多台求波速比方法的再探讨

近年来,多台求波速比广泛采用最小二乘法。这种方法物理基础较好,数学思路比较严谨,在预报实践中取得了一些可喜的苗头。但它要求小地震必须发生在孕震区内,并且要五个以上的台站能记到,才会有较好的和达曲线,为弥补这种局限性。我们提出了多台求波速比的又一新方法。其特点是:一、在正常情况下波速比为常数,有助于突出异常以得到明显的信息;二、尽量增加作资料用的小地震,包括孕震区外的一些邻近地震,以便及时提供震     

A METHOD FOR CALCULATING IP ANOMALIES FOR MODELS WITH SURFACE POLARIZATION*

A numerical method is given for calculating resistivity and induced polarization anomalies produced by a surface polarization model. Surface polarization is generated when a purely electronic conductor is located in an electrolyte environment. The system that develops on the boundary between the conductor and the electrolyte is described macroscopically by a net surface charge distribution and an electric double layer. An integral equation is derived for the potential by assuming that the electronic conductor forms an equipotential system and that the polarization impedance across the boundary is linear. The integral equation is solved by means of the method of subsections. As an application some numerical modeling results are presented. The surface impedance values used in calculations are based on laboratory measurements that are briefly described. Implications of the results for scale modeling are discussed.     

A CONTROL OF TWO-DIMENSIONAL MAGNETIC INTERPRETATION BY THREE-DIMENSIONAL MODEL BODY ANOMALIES*

In magnetic routine interpretation the comparison of two-dimensional model curves with measured magnetic anomalies is widely used for an approximate evaluation of the position and depth of magnetic models. Before starting an interpretation of a survey by means of two-dimensional models, it is very useful to have an idea of the shape of anomalies caused by extended but finite bodies, taking into account various strike directions: Three sets of anomalies of thin plates (horizontal length 19, downward length 9, width 1) dipping 30°, 60°, and 90° resp. for various strike directions and an inclination of 20° were computed. Some of these anomalies, e.g. those with nearly N-S strike direction look rather complicated, and at the first glance one would not expect that they are caused by such simple bodies. Several profiles crossing the computed anomalies perpendicularly were interpreted two-dimensionally. For less extended anomalies the depths determined for the top of the plates are 10-20% too small, the magnetization amounts to 50–75 % of the value of the finite bodies. The interpretation of the profiles covering more extended anomalies gave very accurately the same values for the position, depth and magnetization for the two-dimensional body as for the original three-dimensional model. Anomalies of vertical prisms with varying extensions in the y-direction were computed. Their differences in amplitude and in the distance maximum-minimum show that interpretation of short anomalies by two-dimensional methods yields depth errors of up to 20 percent. To see the possibilities of the separation of superimposed anomalies dike anomalies were added to the anomaly of a broad body in great depth and several attempts were made to interpret parts of the composite anomalies. The interpreted bodies lie too deep. In complicated cases the depth values can have large errors, but experienced interpreters should be able to keep the errors in the range of one third of the depth values.     

A NOTE ON THE USE OF A NOMOGRAM FOR SELF-POTENTIAL ANOMALIES*

A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value. The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Süleymanköy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.     

A NOVEL HIGH-SPEED ALGORITHM FOR SUMMATIONAL TYPE SEISMIC VELOCITY ANALYSES*

Velocity analysis of reflection seismic data has increased in popularity with petroleum exploration personnel to such an extent that it now constitutes a significant tool in the routine digital processing program. One drawback to such an analysis is its computational cost, resulting from the numerous mathematical calculations required by a digital computer to extract comprehensive velocity information. The subject algorithm affords a computational cost saving of approximately one order of magnitude over a straightforward summational type velocity analysis with little sacrifice in accuracy. The utility of the algorithm is demonstrated on some Offshore Louisiana seismic data and a comparison of the results reveals that they are almost identical with a conventional velocity analysis. The algorithm is based on the concept that a normal-moveout pattern of time shifts may be accurately applied over a considerable span of zero-offset times to a CDP trace gather, rather than only at a single zero-offset time. With each application however, the rms-velocity associated with the moveout pattern is different. A specific relationship which associates an rms-velocity with a zero-offset time for the same moveout time delay pattern is approximated by numerical simulation studies on a digital computer.     

VELOCITY ANALYSIS FOR WIDE APERTURE SEISMIC DATA*

Common midpoint data are now being collected with ever increasing source-receiver offsets. For wide aperture seismic data classical methods of interpretation fail, since velocity analyses and signal-to-noise enhancement methods based on hyperbolic traveltime curves are no longer appropriate. Therefore, the goals of increased velocity resolution and signal enhancement, which motivate the increase in offset, are not achieved. Approximate methods, involving higher order traveltime curves or extrapolations, have been developed for velocity analysis but these are ineffective in the presence of refracted arrivals, and lack a physical basis. These problems can be minimized by transforming the observational data to the domain of intercept or vertical delay time τ and horizontal ray parameter p. In this domain headwave refractions are collapsed into points and both near vertical and wide angle reflections can be analyzed simultaneously to derive velocity-depth information, even in the presence of velocity gradients or low velocity zones.     

THREE-DIMENSIONAL SEISMIC MODELING FOR ARBITRARY VELOCITY DISTRIBUTIONS *

The growing awareness of the significance of three-dimensional interpretation of seismic reflection data carries with it a need for better understanding of the role of the velocity configuration in the production of reflection patterns. Modeling the reflection responses of a simple dipping plane reflector through velocity models of various degrees of complexity demonstrates the importance of overlying velocities in determining the reflection pattern. Modeling is accomplished using a raytracing technique which determines total travel time of the normal incidence raypath through an arbitrary iso-velocity layer model.     

一种新的三维速度结构反演模型参数化方法

本文针对三维速度反演问题中的一个重要步骤——模型的参数化作了探讨和研究,提出了一种新的参数化方法.同以往采用的矩形分块或划分网格点的方法不同,将待求扰动场按其空间频率展开,反演各阶频率系数.从三维傅氏级数理论出发,导出了一个简明且便于计算的三维空间频谱展开公式,并从理论上分析了在空间域内离散模型和空间频率域内离散模型的不同之处. 理论分析表明,在空间域内采用过参数化离散模型来反演,会在所得到的解中混入人为的虚假结构,从而使反演解发生畸变.采用在频率域内离散模型的频谱参数化方法反演,可以有效地避免这一点.频谱参数化方法也使得我们可以过参数化（over-parameterization）离散模型,便于最大程度地从资料中提取正确信息,对模型的分辨程度完全取决于观测系统的分辨能力.这种方法在得到稳定的反演解的同时,还可得到观测系统在空间三个方向上的分辨率.数值模拟实验结果证实了以上结论.     

一种新的三维速度结构反演模型参数化方法

本文针对三维速度反演问题中的一个重要步骤--模型的参数化作了探讨和研究,提出了一种新的参数化方法.同以往采用的矩形分块或划分网格点的方法不同,将待求扰动场按其空间频率展开,反演各阶频率系数.从三维傅氏级数理论出发,导出了一个简明且便于计算的三维空间频谱展开公式,并从理论上分析了在空间域内离散模型和空间频率域内离散模型的不同之处. 理论分析表明,在空间域内采用过参数化离散模型来反演,会在所得到的解中混入人为的虚假结构,从而使反演解发生畸变.采用在频率域内离散模型的频谱参数化方法反演,可以有效地避免这一点.频谱参数化方法也使得我们可以过参数化（over-parameterization）离散模型,便于最大程度地从资料中提取正确信息,对模型的分辨程度完全取决于观测系统的分辨能力.这种方法在得到稳定的反演解的同时,还可得到观测系统在空间三个方向上的分辨率.数值模拟实验结果证实了以上结论.     

A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*

This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.     

ESTIMATING MODAL PARAMETERS FOR A SIMPLE SOFT-SOIL SITE HAVING A LINEAR DISTRIBUTION OF SHEAR WAVE VELOCITY WITH DEPTH

Simple approximate expressions are derived for estimating equivalent modal parameters of a single soft-soil layer that has a straight line distribution of shear wave velocities and is on a flexible half space which is more rigid than the overlying soil layer. It is shown that radiation damping from the flexibility of the half space can be converted approximately into an equivalent material damping and that a site of a single soft-soil layer on a flexible half space can be replaced by an equivalent single layer, with the same shear wave velocity distribution, on a rigid bedrock. The implementation for modal analyses and non-linear analyses of the equivalent site under earthquake excitation is discussed.     

OPTIMIZATION OF SHORT DIGITAL LINEAR FILTERS FOR INCREASED ACCURACY*

The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest. As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter. The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.     

SIMULATIONS OF REFLECTIONS AND DIFFRACTIONS FROM TARGETS BURIED IN A MEDIUM WITH LINEAR VARIATION OF VELOCITY WITH DISTANCE*

A combination of ray theory and diffraction theory has been used to simulate reflections of seismic pulses from a full plane and reflections and diffractions from a half plane buried horizontally in earth models with linear increase of velocity with depth. Wave forms of signals reflected from a full plane in this case are modifications of the source pulse, even if the medium is assumed to be perfectly elastic. The extent of pulse modification increases with increase of the velocity gradient. The duration of the reflected pulse is always longer than that of the source pulse. The pulses diffracted from the edge of the half plane in such cases do not lie along hyperbolic curves in the time-offset plane. Diffracted signals can be observed only up to a limited distance from the edge of the half plane equalling half the horizontal range of the ray which is tangential to the half plane and has its end points at the level of the source and the receiver.     

INVERSION OF AN UNMIGRATED STACKED SECTION TO DETERMINE AN INTERVAL VELOCITY MODEL*

A seismic inversion procedure is developed that inverts data available from an unmigrated stacked section to produce an interval velocity model. It attempts to overcome some of the limitations of existing methods by using a generalized linear inversion technique. The inversion process incorporates several features: (i) Lateral interval velocity variations are permitted, (ii) A fast accurate forward model was developed, (iii) Input data is weighted according to the accuracy with which it has been acquired. The procedure is applied to seismic data from the Gippsland Basin, an area offshore South-East Australia.     

SIMPLIFIED EXPRESSIONS FOR THE MAGNETIC ANOMALIES DUE TO VERTICAL RECTANGULAR PRISMS*

The magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two-dimensional and three-dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non-linear optimization techniques or related methods.     

VELOCITY DETERMINATION AND ERROR ANALYSIS FOR THE SEISMIC REFRACTION METHOD*

A careful examination of the seismic refraction technique details the general assumptions and processes on which it is based. It is apparent that the normal interpretive process of determining velocity by hand fitting time breaks, while necessary to identify the refractors, is subject to imprecision. We describe a digital technique that calculates velocity and its precision from the time break measurements. The technique also facilitates examining for the possibility of systematic errors. Having observed the kind of imprecision that was apparent with velocity we extended our study to layer thicknesses (and thus depth) and found that the imprecision was significantly magnified. The technique and our claims for it are supported by an example of its application to a refraction survey in the Sturt Block, Western Australia.     

SEISMIC VELOCITY ESTIMATION*

The accuracy of the two most common arrival time functions used in seismic velocity estimation is investigated. It is shown that the hyperbolic arrival time function is more accurate than the parabolic arrival time function for a horizontally layered elastic medium. An upper bound on the difference between the two arrival time functions is given. A maximum-likehood detector for estimating the arrival time of the signals is given. For the signal-in-noise model that is used the maximum-likelihood detector is equivalent to a least-squares detector which corresponds to using the signal energy as coherency measure. The semblance coefficient corresponds to a normalized least-squares detector. The semblance coefficient is very similar to a filter performance measure that is used in least-squares filter design.     

GEOELECTRICAL MODEL CALCULATIONS FOR TWO-DIMENSIONAL RESISTIVITY DISTRIBUTIONS*

For the calculation of geoelectrical model curves for a two-dimensional resistivity distribution, the potential equation is transformed by means of a Fourier cosine transform into a two-dimensional Helmholtz equation containing the separation parameter λ. The numerical solution of this equation for different values of λ for an irregular grid is obtained using the method of finite differences combined with the method of overrelaxation. The method by which derivatives are replaced by finite differences turned out to be very important, especially for high resistivity contrasts. After testing several methods designed to deal with any type of resistivity distribution, a method of discretization similar to that used by Brewitt—Taylor and Weaver (1976) for magnetotelluric modeling for H polarization was found the best. Examples are given of model curves for Schlumberger soundings over a vertical fault covered by overburden. The incorrect use of horizontal-layer models leads to erroneous interpretations that are more complex than the real subsurface situations.     

ENHANCEMENT OF ELECTROMAGNETIC ANOMALIES BY A CONDUCTING OVERBURDEN*

The effect of a conducting overburden on the electromagnetic response of sulphide ore-bodies has been studied with the help of quantitative electromagnetic model experiments. These experiments were conducted at a fixed, crystal controlled, frequency of 100 kHz using a number of transmitter-receiver configurations, though the results discussed here mostly pertain to a horizontal coplanar system. An analysis of the anomaly profiles—after accounting for the regional anomaly—indicates a general enhancement of the response. This is attributed (a) to the concentration of the current lines in the host-rock effected by the embedded target and (b) to the change in the phase and space orientation of the field vectors, brought about by the conducting overburden. The enhancement is most pronounced in the case of non-symmetrical bodies such as veins and ribbon-like structures represented by sheet models, but is also observed to a lesser degree for isometric structures. These results are expected to pave the way for a more accurate interpretation of the induction prospecting data.