NEW ASPECTS IN THE INVERSION OF GRAVITY PROFILES BY POLYNOMIAL METHOD*

The gravity anomaly caused by a deviation of a density interface that is of constant profile but finite extension (a so-called 2 1/2-dimensional structure) can be expressed in polynomial form that can be inverted. Numerical experiments with synthetic structures show the viability of this inversion method.     

RAPID NUMERICAL EVALUATION OF TWO-DIMENSIONAL GRAVITY PROFILES*

A precise method of gravity interpretation is described which uses tables for the attraction of rectangular prisms in all positions relative to a given point. Hence the attraction of any body or combination of bodies may be assessed without complicated mathematical procedures.     

A NEW APPROXIMATE METHOD FOR DIRECTLY INTERPRETING GRAVITY ANOMALY PROFILES CAUSED BY SURFACE GEOLOGIC STRUCTURES*

For outcropping bodies an approximate direct interpretation of the associated gravity anomaly is generally obtained with the flat plate formula. Results can be significantly improved if the causative body is approximated by a bell shape instead of a flat plate. A set of parameter curves allows the conversion to depth data. The validity of the method is borne out by synthetic models and by field examples in a Nevada valley with Tertiary and in the Los Angeles Basin. The method provides structural definition more accurate than can be obtained with the flat plate formula, particularly in the case of narrow anomalies.     

深部大尺度单一密度界面重力异常迭代反演

对于深部大尺度单一密度界面的重力异常反演,需顾及球形观测面和重力铅垂线变化的影响。为此,本文通过球谐展开,得到重力异常的级数展开式,并推导出积分形式的反演迭代解。该迭代方法要求设法分离出单一密度界面的重力异常,已知界面上、下层的密度差和尽可能多的深度控制点。模型和实例显示其效果良好,可用于莫霍界面、岩石层底界面等深部密度界面重力异常的反演。     

深部大尺度单一密度界面重力异常迭代反演

对于深部大尺度单一密度界面的重力异常反演,需顾及球形观测面和重力铅垂线变化的影响。为此,本文通过球谐展开,得到重力异常的级数展开式,并推导出积分形式的反演迭代解。该迭代方法要求设法分离出单一密度界面的重力异常,已知界面上、下层的密度差和尽可能多的深度控制点。模型和实例显示其效果良好,可用于莫霍界面、岩石层底界面等深部密度界面重力异常的反演。     

变密度界面模型重力异常反演的B样条函数法

重力异常反演是一个求解第一类非线性积分方程的问题。当三维界面起伏满足│Δｈ│〈０．４１４ｈ０和二维界面起伏满足－ｈ０〈Δｈ〈０．４１４ｈ０时，积分方程的被积函数可Δｈ的级级数形式。     

SIMULTANEOUS INTERACTIVE MAGNETIC AND GRAVITY INVERSION*

Gravity and magnetic anomalies may have the same source but it is always difficult to achieve correlated solutions if interpretations are carried out separately. Therefore it is useful to invert both anomalous gravity and magnetic profiles at the same time, so that the solution mav be more constrained. Existing inversion techniques do not lend themselves equally to this kind of extension, since the parameters—such as density and susceptibility contrasts—should not be related. The algorithms more easily adaptable to simultaneous inversion are those which look for the shape and the position of anomalous bodies with constant unknown density or susceptibility contrasts. In this study, we use the generalized inverse method in the 2 1/2 D case. Parameters are the coordinates of the vertices of the polygonal cross-sections of the anomalous bodies and both density and susceptibility contrasts of each body. The two types of profile to be processed must be superposable but may have different lengths, spacings, and coordinate origins. Both synthetic examples and field data from geologically known areas have been processed, and it appears that the simultaneous inversion technique may provide an important additional degree of control in the interactive interpretation process.     

重磁反演中的Backus-Gilbert方法

本文讨论了重磁反演中的Backus-Gilbert方法的应用.由于重磁位场公式中核函数的奇异性和观测数据有误差,给广义线性反演带来了很大的困难.为此,本文采用了正则化方法,其效果与谱展开法完全相同.而且,其法计算速度快,使用也方便.为了提高解的分辨力和降低方差,同时加快反演迭代的收敛速度,本文采用了约束条件下反演的方法.文中最后对山西运城二条剖面作了具体分析,反演了莫霍面和居里面.     

NVESTIGATION OF TECTONICS BY GRAVITY DETAILING*

Mapping of fault patterns is an important part of geophysical exploration. A computerized digital template analysis method is described which tests gravity maps for the effects of faults by comparing measured gravity data with calculated master curves. The interpreted gravity data are incorporated in a tectonic map using geological symbols and units, for ready use by the geologists. Tectonics can be investigated by gravity detailing if the smallest undulations on the Bouguer map are taken into consideration. Up to now, residual and derivative gravity maps have explained gravity effects by assuming spherical bodies which are almost unknown in geology. The method discussed here uses tectonic elements, such as fault-blocks and dikes as a basis of interpretation instead of the spherical bodies of the conventional interpretation methods. Gravity data can be easily and relatively cheaply obtained in the early phases of exploration by area wide spot coverage following lines of easy access such as roads, etc. Seismic studies, by contrast, have the disadvantage of being executed along predetermined profile lines. Only after sufficient detailing do seismic profiles permit-if at all -an areal mapping of faults. Thus a tectonic map is obtained only at the end of a geophysical survey instead of being available prior to the planning of costly seismic profiles. The use of gravimetric data and their interpretation by the suggested method provides tectonic detail maps in the early phases of geophysical studies. In addition, this article discusses a general geophysical interpretation method, using the investigation of faults by gravity as an example. Applications of this method for different gravity and magnetics problems as well as for combined interpretations are outlined. Detailed case histories will be published in later articles.     

利用重力资料研究地壳分层结构的遗传反演方法

根据模型分解思想，采用变密度多层地壳密度模型，据此推导了相应的重力异常正演计算公式。以遗传算法为基础，结合上述重力异常正演公式，形成了地壳多层密度结构的遗传反演方法。     

用压缩质面法反演重力资料以估算地壳构造

本文用压缩质面来近似二维地质体。先由地面上测得的重力数据用矩阵方法反演此压缩质面各单元的面密度,然后从面密度与体密度差的关系求得各二维质体单元的厚度,进而得到各单元的近似地壳厚度。经正演校验和反复调整结果,使计算的重力异常值与实际测量值之残差小到满足要求,从而得到较准确的地壳底部界面。 由上地幔,玄武岩层和花岗岩层的密度差异及已算出的地壳厚度,从重力异常中分解出莫霍界面和康腊界面起伏所分别引起的重力异常。将后者同样用反演地壳厚度的压缩质面法进行计算,得到康腊界面。 文中以三种假想的地壳模型和一个实测剖面为例来检验本方法,并用其他确定地壳界面方法所得到的结果相比较,表明本文提出的压缩质面法结果较好。     

CORRECTION OF ACCURATE GRAVITY SURVEYS BY CAREFULLY OBSERVED VERTICAL GRADIENTS OF GRAVITY*

Gravity surveys in western Texas with station spacing of about 400 m were complemented by carefully observed vertical gradients of gravity making use of specially designed and automated instrumentation. The presented areal surveys of 51 and 52 stations taken in relatively flat terrain are parts of a large survey of close to 1000 stations complemented by an equal number of vertical gradient measurements. Quite irregular anomalous vertical gravity gradients surpassing 10 microgal/m were often encountered. Assuming the causative density contrasts to be located not more than 10 m below ground surface then free air correction errors of ± 0.1 mgal and more must be accepted. From a practical point of view there seems to be no other way to control such unpredictable errors than to carefully observe the local variation of vertical gravity gradients with adequate equipment. Making use of very closely spaced gravity measurements to derive these anomalous features seems more costly and cumbersome.     

INTERPRETATION OF GRAVITY ANOMALIES BY NON-LINEAR OPTIMISATION*

The interpretation of a gravity anomaly in terms of the shape of the anomalous body is a non-linear problem and may, therefore, be carried out using non-linear optimisation techniques. The formulation is extended to include cases where the density contrast and the regional background are also unknown. For a given model the objective function is provided by the discrepancy between the observed anomaly and the calculated anomaly due to the model. Given an initial model, the optimisation procedure searches for a minimum of the objective function by an iterative adjustment of the parameters. A number of suitable objective functions is given. The behaviour of these functions in the parameter hyperspace is quite complex. Accordingly, direct search methods should be employed at the early stages of the search, changing to gradient methods at later stages. The use of constraints is also necessary to ensure the geological feasibility of the model. The required computer time may be largely reduced by careful programming. Two examples of interpretation by optimisation methods are given.     

A GENERALIZED METHOD OF COMPUTING SECOND DERIVATIVE OF GRAVITY FIELD*

The unsuitability of a particular method of computation of second derivative to varying types of field problems evinces the need of a method by which it may be possible to obtain a wide range of filters. This requirement is achieved by incorporating a mathematical smoothing operator, e^-λρ2, λ and ρ being the smoothing parameter and radial frequency respectively, in the theoretical frequency response of second derivative operation. A few sets of weights for various smoothing parameters, are presented. The analysis of Bouguer gravity anomaly map of Los Angeles Basin, California, U.S.A., is carried out by Elkins's (1951) and Rosenbach's (1953) methods and the sets of weights given in this paper which clearly establishes their filtering equivalence.     

对“用压缩质面法反演重力资料以估算地壳构造”一文的讨论

“用压缩质面法反演重力资料以估算地壳构造”一文发表在1977年第一期《地球物理学报》上。在应用过程中,我们发现一些问题,在此提出讨论。 1.平均密度问题 假定“深部重力异常”是由康腊界面与莫霍界面的起伏引起的(为了便于讨论,其它界面从略)。我们根据文献[1]作者常用的参数,做了两个起伏界面与对应的重力异常图(见     

对“用压缩质面法反演重力资料以估算地壳构造”一文的讨论

This paper sets forth an adverse view on the calculation method expounded in the paper "Inversion of Gravity Data by Use of a Method of 'Compressed Mass Plane' to estimate Crustal Structure",published in No. 1,1977 of Acta Geophysica Sinica. We believe that the author of the above-mentioned paper has adopted self-contradictory hypotheses on the distribution of crustal density in the process of continuous calculations,tus leading to an irrational decomposition of anomalies,forcing an unified solution upon problems which can be solved in many different ways. This is not in conformity with the principles of inferential interpretation of physical field,but also runs counter to the unrelenting logic in mathematics. The inversed computation of the assumed crustal structure models done by us testify to the fact that the results are irrational if we use the method introduced in the said paper to estimate the undulations of crustal interfaces.     

微分方程反演声阻抗剖面

本文就一维波动方程反问题用折叠反演方法和ＣＤＰ道集数据对地层声阻抗进行反演,制做了声阻抗剖面．为物探解释提供新技术．     

重磁异常反演的拟BP神经网络方法及其应用

把神经网络与重磁异常反演理论相结合,提出了用于重磁反演的一种拟BP神经网络方法．基于3层神经网络结构,把隐含层神经元设定为三维空间物性（磁化强度或密度）单元．对实测与理论重磁异常经S型函数变换,采用自动修改物性单元物性值的拟BP算法,反演三维空间的物性分布．利用该网络对理论模型数据和内蒙古某花岗岩体上的航磁资料进行了反演计算,取得了满意的反演效果．     

重磁异常反演的拟BP神经网络方法及其应用

把神经网络与重磁异常反演理论相结合,提出了用于重磁反演的一种拟BP神经网络方法．基于3层神经网络结构,把隐含层神经元设定为三维空间物性（磁化强度或密度）单元．对实测与理论重磁异常经S型函数变换,采用自动修改物性单元物性值的拟BP算法,反演三维空间的物性分布．利用该网络对理论模型数据和内蒙古某花岗岩体上的航磁资料进行了反演计算,取得了满意的反演效果．     

微分方程反演声阻抗剖面

本文就一维波动方程反问题用折叠反演方法和ＣＤＰ道集数据对地层声阻抗进行反演，制做了声阻抗剖面．为物探解释提供新技术．