用平面波延拓方程进行地震数据的叠前速度反演

本文讨论地震勘探数据的叠前速度反演方法及其在海洋地震勘探数据上的反演试验.反演主要的计算步骤是:1.采用Fourier-Hankel变换把球面波分解为平面谐波;2.用平面谐波的延拓方程将上行波与下行波同时向下延拓,并计算每一层底部的反射系数和下一层的波阻抗;3.用最小二乘法从波阻抗中确定该层的声波速度.重复第2步与第3步,直到某一预定深度时结束.通过反演试验,对地震振幅比例的改变,子波变形,以及第1层速度和密度的误差对反演方法的稳定性及其精度的影响进行了分析.还通过实际海洋地震勘探数据的反演试验,对这一方法在地震勘探中的应用前景作了论述.     

用平面波延拓方程进行地震数据的叠前速度反演

本文讨论地震勘探数据的叠前速度反演方法及其在海洋地震勘探数据上的反演试验.反演主要的计算步骤是:1.采用Fourier-Hankel变换把球面波分解为平面谐波;2.用平面谐波的延拓方程将上行波与下行波同时向下延拓,并计算每一层底部的反射系数和下一层的波阻抗;3.用最小二乘法从波阻抗中确定该层的声波速度.重复第2步与第3步,直到某一预定深度时结束.通过反演试验,对地震振幅比例的改变,子波变形,以及第1层速度和密度的误差对反演方法的稳定性及其精度的影响进行了分析.还通过实际海洋地震勘探数据的反演试验,对这一方法在地震勘探中的应用前景作了论述.     

LINEARIZED INVERSION OF SEISMIC REFLECTION DATA*

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).     

波动方程CT技术在地震数据处理中的应用

本文从畸变的Born近似的微扰技术出发,给出了利用广义Radon变换和Fourier积分算子的理论反演介质间断性的原理.将声学的广义Radon变换与经典Radon变换进行类比,近似地导出了声学广义Radon变换的反演公式. 本文对于反射地震学的情况,提出了一种拟线性化方法,考虑了成象点的一次散射场,从某种程度上减少了Born近似对弱散射的苛求. 利用同一模型的理论记录和物理实验记录的反演计算结果对提出的方法进行了验证,并讨论了进一步提高成象精度的方法.     

二维地震资料波动方程非线性反演

针对反演的要求和实际问题的需要，提出利用地震资料叠前数据进行二维波动方程反演，采用最小平方拟合修正模型参数的非线性反演方法，构造了问题的加速迭代算法．反演算法充分利用了冗余的叠前数据和多道相关性，可以分离噪声和信号，使噪声不参与或很少参与反演，算法抗噪能力强．数值模拟例子表明算法有效和稳定，得到了令人满意的结果．     

二维地震资料波动方程非线性反演

针对反演的要求和实际问题的需要,提出利用地震资料叠前数据进行二维波动方程反演,采用最小平方拟合修正模型参数的非线性反演方法,构造了问题的加速迭代算法．反演算法充分利用了冗余的叠前数据和多道相关性,可以分离噪声和信号,使噪声不参与或很少参与反演,算法抗噪能力强．数值模拟例子表明算法有效和稳定,得到了令人满意的结果．     

波动方程CT技术在地震数据处理中的应用

本文从畸变的Born近似的微扰技术出发,给出了利用广义Radon变换和Fourier积分算子的理论反演介质间断性的原理.将声学的广义Radon变换与经典Radon变换进行类比,近似地导出了声学广义Radon变换的反演公式. 本文对于反射地震学的情况,提出了一种拟线性化方法,考虑了成象点的一次散射场,从某种程度上减少了Born近似对弱散射的苛求. 利用同一模型的理论记录和物理实验记录的反演计算结果对提出的方法进行了验证,并讨论了进一步提高成象精度的方法.     

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.     

OFFSET CONTINUATION OF SEISMIC SECTIONS*

Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data.     

航空重力测量数据向下延拓方法比较

首先介绍了空中重力异常向下延拓的直接代表法、正则化法、点质量法和基于球内Dirichlet问题的调和解法,分析了它们各自的特点.然后利用这些方法对中国大同航空重力测量数据进行向下延拓计算.通过对延拓结果与地面实测数据的比较分析,比较客观地评价了不同延拓方法的计算精度、可靠性及适应性.实际计算结果表明,直接代表法和正则化法的延拓结果具有较高的精度和可靠性,而球内Dirichlet问题调和解法的精度较差.     

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.     

TUTORIAL THE PROGRESSIVE ATTENUATION OF HIGH-FREQUENCY ENERGY IN SEISMIC REFLECTION DATA*

Seismic reflection data always exhibit a progressive loss of high-frequency energy with time. This effect is partly attributable to irreversible processes such as the conversion of elastic energy into heat (commonly known as absorption), and partly to reversible processes associated with interference between reflected waves arriving at different times. This paper looks only at reversible linear elastic effects at normal incidence and asks the following question: if there were no such absorption, would there still be a progressive loss of high-frequency energy? Using normal incidence and a layered elastic earth model we prove the following results. 1. The normal incidence response of a sequence of plane parallel elastic layers is non-white. 2. The pressure wave reflected by a layer that is thin compared with a wavelength is differentiated with respect to the incident wave. 3. The transmission response of a thin layer is consequently low-pass and the transmission response of a sequence containing many thin layers is very low-pass. 4. The well-known effect of the transport of acoustic energy by peg-leg multiples within thin layers is identical with this low-pass transmission response. 5. It follows that the high frequency energy is reflected back early in the seismogram. 6. By comparison, very low-frequencies are transmitted through the layered sequence easily and are reflected with difficulty. There is probably a lack of low-frequency energy in the reflection seismogram, by comparison with the spectrum of the incident plane wave. It follows that any meaningful evaluation of frequency-dependent absorption in seismic data cannot take place unless the frequency-dependent linear elastic effects are taken into account first.     

带阻尼的一维地震反射波成像

本文是文献［８］的继续，文中提出了地震勘探的带阻尼波动方程反演的新方法，应用此反演算法可以通过微机识别地层的波阻抗，这里把地层分成１００层，地震数据含有１０％的误差，且反演计算时间仅仅是正演计算时间的三倍．文献［１］－［４］的计算方法是基于波动方程的混合问题，而文献［８］所提出的反演算法是基于波动方程的哥西问题，许多例子充分说明后者更有效．     

地震折射法中波场延拓技术的应用

从波动方程出发,推导出平面波场传播基本公式,阐述了利用地表观测波场反演地球内部波速结构的理论关系.观测波场可通过-p 变换分解为地表平面波场,其最大振幅的轨迹能稳定地反映出地球内部波速随深度变化的趋势,这一特征可用来对反演解空间进行约束.波场延拓技术可以充分地利用观测波场中包含的丰富信息,在迭代反演中不仅能简单快速地得到反演解,而且所得解具有良好的稳定性,较少受主观因素影响,这是一种很好的反演技术.对波场延拓进行了理论分析与数值模拟,采用了同态反褶积等改善资料信噪比的措施,使解的分辨能力得到了提高.文中对南海北部一个声纳折射剖面进行了分析和计算.结果表明:该区1.4km 深处,存在一个从1.76km/s 到2.21km/s 的速度间断面.间断面上下两层的速度梯度分别为0.54kms-1/km,0.63kms-1/km.最后,从构造演化的角度对浅海构造特征进行了探讨.      

OFFSET CONTINUATION FOR SEISMIC STACKING*

Wave equation migration techniques have shown the limits of traditional stacking methods with data from tectonically complicated areas. An improved stack can be obtained utilizing the dip-moveout correction technique based on offset continuation. The properties and the limits of the algorithms used are summarized briefly. Several synthetic and real data examples are shown and compared with the results obtained using conventional processing in order to show the focusing effects and the strong improvement in signal-to-noise ratios, both at the stacked and migrated section level. The possibility of exploiting this technique to transform multiple coverage into increased spatial resolution is illustrated with examples.     

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 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.     

MAXIMUM LIKELIHOOD ESTIMATION OF SEISMIC REFLECTION COEFFICIENTS*

A seismic trace is modeled as a moving average (MA) process both in signal and noise: a signal wavelet convolved with a reflection coefficient series plus colored random noise. Seismic reflection coefficients can be estimated from seismic traces using suitable estimation algorithms if the input wavelet is known and vice versa. The maximum likelihood (ML) algorithm is used to estimate the system order and the reflection coefficients. The system order is related to the arrival time of the latest signal in a complex seismic reflection event. The least-squares (LS) method does not provide such information. The ML algorithm makes assumptions only about the Gaussian nature of the noise. It is better suited for seismic applications since the LS method inherits the white noise assumption. The Gauss-Newton (G-N) and Newton-Raphson (N-R) optimization algorithms are used to obtain the ML and the LS estimates. Reflection coefficient estimations are affected by the choice of sampling rate of seismic data. Theoretically, the optimum choice in system identification is the Nyquist rate. Experience with synthetic data confirms the theory. In practice, good estimates of reflection coefficients are possible only up to certain pulse separations (or, equivalently, orders). This is mostly due to numerical problems with the optimization algorithms used and partly due to the limited bandwidth of seismic signals. Good estimates from data simulated using three airgun array pulses recorded with 6–128 Hz filter setting are possible up to about 40.0 ms pulse separations. Successful estimations from pinchout and thin layer simulations and well controlled offshore “bright-spots” are given.     

INVERSION OF FIRST-BREAK TRAVELTIME DATA OF DEEP SEISMIC REFLECTION PROFILES1

First breaks of 2D deep reflection data were used to construct velocity-depth models for improved static corrections to a deeper datum level and for geological interpretations. The highly redundant traveltime data were automatically picked and transformed directly into a velocity-depth model by maximum depth methods such as the Giese- and the Slichter-method. Comparisons with the results of synthetic calculations and a tomographic approach using iterative inversion methods (ART, SIRT) showed that maximum depth methods provide reliable velocity models as a basis for the computation of static corrections. These methods can economically be applied during data acquisition in the field. They provide particularly long-period static anomalies, which are of the order of 20–40 ms (0.5-1 wavelength) within CMP gathers of an example of a deep reflection profile in SW-Germany sited on crystalline basement. Reprocessing of this profile, which was aimed at the comparison between the effects of the originally used and the new statics, did not result in dramatically improved stacking quality but showed a subtle influence on the detailed appearance of deep crustal events.     

位场向下延拓的正则化方法

本文讨论了正则化方法位场向下延拓的四个频率响应公式,分析了它们的特点。这些方法大都能有效地压制由于观测误差或高频干扰所引起的振荡,使下延结果趋于稳定。给出了各种试验的结果。