A COMPARATIVE STUDY OF THE SHORTENING OPERATORS USED IN VARIOUS DATA PROCESSING TECHNIQUES IN GRAVITY INTERPRETATION*

Discrete Fourier transform analysis provides an infinite number of weight coefficients for filters like upward and downward continuation. For practical applicability, the lengths of such filters have been reduced to a manageable number by various shortening operators, viz. those by Peters, Martin, Mufti, v. Hann, Hamming, and the truncation operator. A comparative study for choosing an operator which approximates the theoretical filter response best has indicated that Martin's shortening operator and the truncation operator are best, respectively, for normalized and non-normalized sets of weight coefficients.     

A generalized method for various data processing techniques in gravity interpretation

Summary The various data processing techniques (downward continuation, first and second derivatives and their downward continuation) used in gravity interpretation, are analogous to different types of linear filtering operations whose theoretical filter (amplitude) responses can be derived from by suitably choosingN andd, whereu andv are angular frequencies in two perpendicular directions,d the height or depth of continuation in unit of grid interval; andN denotes the order of the vertical derivative. By incorporating a mathematical smoothing function, ( being the smoothing parameter) in the theoretical filter response function, it has been possible, by selecting a suitable value of smoothing parameter, to establish an approximate equivalence of the effect of the mathematical smoothing with the inherent smoothing introduced, because of the numerical approximation (approximation error) for practically all data-processing techniques. This approximate equivalence leads to a generalized method of computing sets of weight coefficients for various data-processing techniques from filter response matching method. Several sets of weight coefficients thus have been computed with different smoothing parameter. The amplitude response curves of the various existing sets of weight coefficients have also been calculated for assessing the quality of the approximation in achieving the desired filtering operation.     

共炮检距道集波动方程保幅叠前深度偏移方法

本文提出了一种基于双平方根算子的共炮检距道集波动方程保幅叠前深度偏移方法,将振幅误差补偿作为偏移的一部分与“运动学偏移”一起在偏移过程中实现.其基本内容包括：(1)从保幅的单平方根算子方程出发,推导出由双平方根算子定义的保幅单程波方程;(2)根据地震波摄动理论把速度场分裂为层内常速背景和变速扰动,分别在频率－波数域和频率－空间域求得波场深度延拓的偏移时移量及振幅校正系数,从而得到最终的DSR保幅波场延拓算子;(3)在高频假设条件下,把DSR保幅波场延拓公式中的积分运算进行稳相近似,得到保幅波场延拓的相移公式.理论分析和模型数值试验表明,该方法不但可以使散射能量聚焦、归位,提高成像精度;而且可以输出正确反映地下反射系数的振幅信息,为后续的地震属性分析（如AVO/AVA）提供更真实的地震信息.     

一类非均匀介质中电磁场的延拓

本文讨论具垂向光滑变化的非均匀介质中电磁场延拓的数学物理问题及稳定化的算法原理。首先从电磁场的基本方程出发,导出了垂向非均匀介质下磁场的垂直分量所满足的二阶偏微分方程,并且依照实际背景将场的延拓问题化归为解相应二阶椭圆型方程的Cauchy问题。接着利用Fourier变换方法得到了场延拓的形式表达式,然后给出了几种特殊垂向非均匀介质下场延拓的精确解析公式。最后,应用正则化方法建立了场延拓的稳定化的公式,给出了所得公式的离散化形式,同时指出了相应正则化参数的选择原则。     

转换函数和磁场振幅比的水平源场效应的数值计算研究

本文用三维有限差分法研究转换函数和磁场振幅比的某些源场效应,这些物理量常用于地震预报的研究工作。我们研究了几种水平均匀源场的情况,其中包括圆偏振的源场和极化方向不同的几种线性枞化源场。结果表明,即使在最简单的均匀水平源场的情况下,磁场振幅比肯定受源场变化的影响。然而,单台转换函数就不受均匀水平源场性质变化的影响。因此,转换函数随时间的变化适用于监测地震前兆,尤其适用于中低纬度地区,因该地区的源场垂直分量比较小。      

地震波场的共偏移距延拓研究

实现地震波场共偏移距剖面上不同偏移距之间的转换,对于精确的共反射点叠加、速度分析以及研究ＡＶＯ信息等皆具有重要意义。本文从非均匀介质地震记录的微分性质出发,通过对其共反射点变化轨迹的研究,导出基于Ｈａｍｉｌｔｏｎ方程的地震波场共偏移距延拓方程,建立了新的共偏移距延拓算子,通过理论模型的计算验证了此方程的正确性。     

THE MAGNETIC ANOMALY OF 3D SOURCES HAVING ARBITRARY GEOMETRY AND MAGNETIZATION

Magnetic anomalies of complicated 3D sources can be calculated by using a combination of analytical and numerical integration. Two surfaces and the magnetization parameters (the amplitudes of the induced and remanent components and the direction cosines) of the source can be defined by arbitrary functions or by discrete data points in a plane. When combined with a polynomial magnetization function in the direction of the third axis, 3D magnetization distribution can also be modelled. The method gives very general equations for anomaly calculation. It can be used for direct modelling of sources interpreted by seismic or other methods and also for interactive interpretation with fast computers. It is possible to calculate anomalies of, for example, intrusives or folded sedimentary beds whose surfaces are functions of horizontal coordinates and which have polynomial magnetization variations in the vertical direction due to gravitational differentiation and arbitrarily varying magnetization in the horizontal direction due to regional metamorphosis. If the distribution of magnetization parameters in the vertical direction cannot be described satisfactorily by polynomials, models can be used whose surfaces are functions of the vertical coordinate and which can then have any arbitrary magnetization distribution in the vertical direction.     

THE SPECTRAL FUNCTION OF A LAYERED SYSTEM AND THE DETERMINATION OF THE WAVEFORMS AT DEPTH*

Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram.     

MIGRATION TO ZERO OFFSET (DMO) FOR A CONSTANT VELOCITY GRADIENT: AN ANALYTICAL FORMULATION1

Migration to zero offset (MZO) is a prestack partial migration process that transforms finite-offset seismic data into a close approximation to zero-offset data, regardless of the reflector dips that are present in the data. MZO is an important step in the standard processing sequence of seismic data, but is usually restricted to constant velocity media. Thus, most MZO algorithms are unable to correct for the reflection point dispersal caused by ray bending in inhomogeneous media. We present an analytical formulation of the MZO operator for the simple possible variation of velocity within the earth, i.e. a constant gradient in the vertical direction. The derivation of the MZO operator is carried out in two steps. We first derive the equation of the constant traveltime surface for linear V(z) velocity functions and show that the isochron can be represented by a fourth-degree polynomial in x, y and z. This surface reduces to the well-known ellipsoid in the constant-velocity case, and to the spherical wavefront obtained by Slotnick in the coincident source-receiver case. We then derive the kinematic and dynamic zero-offset corrections in parametric form by using the equation of the isochron. The weighting factors are obtained in the high-frequency limit by means of a simple geometric spreading correction. Our analytical results show that the MZO operator is a multivalued, saddle-shaped operator with marked dip moveout effects in the cross-line direction. However, the amplitude analysis and the distribution of dips along the MZO impulse response show that the most important contributions of the MZO operator are concentrated in a narrow zone along the in-line direction. In practice, MZO processing requires approximately the same trace spacing in the in-line and cross-line directions to avoid spatial aliasing effects.     

关千ΔT磁异常的解释

本文对于二度问题证明了总磁場强度△T与垂直磁場强度Z的一般表达式具有相同的形式,因此可以把△T异常曲线看成Z异常曲线,利用复变函数理论中的柯西-黎曼条件我们就可根据△T异常曲线计算出与H异常曲线相当的所谓△T的“负共轭调和函数”△T,文中指出了同时利用△T及其原函数△T将有助于磁测资料的解释工作,还举出了两个应用的例子:1)根据△T与△T计算二度体的磁矩及其倾角;2)利用观测水平上的△T及△T值将△T向下解析延拓。     

江西永平爆破北西测线资料再解释

本文利用江西永平爆破北西测线深地震测深资料,综合分析了其走时、振幅及频率特性,得到江西东北部地壳结构。利用振幅特性来减少反演的非唯一性。关于振幅特性分析,第一步用经典射线理论分析这一地区的振幅响应趋势;第二步用波动理论方法严格计算临界点附近的振幅特性,进一步研究经典射线理论方法的应用可能。最后还利用隧道波理论分析了永平爆破资料,得出这一地区的地壳上部可能存在低速层;地壳深部可能存在高速薄层,厚度在1km以内,速度为7.40km/s左右;莫霍面顶部为一梯度层结构。结果表明,既使在较稳定的地台区,地壳内部的结构也可能是相当复杂的。     

ON THE CONSTRUCTION OF THE 3D BAND-LIMITED EXTRAPOLATION OPERATOR IN THE SPACE-FREQUENCY DOMAIN1

Based on an expansion of the band-limited 3D extrapolation operator in terms of orthogonal Chebyshev polynomials, a closed form expression of the space-frequency response is presented. A key step is an evaluation of the (inverse) 2D Fourier transform of circularly symmetric functions, which is related to the (zero-order) Hankel transform. Hankel transforms of individual members of the orthogonal set of polynomials are available from tables and summation of series; hence, the real and the imaginary parts of the space-frequency response can be found in terms of cylindrical and spherical Bessel functions, respectively. The procedure permits an efficient and accurate evaluation of the space-frequency response.     

三维导电导磁体电磁响应的数值解

本文提出一种关于自由空间三维导电导磁体在谐变磁偶极场中电磁响应的数值计算方法。从麦克斯韦方程组导出以体内涡流密度和磁化强度为未知函数的一个联立微分积分方程组。采用迭代方法计算涡流和极化磁矩之间的相互作用,使联立的微分积分方程转化为两个独立的积分方程,再用积分方程法和有限差分法来求解。这种混合方法的优点在于它的计算速度较快。     

A STUDY OF MAGNETOTELLURIC STATIC DISTORTION IN THE CONTEXT OF INTRUSIVE VOLCANISM1

MT data from a detailed 84-site grid array (28 × 12 km) in the Paraná Basin (Brazil) reveal a high degree of frequency-independent and parallel amplitude distortion. The Palaeozoic sediments across the survey area are covered by 1.2 km of flood basalts. A deep well-log provides some control regarding the emplacement of thin diabase sills but information regarding vertical feeder dikes is non-existent. The degree of parallel behaviour is identified using anisotropy ratios which quantify the extent and bandwidth of the distortion characteristics. A 2D modelling study is carried out using the concept of a horizontally layered (1D) basin with superimposed, small-scale inhomogeneities. Two likely geological distortion structures are considered. The first represents at- or near-surface (0 to 100 m) inhomogeneities. The second represents thin but vertically elongate dikes. The two distortion effects are found to produce different and characteristic behaviour in the H-polarization (TM) mode model data. The modelled E-polarization (TE) mode data are undistorted and provide control. The model developed to represent vertical dikes gives rise to a characteristic frequency dependence which is distinct from that of the undistorted response. This model also generates subparallel distortion effects which give rise to a form of variance in the response estimates as a function of location. The behaviour occurs, importantly, in both the amplitude and phase of the distorted data. A comparison of the normalized amplitude data, observed and modelled, indicates a high degree of correspondence down to a low frequency limit (< 0.1 Hz) where additional and deep contributions to the observed response become apparent. The modelling results and data characteristics indicate that the survey area is underlain by a series of closely parallel, thin intrusive dikes (a dike swarm).     

正则化等效层重力向下延拓方法

近年来,利用时移微重力技术进行储层开发监测受到国内外学者广泛关注.时移微重力观测数据存在信噪比低,信号弱的问题,难以实现储层内物质运移的定量解释.为压制数据噪声,增强有效弱信号,本文研究了利用Tikhonov正则化方法反演等效层（源）,并由等效源实现重力场向下延拓的方法;在此基础上,本文推导了波数域正则化等效源向下延拓算子.针对向下延拓场幅值衰减问题,提出了正则化等效源迭代补偿算法.通过模拟数据实验研究了不同深度正则化等效源滤波算子及向下延拓算子的波数响应;与波数域Tikhonov正则化向下延拓方法相比,正则化等效源向下延拓方法的延拓精度更高、更稳定.最后,将基于迭代补偿的正则化等效源向下延拓技术应用于实测时移微重力数据证实了该方法能够有效增强局部异常,实现时移微重力数据大深度稳定向下延拓.     

中国地区地磁垂直分量日变幅的空间分布及高空电流体系焦点位置的移动

本文利用我国部分台站地磁垂直分量日变幅的资料,采用局部地区日变场的分析方法,研究了地磁垂直分量日变幅在中国地区的空间分布特征.结果表明,在局部地区地磁日变场的研究中,考虑经度影响是必要的,本文所用方法是适宜的;结果还表明,垂直分量日变幅的空间分布呈现出明显的季节变化、逐月变化及逐日变化性.若粗略地把磁静日垂直分量日变幅极大值所处的纬度视为 Sq 高空电流体系的焦点所对应的纬度,则此焦点纬度夏季最高,冬季最低,春秋季居中,并显出明显的逐月及逐日变化性,在相邻的两个静日,焦点纬度的变化可达几度.      

測量大气臭氧垂直分布的逆轉方法<C>——对逆轉方法<A><B>的改进

本文给出了1个新的测量大气臭氧垂直分布的逆转方法,该方法将臭氧层分为6层,各层的臭氧含量,前后两次用图解法由联立方程定量的解出。使用这个方法,我们对在北京观测的10条逆转曲线作了计算,并将这些计算结果作了讨论及初步的误差估计。     

水井含水层导水系数及其对地震波的响应

利用弹性理论和渗流理论研究了井水位振荡试验,给出了一种计算水井含水层渗流特性参数的新方法。该方法不是用井水位的恢复曲线,而是用井水位的振荡曲线计算出水井含水层的导水系数。对５ 口水井的导水系数及其对地震波的响应进行了统计,结果表明：水井含水层的导水系数越大,井水位对地震波响应的幅度越大,响应的次数越多。     

双复杂介质条件下频率空间域有限差分法保幅偏移

油气勘探的重点正转向复杂地表条件和复杂地质条件的区域.双复杂条件下的叠前深度偏移是解决复杂地表条件和复杂地质构造成像的有效手段.基于“逐步累加”的“直接下延”法是解决复杂地表成像的有效手段,能够较好地消除地形起伏的影响.波动方程频率空间域有限差分(xwfd)叠前深度偏移对介质速度横向变化有较强的适应性,适宜于复杂构造的偏移成像,同其他常规波动方程深度偏移一样,常规的xwfd偏移方法,主要也是针对相位进行波场延拓,没有对振幅做任何处理.我们基于保幅单程波方程,推导出了基于xwfd的保幅波场延拓算子,针对xwfd求解时引入误差的影响,我们在xwfd保幅波场延拓过程中加入了误差补偿,实现了带误差补偿的xwfd保幅偏移.基于带误差补偿的xwfd保幅算子,应用适合起伏地表的直接下延法,对双复杂介质模型和实际资料进行了试算,改善了双复杂介质的成像效果.其中,误差补偿可以在若干个外推步长上进行,所以相对于保幅傅里叶有限差分(ffd)法偏移来说,该方法在改善成像质量的同时,也具有较高的运算效率.     

上部岩石圈应力状态的三维有限元模拟

本文较详细地介绍了上部岩石圈应力状态的三维有限元模拟的方法及得到的垂直应力特征。假设在地质时间尺度上,上部岩石圈0～40公里范围内(简称地壳)以线弹性变形为主。考虑到地壳三维不均一性对地壳应力场的影响,将地壳沿水平方向分成七种地质构造单元:大洋、大陆、高原、洋中脊、海沟、转换断层和三联点,沿径向方向分成二层,以重力(包括引力和离心惯性力)和温度变化作为载荷,采用三维有限单元法计算了地壳的应力场。计算结果表明:(1)地壳垂直应力以压应力占绝对优势,张应力只发生在洋中脊等异常带及其它特定地区,(2)在同一深度上,垂直应力随纬度的增大而线性增加,(3)在深25公里范围内,垂直应力随着深度的增加而增大,其值与海姆法则预测值吻合;(4)异常高的垂直应力梯度往往发生在异常带(板块边界)邻近地区。