位场DFT算法研究

本文推广了经典的抽样定理,并据此导出了函数有限离散傅里叶变换误差方程（简称DFT误差方程,下同）。该方程把有限离散傅里叶变换中固有的离散效应和有限效应表示为确切的数学形式。离散效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数;有限效应被表示为一个含整参变量（参变量取0,1,…,N-1）的复无穷级数的DFT。 基于DFT误差方程和位函数特点,作者提出了两种位场数值傅里叶变换新算法--移样法和等效源续尾叠样法。移样法可近百倍地提高位场数值傅里叶反变换的精度,等效源续尾叠样法可数十倍地提高正变换精度。两种算法都不需要增加资料长度和取样密度,因而基本不需要增加计算机时间和内存。文中给出了算例。     

ANALYSIS OF GRAVITY ANOMALIES OF TWO-DIMENSIONAL FAULTS USING FOURIER TRANSFORMS*

The Fourier transform formula for a two-dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault-plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of the gravity anomaly. A field example from the Logan fault area near Montreal, Que., Canada, is given.     

ANALYSIS OF THE FOURIER SPECTRUM OF THE GRAVITY EFFECT DUE TO TWO-DIMENSIONAL TRIANGULAR PRISM *

Rao , K. G. C. and D. N. Avasthi , 1973, Analysis of the Fourier Spectrum of the Gravity Effect Due to Two-Dimensional Triangular Prism, Geophysical Prospecting 21, 526-542. Fourier Transform of the theoretical gravity effect due to a two-dimensional isosceles triangular prism has been derived. Evaluation of the model parameters from the analysis of the Fourier Spectrum has been outlined. Application of this method to synthetic gravity anomalies is shown.     

引力场球谐综合的Walsh变换方法

提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。     

华北东部地区上地幔运动与盆地形成关系的模拟研究

在综合分析华北东部深部构造、盆地构造及其动力学特征等资料的基础上,运用离心技术讨论了该区盆地形成机制与上地幔运动的关系。这种离心技术采用物质密度差代替温度差是一种新的实验方法。 实验结果表明,上地幔对流、上地幔隆起(或底辟)以及重力均衡作用产生了华北地壳的单向引张力,从而导致箕状盆地的形成。 作者认为,华北东部地区盆地形成和发展的动力源与上地幔的运动和重力作用密切相关     

THREE-DIMENSIONAL INTERPRETATION OF GRAVITY DATA FROM SEDIMENTARY BASINS USING AN EXPONENTIAL DENSITY-DEPTH FUNCTION*

In mapping the topography of the basement of deep sedimentary basins by gravity modelling, the accuracy can be improved by incorporating an exponential increase in density with depth. For calculating the gravity effect of a three-dimensional (3D) structure with such an exponential density-depth relation a frequency-domain forward algorithm based on series expansion is presented, the numerical evaluation of which can be performed efficiently by fast Fourier transform. The algorithm can be applied in a recursive procedure to give the inverse solution in terms of basement relief. The inversion procedure is satisfactorily tested on a 2D synthetic example and a 3D field example of gravity data from the western margin of the Pannonian Basin in eastern Austria, where up to 2.2 km of Tertiary sediments overlie an igneous or metamorphic basement. The results are confirmed by basement intersections in several wells.     

重、磁场三维傅里叶变换的若干问题

本文利用极限变换的概念,推导了质点的重力位及偶极子的磁位的三维傅里叶变换。在这个基础上,推导了任意形状物体的重、磁场的三维傅里叶变换的一般表达式。根据这些式子,讨论了文[1]中由三维谱求二维谱存在的问题,即对三维谱而言,不存在u²+v²+w²=0。     

黑水─泉州地学断面的重磁解释

讨论华南黑水─泉州地学断面的重磁解释。在解释中除应用常规的２．５维重磁异常反演外，还采用等密度线算法构制梯度层密度模型，用于分辨地壳密度细结构，以及计算自由地幔而深度用于分析上地幔密度的横向不均匀性。重磁模拟结果揭示了１０ｋｍ深度内的上地壳构造以及地壳与上地幔密度的分布。提出华南造山带以低密度上地幔为特征，它可能与上地幔的改造有关；四川盆地具有较高的上地幔密度，为未经改造的原始地幔。扬子克拉通与华南造山带的分界线与上地幔密度的分界线一致。根据布格异常、地表岩石密度和地形资料的综合分析，圈定出反映内生成矿作用深部标志的密度倒转区，可作为进一步找矿的远景区。     

CHARACTERISTICS OF MULTI-SCALE GRAVITY FIELD VARIATION AND SEISMOGENIC MECHANISM ANALYSIS IN THE SOUTHEASTERN TIBETAN PLATEAU

As the most basic geophysical field, the earth gravity field has achieved wide attention, and its spatial anomaly characteristics and dynamic variation can provide important scientific basis for studying the internal structure and dynamics of the Earth. Based on the mobile gravity observation data of the southeastern Tibetan plateau from 2013 to 2016, the dynamic variation tendency and anomaly characteristics of the regional gravity field in different temporal resolutions are obtained before and after the Ludian and Jinggu earthquakes in the study area respectively. The method of wavelet multi-scale decomposition is used to analyze the relationships of gravity field variation with the earth movement, material density change, and strong earthquake preparation. The deep material variation, dynamic process and the mechanism of earthquake inoculation in the southeastern Tibetan plateau are further discussed. Results indicate that the gravity field variation in the source region before the Ludian and Jinggu earthquake respectively is characterized by obvious positive and negative anomalous transition zone and gradient zone that are consistent with the direction of fault tectonics, suggesting the strong crustal movement and mass migration during the earthquake incubation period. The result of wavelet multi-scale decomposition of the gravity field during the period from September 2013 to April 2014 shows that the gravity field variation at different depth and space scale in the crust and upper mantle of the southeastern Tibetan plateau is significantly correlated with seismic distribution and the location of active fault zone. This indicates that the earthquake inoculation in the study area is closely related to the fault movement and the distribution of material density in the crust and upper mantle, which may be affected by the complex deep dynamic process of the material migration in the crust and mantle. The characteristic that strong earthquakes always occur near positive and negative anomaly transition zones and gradient zones of gravity field change is preliminarily explained, based on the dynamic process of material migration in the crust and upper mantle of the southeastern Tibetan plateau. The research results of this paper have some reference value to the study on the earth movement and seismogenic mechanism.     

重力位谱分析及重力异常导数换算新方法——余弦变换

为了提高重力异常导数换算的精度，真实有效地反映地质体的异常特征，提出用余弦变换计算异常导数的新方法. 给出并证明了两个定理，利用它们推导出重力位余弦谱一般表达式以及重力异常各阶导数计算公式，建立了位场余弦谱分析理论. 模型实验中发现，用Fourier变换计算的一阶导数与理论导数偏差很大，而余弦变换计算的导数与理论异常导数拟合效果非常好，除边界几个数据因重力异常的有限截断产生的吉布斯效应残留使误差较大外，数据的计算精度均很高，误差为-009%～5%.     

太行山重力梯级带的密度结构及其地质解释

斜贯中国东部地区的大兴安岭 -太行山 -武陵山重力梯级带是一条地壳深部构造变异带。选择与其中段———太行山重力梯级带相垂直的阜平 -定州剖面 ,利用人工地震测深与布格重力异常资料 ,进行了地壳 -上地幔密度反演分析。结果表明 ,该剖面的地壳 -上地幔密度分布具有明显的不均匀性。总体特征是剖面西部密度较低 ,东部密度较高 ,地壳厚度的横向变化基本上决定了布格重力异常梯级带的形成。结合华北地区的中新生代构造演化 ,认为太行山重力梯级带是燕山期以后形成的 ,它与板块之间的相互作用及上地幔热物质的运动相关     

东海及邻区重力异常多尺度分解

海洋深部地壳结构研究 ,主要研究沉积基底面与莫霍面的形态与埋深 .这两个界面 ,上、下地质体的密度差异分别约为 0 .1g/cm3和 0 .4g/cm3,采用重力测量成果来研究这两个界面 ,具有充分的物性前提 .但是 ,重力测量成果是整个岩石圈甚至包括上地幔物质的综合反映 ,如果能从测量成果中分离得到上述两个界面的重力效应 ,再据此来研究它们的形态 ,就会简单、准确一些 .我们采用二维小波多尺度分解技术 ,首次对东海及邻区自由空间重力异常进行分解 ,目的在于获取沉积基底面、莫霍面所产生的重力异常 .对分解结果进行了分析研究后认为 ,四阶变换异常细节主要由沉积基底面的起伏引起 ,四阶变换异常逼近则主要由莫霍面的起伏所引起 .本文介绍了二维小波多尺度分解方法与算法 ,展示了分解结果 ,论述了对分解结果的初步认识 .     

中国地壳厚度及上地幔密度分布(三维重力反演结果)

根据我国11平均布格重力异常图,采用Parker-Oldenbug位场反演方法,做了全国范围的三维重力反演。Parker的位场理论公式不仅数学上严密,而且运算速度甚高。本文将近些年大量的地震测深资料做为三维模型的控制点输入,并对反演计算采取了多种措施,以改善结果的合理性。本研究不仅得到了中国地区地壳厚度的分布,还首次给出了至120公里深处上地幔的密度分布。 结果表明,地壳厚度自东部沿海地区30——40公里逐渐增至青藏高原大部分地区的68公里,东部变化平缓,西部复杂,与大地构造有一定对应性。青藏高原及西部地区的上地幔密度总体偏高,一般3.40——3.65克/厘米3。东部广大区域在3.23——3.30克/厘米3。东部重力梯度带反映着下地壳与上地幔中一条深层构造带的存在,它不仅是地壳厚度陡变带,也是上地幔中的高密度带（3.29——3.35克/厘米3）,具有大区域性的控制作用。重力的均衡调整是青藏高原隆起的重要因素之一。 作者初步推断,中国地区的上地幔可大体分为青藏高原区、中部过渡区和东部正常区等三个大区,反映着上地幔结构的横向不均匀性。据此,本文解释了某些地球物理现象。      

三度体（均质模型）位场波谱的正演计算

本文给出任意指向的均质直线段、多边形面和多面体的重磁异常谱的解析表达式。利用它们可以进行不规则三度体的重磁异常谱的数值计算。此外,尚导出任意指向的斜平行六面体重磁异常谱的解析表达式。这些表达式结构简单,易于计算,用作位场的正演反演计算都十分方便。     

Interpretation of the gravity effect due to two-dimensional asymmetrical triangular prism by fourier transforms

Fourier transforms of the theoretical gravity effect due to a two-dimensional asymmetrical triangular prism have been derived. Evaluation of the parameters from the analysis of the Fourier Spectra has been outlined.     

TRANSVERSE STRUCTURES FEATURES OF DIFFERENT DEPTHS DERIVED FROM BOUGUER GRAVITY ANOMALIES IN THE SOUTHERN SEGMENT OF TAN-LU FAULT ZONE

To research the faults distribution and deep structures in the southern segment of Tan-Lu fault zone(TLFZ) and its adjacent area, this paper collects the Bouguer gravity data and makes separation by the multi-scale wavelet analysis method to analyze the crustal transverse structure of different depths. Meanwhile Moho interface is inversed by Parker variable density model. Research indicates that the southern segment of TLFZ behaves as a NNE-directed large-scale regional field gravity gradient zone, which separates the west North China-Dabie orogen block and the east Yangtze block, cutting the whole crust and lithosphere mantle. There are quite differences of density structures and tectonic features between both sides of this gradient belt. The sedimentary and upper crustal density structure is complex. The two east branches of TLFZ behave as linear gravity anomalous belt throughout the region, whereas the two west branches of TLFZ continue to extend after truncating the EW-trending gravity anomaly body. The lower crustal density structure is relatively simple. TLFZ behaves as a broad and gentle low abnormal belt, which reflects the Cretaceous-Paleogene extension environment caused graben structure. The two west branches of TLFZ, running through Hefei city, extend southward along the west margin of Feidong depression and pinch out in Shucheng area due to the high density trap occlusions in the south of Shucheng. The Feizhong Fault, Liu'an-Hefei Fault, and Feixi-Hanbaidu Fault intersect the two west branch faults of TLFZ without extending to the east. Recent epicenters are mainly located in conversion zones between the high-density and the low-density anomaly, especially in TLFZ and the junction of the faults, where earthquakes frequently occurred in the upper and middle crust. As strong earthquakes rarely occur in the southern segment of TLFZ, considering its deep feature of abrupt change of the Moho and intersections with many EW-trending faults, the hazard of strong earthquake cannot be ignored.     

利用余弦变换计算重力异常的向上延拓

利用余弦变换计算重力异常的向上延拓是一种新方法.根据余弦变换的基本性质，推导了二度、三度体异常向上延拓余弦变换谱理论公式，采用离散余弦变换实现了该法的数值计算；研究了无限长水平圆柱体的补偿因子中主频段的特性，给出了二度体的线性补偿方式；补偿后的理论模型异常向上延拓具有较高的计算精度，除边部几个数据因数据的离散和有限截断使误差较大外（最大误差为6.23%），其余数据的误差均在1%以内，理论值和计算值曲线基本重合.这说明，与Fourier变换相比，离散余弦变换在数值计算中，受非周期性深度因子的影响小，补偿方式易于选择，其计算方法优于Fourier变换.     

ACCURATE DETERMINATION OF THE DIP ANGLE OF A GEOLOGICAL CONTACT USING THE GRAVITY METHOD*

From a gravity profile over a truncated horizontal plate, the horizontal derivative and, by means of the Hilbert Transform, the vertical derivative are obtained. When the horizontal derivative is plotted against the vertical derivative, the axis of symmetry of the resulting curve is inclined at the angle of dip of the face of the truncated plate. The depths to the upper and lower surfaces of the plate can be obtained uniquely from the symmetrical figure. Because of the derivatives being used, the method avoids the difficulties which arise from other methods of interpretation which depend upon a knowledge of the position of the origin of the gravity field data. The entire procedure for interpretation can be accommodated on a programmable calculator. An illustrative example is given.     

不同地球模型对负荷潮汐改正的影响

负荷潮汐改正与地壳上地幔结构有密切关系,主要原因是负荷潮汐取决于高阶勒夫数。利用较新的1066A地球模型,对负荷勒夫数进行了重新推算,并依据负荷勒夫数组成重力、倾斜、应变及位移格林函数。发现在近区用1066A模型和经典的G-B模型求出的格林函数值差别较大。据此,推估出不同地球模型对负荷潮汐改正的影响,其中远区估算按解析方法进行,近区由数值法进行。     

ORIGIN OF THE ANOMALIES OF GRAVITY AND ITS VERTICAL GRADIENT OVER CAVITIES IN BRITTLE ROCK*

Investigations show that the depth range of the gravity method for detecting cavities is considerably greater than expected on the basis of theoretical calculations that consider only the depth and shape of the cavity. The cavity generates its own gravity field that is the sum of the activity of the cavity itself and the density changes caused in the surrounding rocks by the process of their destruction as a result of the cavity's expansion. The latter factor is decisive for the cavity's detection by the gravity method in several cases. The extent of the zones of change density in the surrounding rocks and their actual shape depend on many parameters. Thus, the determination of the depth of the cavity cannot be made by comparing measured and theoretical curves of gravity anomalies. The location of the center of gravity of the area disturbed by the cavity or upper boundary of its development towards the ground surface can be determined by denoting the singular point of gravity as a result of the downward analytical continuation of Ag. The Strakhov-Grigorieva-Lapina (1977) method fulfils the necessary conditions in the field.