negatively affect the interpolation process. In fact, a numerical experiment conducted in one part of Rocky Mountains revealed large and systematic differences. The effect of these differences on the geoid model is more then two meters in the test area. Our investigation shows that this bias is caused by the location of gravity measurement points, chosen mostly on hill-tops. At such points, the terrain correction to gravity is systematically larger than the mean value of the correction. Therefore, it is not possible to prevent the mean free-air gravity anomalies obtained from simple Bouguer gravity anomalies from having a systematic bias. One can see this bias as a result of the aliasing effect because the simple Bouguer gravity anomalies in the mountains contain a higher frequency signal (terrain effect) that is, according to sampling theorem, impossible to reconstruct by sparse measured gravity data, see e.g. (Goos et al., 2003). Therefore, the more rigorous way of computing the mean free-air gravity anomalies is via refined Bouguer gravity anomalies.     

辽宁义县—内蒙古东乌珠穆沁旗剖面深部电性研究

本文给出了沿辽宁义县—内蒙古东乌珠穆沁旗大地电磁测深剖面的电性结构。研究结果表明,沿该剖面壳内和上地幔高导层的埋藏深度与温度场有着良好的对应关系,即壳内、上地幔高导层埋深愈浅,其热流值愈高,反之就越低。大地电磁测深结果还表明,辽西隆起区继承了辽南地区上地幔高导层起伏形态。本文还从电性结构特征探讨了西拉木伦河断裂带可能是西伯利亚板块和中国板块的缝合线     

新疆伽师强震群区基底界面结构特征

用射线分布分析法对伽师强震群区的高分辨折射地震剖面资料进行了更进一步的分析处理， 得到了伽师强震群区更完整的基底界面结构特征. 结果表明，在伽师强震群区地壳上部存在两个明显的结构界面:第一个界面的结构连续、完整，其埋深变化不大， 在2.6～3.3 km之间，为一向天山方向逐渐抬升、 近平直的倾斜界面；第二个界面的埋深变化较大， 在8.5～11.8 km之间，为古老的塔里木盆地结晶基底. 在约37 km桩号附近结晶基底有近2.5 km的深度突变， 推断可能是伽师强震群区超基底断裂所致. 以该断裂为界，结晶基底分为西南、东北两段. 每段内界面的埋深变化不大， 西南段的埋深约11.5 km， 东北段的埋深约为8.5～9.0 km，该段在从西南向东北整体抬升的背景上略有上隆，反映出在塔里木地块西北缘特殊的构造环境下上部地壳的变形特征.      

南海海盆三维重力约束反演莫霍面深度及其特征

利用南海海盆及周边最新的重力,经过海底地形、沉积层的重力效应改正,并采用岩石圈减薄模型的温度场公式,校正了从张裂边缘到扩张海盆的热扰动重力效应.通过研究区的地震剖面和少量声呐数据得到的莫霍面深度点作为约束,采用基于"起伏界面初始模型"的深度修正量反演迭代公式,反演、计算了研究区的莫霍面深度及地壳厚度.结果表明,海盆区莫霍面深度在8~14 km之间,地壳厚度在3~9 km之间;东部海盆和西南海盆残留扩张中心沿NNE向展布向西南延伸至112°E,莫霍面深度超过12 km,地壳厚度在6 km以上,而西北海盆没有明显的增厚扩张中心;在西南海盆北缘的中沙地块南侧,存在一个近EW向地壳减薄带,地壳厚度在9~10 km;莫霍面深度14 km的等深线和地壳厚度9 km的等值线可指示洋陆边界位置.     

位场垂向导数零值位置空间变化规律研究(英文)

本文推导了简单规则形体(单一边界、双边界和多边界)重力异常垂向一阶导数和重力异常垂向二阶导数零值位置的解析表达式,并研究了其空间变化规律;对难以得到其零值位置解析表达式的简单规则形体,利用其剖面图和断面图上的零值位置来研究其空间变化规律。研究结果表明,重力异常垂向二阶导数与重力异常垂向一阶导数零值位置的空间变化规律基本一致,只是重力异常垂向二阶导数零值位置比重力异常垂向一阶导数的零值位置更靠近地质体上顶面边缘位置,且其分辨能力更强。对于单边界模型,随着埋深的增加,重力异常垂向导数的零值位置均自形体上顶边缘位置向外侧偏移,但最终均能收敛于某一固定值;对于双边界模型,随着埋深的增加,重力异常垂向导数的零值位置自形体上顶边缘位置一直向外侧偏移;对于多边界模型,随着埋深的增加,重力异常垂向导数零值位置自形体上顶边缘位置向外侧收敛,部分边界的零值位置重合并消失。最后通过实际资料检验了方法的有效性和可靠性。