SAMPLING AND MINIMUM PHASE FROM BOTH A CONTINUOUS AND DISCRETE POINT OF VIEW*

Examples show that the sampling operation–i.e., the change from the continuous time domain to the discrete time domain–does not necessarily preserve the minimum-phase property. Further examples can be constructed to show that the resampling operation on the discrete time domain does not necessarily preserve the minimum-phase property. Finally it can be shown that the minimum-phase property can be either created or destroyed by sampling or resampling.     

ESTIMATION OF REFLECTOR PARAMETERS BY THE VIRTUAL IMAGE TECHNIQUE*

The seismic interpretation process generally exploits three of the following independent basic assumptions:

• 1 Input quantities are obtained by simplification of measured data (travel time curves).
• 2 2. The geological model contains only a few parameters (for example, plane interfaces and constant interval velocities).
• 3 3. Approximate transformations may be applied.

The first two are related to the simplification of the phenomena and enhance their essential features. The transformation which establishes relations between simplified data and model is required to be unique, stable, and sufficiently accurate. Practically, the travel time curves are almost exclusively regarded as hyperbolas. We also accept this approximation. The paper presents a simple recursive algorithm for the evaluation of the depth and dip of plane reflectors and the interval velocities. It is a simple fact, that there exists a unique relationship between three hyperbolic parameters and a homogeneous dipping layer. Accordingly, two layers can be replaced by a single layer and the parameters of the lower boundary can be estimated when the upper one is known, initiating virtual shotpoints and geophone points (virtual surface). So, the case of multilayered media can be reduced in sequential steps to the case of a single homogeneous layer using a stripping type procedure. Some synthetic model examples are provided to demonstrate the abilities of the algorithm.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

EXPLORATION OF HIGH RESISTIVITY BASEMENT USING ELECTRICAL AND MAGNETIC FIELDS OF QUASI-STATIC POINT SOURCES*

Determination of thickness of sediments (usually of high conductivity) overlying a high-resistivity basement is one of the basic problems of electrical exploration methods. This paper proposes to determine horizontal electrical conductance on the basis of impedance calculated from electrical and magnetic fields of distant quasi-static (low-frequency) point sources. Using the proposed method, horizontal conductance of the sediments can be determined also from artificial quasi-static noise-impulses coming from sources of unknown position and intensity. The results of analogue modeling and field examples prove the potential of the proposed technique.     

A SIMPLE EFFICIENT METHOD OF DIP-MOVEOUT CORRECTION1

Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack. In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.     

西南海海槽地震资料处理及其似海底反射层特征

对西南海海槽的NT2-2地震测线进行了重新处理,突出了天然气水合物似海底反射层(BSR)的特征.比较了近炮检距剖面、叠加剖面、偏移剖面、瞬时振幅剖面与瞬时相位剖面上BSR的显示特征.指出了BSR在炮道集与共中心点道集上的分布.虽然在近炮检距剖面上能分辨部分BSR,但通过叠加与偏移可以得到BSR较清晰的图像.BSR的高振幅特征在瞬时振幅剖面上最为明显,而在瞬时相位剖面上容易勾画BSR的横向展布.     

含天然气水合物沉积物的岩石物性模型与似海底反射层的AVA特征

研究含天然气水合物沉积物的岩石物性模型与似海底反射层的振幅随入射角变化(AVA)特征. 基于时间平均-Wood加权方程、三相介质波传播理论模型和弹性模量模型,计算并阐述含天然气水合物岩石弹性参数与水合物饱和度、含游离气岩石弹性参数与游离气饱和度的关系;给出不同模型AVA特征. 结果表明,不同天然气水合物饱和度、不同游离气饱和度的各种组合呈现形态相似但反射系数值不同的AVA特征.     

西南海海槽地震资料处理及其似海底反射层特征

对西南海海槽的NT2-2地震测线进行了重新处理,突出了天然气水合物似海底反射层(BSR)的特征.比较了近炮检距剖面、叠加剖面、偏移剖面、瞬时振幅剖面与瞬时相位剖面上BSR的显示特征.指出了BSR在炮道集与共中心点道集上的分布.虽然在近炮检距剖面上能分辨部分BSR,但通过叠加与偏移可以得到BSR较清晰的图像.BSR的高振幅特征在瞬时振幅剖面上最为明显,而在瞬时相位剖面上容易勾画BSR的横向展布.     

含天然气水合物沉积物的岩石物性模型与似海底反射层的AVA特征

研究含天然气水合物沉积物的岩石物性模型与似海底反射层的振幅随入射角变化(AVA)特征. 基于时间平均-Wood加权方程、三相介质波传播理论模型和弹性模量模型,计算并阐述含天然气水合物岩石弹性参数与水合物饱和度、含游离气岩石弹性参数与游离气饱和度的关系;给出不同模型AVA特征. 结果表明,不同天然气水合物饱和度、不同游离气饱和度的各种组合呈现形态相似但反射系数值不同的AVA特征.     

北京首都机场的人工消雾及大气边界层特征的演变

在首都机场人工消雾作业过程中进行了大气边界层特征的观测,观测结果表明：用喷洒液氮进行人工消雾可以形成小面积降雪从而提高能见度,达到安全飞行的目的．人工消雾作业过程可影响小面积大气湍流特征,使湍流谱略偏离-5／3规律．人工消雾作业期间潜热通量明显大于作业期后．     

北京首都机场的人工消雾及大气边界层特征的演变

在首都机场人工消雾作业过程中进行了大气边界层特征的观测,观测结果表明：用喷洒液氮进行人工消雾可以形成小面积降雪从而提高能见度,达到安全飞行的目的．人工消雾作业过程可影响小面积大气湍流特征,使湍流谱略偏离-5／3规律．人工消雾作业期间潜热通量明显大于作业期后．     

ELECTRICAL POTENTIAL DUE TO A POINT CURRENT SOURCE OVER AN INHOMOGENEOUS ANISOTROPIC EARTH*

A mathematical expression for potential of a direct current point source in an inhomoge-neous anisotropic earth is derived. The coefficient of anisotropy is given by f= (σ_r/σ_z), where σ_r and σ_z are the conductivities parallel and perpendicular to the bedding plane. It is assumed that σ_z varies with depth, whereas σ_r varies transversely. This potential may be useful in interpretation of geoelectrical data in specified geological situations. Master curves for Wenner and Schlumberger configurations are presented     

A RESPONSE OF A RANDOMLY LAYERED EARTH TO AN ELECTRIC POINT OR DIPOLE SOURCE*

A point source or a dipole source of electric current, placed on a randomly layered semi-infinite medium, produces an inhomogeneous random potential field on the surface. The variance of the random potential, normalized with reference to the normal field (that is, a field due to a point source or a dipole source on a homogeneous medium), falls off inversely as the distance from the source. The conductivity of the layers is assumed to vary randomly about a mean value (unity) such that the variations can be represented by a zero mean homogeneous random function. Further the variations are assumed to be small compared to the mean so that the first order perturbation is adequate. The analysis shows that the dipole field is more sensitive than the single pole field to the conductivity variations.     

ANISOTROPY AND TRANSVERSE ISOTROPY*

A number of authors in the exploration literature have written about anisotropy, but have restricted their discussions to wave propagation through rock having transverse isotropy with a vertical symmetry axis. This note shows that there are fundamental differences between transverse isotropy when the symmetry axis is vertical (normal to the free surface) and more general anisotropy with an azimuthal variation of properties. These differences are important now that effective azimuthal shear-wave anisotropy resulting from aligned cracks and pores is becoming recognized as a significant property of crustal rocks.     

TRANSIENT FINITE INTEGRAL POINT SOURCE RESPONSE FROM A PLANAR ACOUSTIC INTERFACE: THE CAUSALITY APPROACH*

Point source reflection/transmission responses from planar interfaces based on the Sommerfeld-Weyl integral are causal and are given in the form of a solution integral with an infinite integration limit. They can be simply transformed to integrals with a finite limit by an approach that takes into account causality as well as time-symmetry aspects. To introduce the fundamental principles involved, the transformation is applied to the simple case of a point-source response from a planar acoustic interface. For a point source above a planar interface separating an upper and lower acoustic half-space of velocity c₁and c₂ the inhomogeneous plane waves in the Sommerfeld-Weyl source representation do not contribute to the final result if c₁≤c₂ and only a limited spectrum of inhomogeneous plane waves comes into play if c₁c₂.     

THE SOLUTION OF THE STATIONARY ELECTRIC FIELD STRENGTH AND POTENTIAL OF A POINT CURRENT SOURCE IN A 2 1/2- DIMENSIONAL ENVIRONMENT*

A method is given for solving the dc electric field problem of a point current source in an anisotropic 2 1/2-dimensional structural model. The surface integral equation of the field strength is given. Parallel to the strike the field strength is represented by a Fourier series. On the plane perpendicular to the strike each term of the field strength series is solved by means of the method of sub-sections, where linear behaviour of field strength over the sub-sections is assumed. Some numerical examples for different galvanic effects are given.     

WAVELET SHAPING AND NOISE REDUCTION *

Approximate deconvolution by means of Wiener filters has become standard practice in seismic data-processing. It is well-known that addition of a certain percentage of noise energy to the autocorrelation of the signal wavelet leads to a filter that does not increase, or even reduces, the noise level on the seismogram. This noise addition will, in general, cause a minimum phase signal to become mixed phase. A technique is presented for the calculation of the optimum-lag shaping filter for a contaminated signal wavelet. The advantages of this method over the more conventional approach are that it needs less arithmetic operations and that it automatically gives the filter with the optimum combination of shaping performance and noise reduction.     

SEPARATION OF P- AND S-WAVES*

In combined P- and SV-observations with vertical and in-line horizontal geophones, recognition and separation of the individual P- and S-arrivals may form a considerable problem. Due to the geophone receiving characteristics, P- and S-waves are observed on both horizontal and vertical geophones. A new method of separating P- and S-waves is presented that inverts the geophone records for the receiving characteristics, thereby separating the two wavetypes. The filter coefficients are determined from the near-surface P- and S-wave velocity and from the geometry of the geophone groups. The P/S-separation filter was tested on synthetic data with good results. Even PS- and SP-converted reflections, which are completely coinciding for horizontal reflectors, could be well separated. The filter appears to be stable and to have low sensitivity to noise in the data or to errors in the near-surface P- and S-wave velocity. The filter is superior to other separation methods, which were applied to the same dataset for comparison. This method can also be applied to VSP data.     

SELF POTENTIAL AND CURRENT CHANNELLING*

Anomalies in self potential (SP) are usually explained in terms of geochemical activity. However, there are other sources of current which cause complications in the interpretation. In particular, DC telluric currents can be generated outside the survey region. Contrasts in resistivity cause current channelling and secondary voltages can be induced by leakage. The effect can be demonstrated using network theory and internal sources can be emphasized by subtraction. Joint surveys are required to demonstrate correlations with apparent resistivity.