有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

REFLECTION OF ELASTIC WAVES FROM PERIODICALLY STRATIFIED MEDIA WITH INTERFACIAL SLIP*

A periodically stratified elastic medium can be replaced by an equivalent homogeneous transverse isotropic medium in the long wavelength limit. The case of a homogeneous medium with equally spaced parallel interfaces along which there is imperfect bonding is a special instance of such a medium. Slowness surfaces are derived for all plane wave modes through the equivalent medium and reflection coefficients for a half-space of such a medium are found. The slowness surface for the SH mode is an ellipsoid. The exact solution for the reflection of SH-waves from a half-space with parallel slip interfaces is found following the matrix method of K. Gilbert applied to elastic waves. Explicit results are derived and in the long wavelength limit, shown to approach the results for waves in the equivalent homogeneous medium. Under certain conditions, a half-space of a medium with parallel slip interfaces has a reflection coefficient independent of the angle of incidence and thus acts like an acoustic reducing mirror. The method for the reflection of P- and SV-waves is fully outlined, and reflection coefficients are shown for a particular example. The solution requires finding the eigenvalues of a 4 × 4 transfer matrix, each eigenvalue being associated with a particular wave. At higher frequencies, unexpected eigenvalues are found corresponding to refracted waves for which shear and compressional parameters are completely coupled. The two eigenvalues corresponding to the transmitted wavefield give amplitude decay perpendicular to the stratification along with up- and downgoing phase propagation in some other direction. Much of this work was performed while the author was at the Department of Geophysics and Planetary Sciences, Tel-Aviv University, Ramat-Aviv, Israel. The author is grateful for illuminating discussions with K. Helbig and K. Gilbert.     

THEORETICAL REFLECTION SEISMOGRAMS FOR ELASTIC MEDIA*

Theoretical seismograms for an explosive source in a multilayered elastic medium are constructed by Fourier synthesis and plane wave superposition. The calculation scheme which builds up a reflection matrix layer by layer in the frequency and wave number domain allows the inclusion of attenuation and a choice of the level of internal multiples in each layer. Comparative calculations of theoretical seismograms for an elastic model and in the acoustic approximation, neglecting shear, show that the main differences arise at large offsets. The inclusion of shear waves leads to lower reflected P wave amplitudes at the end of the spread but only small amounts of converted phases.     

CALCULATION OF VELOCITY FROM SEISMIC REFLECTION AMPLITUDE *

It is not possible to determine accurate geological velocities from seismic velocity analysis for thin layers or complex structural features, especially under an unconformity. Instead, we can approach the problem of interval velocity with seismic amplitudes analysis and compute the reflection coefficient along the unconformity surface. An error estimation has been made on a model to test the possibility of such a method and to choose the best parameters to be used. The method has been applied on an actual case: the computed interval velocities show good correlation with the values obtained by a sonic log.     

AN ATTEMPT AT THE INVERSION OF REFLECTION DATA*

The main problem in seismic prospecting is to infer from the observed reflection response the distribution of density and seismic velocity with depth. This process is generally called the inversion of the reflection data. For plane waves propagating through plane parallel stratification, it can be shown that at any depth the ratio between the amplitude of the transmitted and reflected wave satisfies the Riccati equation. Based on this equation we have formulated an iterative inversion method, which is found to be suitable for numerical computations. We have applied this method on synthetic reflection data, and found that it provides a very fast and accurate inversion.     

关于弹性体内充流体圆形钻孔的简正模

本文运用声波导的理论讨论钻井声场的共振模式问题,特别注意稳态现象和暂态现象的区别与联系.本文考察了共振模式的存在性及其在声波测井信号中的反映.     

关于弹性体内充流体圆形钻孔的简正模

本文运用声波导的理论讨论钻井声场的共振模式问题,特别注意稳态现象和暂态现象的区别与联系.本文考察了共振模式的存在性及其在声波测井信号中的反映.     

AN OPTIMIZED TECHNIQUE FOR DETERMINING STACKING VELOCITY FROM SEISMIC REFLECTION DATA*

A new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.     

NON-LINEAR ESTIMATION OF REFLECTION COEFFICIENTS FROM SEISMIC DATA*

For years, reflection coefficients have been the main aim of traditional deconvolution methods for their significant informational content. A method to estimate seismic reflection coefficients has been derived by searching for their amplitude and their time positions without any other limitating assumption. The input data have to satisfy certain quality constraints like amplitude and almost zero phase noise—ghosts, reverberations, long period multiples, and diffracted waves should be rejected by traditional processing. The proposed algorithm minimizes a functional of the difference between the spectra of trace and reflectivity in the frequency domain. The estimation of reflection coefficients together with the consistent “wavelet’ is reached iteratively with a multidimensional Newton-Raphson technique. The residual error trace shows the behavior of the process. Several advantages are then obtainable from these reflection coefficients, like conversion to interval velocities with an optimum calibration either to the well logs or to the velocity analysis curves. The procedure can be applied for detailed stratigraphic interpretations or to improve the resolution of a conventional velocity analysis.     

AN INVESTIGATION OF THE SPECTRAL PROPERTIES OF PRIMARY REFLECTION COEFFICIENTS*

This paper investigates the form of the nonwhiteness found in the reflection coefficients from a wide variety of rock sequences around the world. In all but one case densities are taken as constant due to the paucity of suitable density data. The reflection sequences are pseudo-white only above a corner frequency, below which their power spectrum falls away according to a power law f^β, where β is between 0.5 and 1.5. This spectrum can be adequately modelled in practice very simply with an ARMA (1, 1) process which acts on a white innovation sequence. The corollary of this is that before wavelet estimation methods are applied (all of which-except those based on synthetic seismograms—presuppose white reflection sequences) or deconvolution filters estimated, seismic traces should be filtered with the inverse of this process. Interestingly, the estimated ARMA processes group themselves into two clearly differentiated categories, having very different indices of predictability (or, strictly, indices of linear determinism). The two categories apparently correlate precisely with two kinds of sedimentation: one which consists largely of sequences of rocks with repeating properties, called “repetitive” in this paper but perhaps loosely describable as “cyclic”, and the other which is randomly bedded with no apparent pattern of components. The former has indices of predictability which are two to four times as great as those of the latter. Another, probably related, property is that β for the repetitive sequences tends to be greater than that for non-repetitive rock columns. The observed power spectra are shown to be consistent with a simple model for the logarithm of acoustic impedance consisting of a mixture of processes where the distribution of (time) scale parameters is reciprocal. Detailed effects of block-averaging and sampling the logs are shown to depend on the type of sequence under examination.     

ESTIMATION OF ELASTIC PARAMETERS FROM AVO EFFECTS IN THE TAU-P DOMAIN1

A quantitative AVO algorithm suitable for media with slow lateral parameter variations is developed. The method is based on a target-oriented inversion scheme for estimation of elastic parameters in a locally horizontally stratified medium. The algorithm uses band-limited PP reflection coefficients in the τ-p domain to estimate P- and S-wave velocities, densities and layer thicknesses. To obtain these reflection coefficients, a pre-processing involving the Radon transform and multiple attenuation is necessary. Furthermore, a macromodel for the velocities above the target zone must be found prior to the inversion. Various inversion tests involving synthetic data with white Gaussian noise and modelling errors that are likely to occur in conjunction with real data have been performed. In general, the inversion algorithm is fairly robust, since it is able to reproduce the main features of the reference model: main interface locations and relative contrasts in the three unknown layer parameters are recovered. From a test combining the effect of source directivity, one thin layer and 20% white Gaussian noise, it was found that neglect of the source directivity in the inversion caused the largest errors in the estimates. This indicates that it is very important either to eliminate the source directivity in a preprocessing step, or to take the directivity into account in the present algorithm. Despite these problems it was concluded that the inversion algorithm was able to reproduce the main features of the reference model.     

ON GETTING REFLECTION COEFFICIENTS FROM WAVES *

A horizontally layered non-absorptive system of homogeneous layers may be specified by giving the reflection coefficients at each interface. Provided the layers have equal vertical travel time and a perfect reflector as a free surface, the reflection coefficients are generally reconstructed from the reflected pulses by way of solving simultaneous equations of the Toeplitz matrix form with the Levinson recursion method. There exists an alternative approach to solving this problem which by simple reasoning immediately turns out the (Levinson) recursion scheme. The method is based on formulas that relate to solving the forward problem. It resembles Kunetz's (1962) original inverse solution in as much as the computation of the reflection coefficients is based on the idea of separating the contribution of a primary from the sum of all multiples.     

PROPERTY MATRICES IDENTIFICATION OF UNBOUNDED MEDIUM FROM UNIT-IMPULSE RESPONSE FUNCTIONS USING LEGENDRE POLYNOMIALS: FORMULATION

A systematic procedure to construct the (symmetric) static-stiffness, damping and mass matrices representing the unbounded medium is presented addressing the unit-impulse response matrix corresponding to the degrees of freedom on the structure–medium interface. The unit-impulse response matrix is first diagonalized which then permits each term to be modelled independently from the others using expansions in a series of Legendre polynomials in the time domain. This leads to a rational approximation in the frequency domain of the dynamic-stiffness coefficient. Using a lumped-parameter model which provides physical insight the property matrices are constructed.     

INVERSION OF REFLECTION DATA *

An iterative inversion method which also takes into account wave energy absorption is described. This method allows estimates of the acoustic impedance in sedimentary layers with nearly plane and parallel stratification. A set of reflection data has been inverted and an impedance model was obtained which correlates well with the essential features of the borehole velocity log.     

地球介质非弹性参数测定方法

地球介质非完全弹性参数对于研究地体稳定、地震孕育、地幔对流、大陆动力学是 非常重要的．在精确的工程勘探、油气勘探中也是一个不可缺少的参数．为了用实测的地震 体波确定非弹性参数,本文从一般线性流变体介质内波动方程出发,导出了由观测的地震波 体波波速和振幅确定一般线性流变体介质内虎克定律系数的两种具体方法及其相应的理论 公式,并给出了体波振幅法的一个模型实例．在线性近似下,这些参数可确定地球介质的非 弹性性质．     

地球介质非弹性参数测定方法

地球介质非完全弹性参数对于研究地体稳定、地震孕育、地幔对流、大陆动力学是 非常重要的．在精确的工程勘探、油气勘探中也是一个不可缺少的参数．为了用实测的地震 体波确定非弹性参数,本文从一般线性流变体介质内波动方程出发,导出了由观测的地震波 体波波速和振幅确定一般线性流变体介质内虎克定律系数的两种具体方法及其相应的理论 公式,并给出了体波振幅法的一个模型实例．在线性近似下,这些参数可确定地球介质的非 弹性性质．     

THE RADIATION OF ACOUSTIC WAVES FROM AN AIR-GUN*

A theoretical model is developed for predicting three important parameters of the pressure pulse radiated by an air-gun, namely the rise time, the amplitude of the initial pulse, and the period of the bubble pulse. A knowledge of these three parameters is essential for the efficient design of air-guns arrays. The prediction of the amplitude of the initial pulse is based on the assumption that the initial pulse is radiated by a spherical source with surface area equal to that of the air-gun ports and not by a spherical source with initial volume equal to that of the air-gun chamber, as has been assumed previously. A simple equation is obtained for predicting the period of the bubble pulsation, taking into account the effect of the air-gun body, boundaries such as the sea-surface and seabed and the presence of a number of identical air-guns placed at the same depth and fired simultaneously.     

A NEW DERIVATION OF THE WAVEFRONT CURVATURE TRANSFORMATION AT AN INTERFACE BETWEEN TWO INHOMOGENEOUS MEDIA*

The principles for ray-tracing and wavefront curvature calculations in a three-dimensional medium are reviewed. A new derivation of the transformation of the wavefront curvature matrix at an interface between two inhomogeneous media is given. The derivation is based on a Taylor series expansion of the ray refraction equation at the interface between two inhomogeneous media, and only elementary geometric arguments are used. The wave-front curvature transformation at the interface is obtained by neglecting all terms in the direction of the surface normal. With proper definition of the variables, the derivation is also valid for a reflected wave-front. A simplified transformation rule is derived for a reflected wave of the same type as the incident wave.     

一种新的地层弹性参数直接反演方法

地震资料反演的目的是估计地层的物理参数（密度、弹性和粘弹性参数）的实际值．本文中将最佳估计值定义为一种参数集,由该参数集可以算出与地震实际资料最佳拟合的合成地震记录．本文提出一种新的地层弹性参数反演方法,主要适用于各向异性介质（横向各向同性介质）中地层弹性参数的反演．本方法不同于过去传统的反演方法,它是一种完全意义上的全波波动方程反演,利用地震勘探中的多波多分量记录（PP反射波记录和PSV转换波记录）联合进行地层弹性参数犆11和犆33反演,用以判断地层的属性．