ADAPTIVE PREDICTIVE DECONVOLUTION OF SEISMIC DATA*

The Wiener prediction filter has been an effective tool for accomplishing dereverberation when the input data are stationary. For non-stationary data, however, the performance of the Wiener filter is often unsatisfactory. This is not surprising since it is derived under the stationarity assumption. Dereverberation of nonstationary seismic data is here accomplished with a difference equation model having time-varying coefficients. These time-varying coefficients are in turn expanded in terms of orthogonal functions. The kernels of these orthogonal functions are then determined according to the adaptive algorithm of Nagumo and Noda. It is demonstrated that the present adaptive predictive deconvolution method, which combines the time-varying difference equation model with the adaptive method of Nagumo and Noda, is a powerful tool for removing both the long- and short-period reverberations. Several examples using both synthetic and field data illustrate the application of adaptive predictive deconvolution. The results of applying the Wiener prediction filter and the adaptive predictive deconvolution on nonstationary data indicate that the adaptive method is much more effective in removing multiples. Furthermore, the criteria for selecting various input parameters are discussed. It has been found that the output trace from the adaptive predictive deconvolution is rather sensitive to some input parameters, and that the prediction distance is by far the most influential parameter.     

频率-波数域递推计算海底多分量地震记录中的反射系数

在频率-波数域中采用解析法,解出多层条件下海底实测的多分量地震数据分解成上行和下行P波和S波的算法,导出海底各层地震反射系数随入射角变化(简称RVA)的递推计算公式,为海底多波多分量AVO弹性参数的反演及流体因子预测提供基础数据.合成数据的计算结果表明,本文给出的算法能较可靠地从海底多波多分量记录中提取RVA信息.     

频率-波数域递推计算海底多分量地震记录中的反射系数

在频率-波数域中采用解析法,解出多层条件下海底实测的多分量地震数据分解成上行和下行P波和S波的算法,导出海底各层地震反射系数随入射角变化(简称RVA)的递推计算公式,为海底多波多分量AVO弹性参数的反演及流体因子预测提供基础数据.合成数据的计算结果表明,本文给出的算法能较可靠地从海底多波多分量记录中提取RVA信息.     

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.     

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).     

STACKING OF P-SV SEISMIC REFLECTION DATA USING DIP MOVEOUT1

The moveout of P-SV mode-converted seismic reflection events in a common-midpoint gather is non-hyperbolic. This is true even if the medium has constant P- and SV-wave velocities. Furthermore, reflection-point smear occurs even along horizontal reflectors. These effects reduce the resolution of the zero-offset stack. In such a medium, the generalization of the dip moveout transformation to P-SV data can be calculated analytically. The resulting P-SV dip moveout operators solve the problem of reflection-point smear, and image any reflector regardless of dip or depth. The viability of this technique is demonstrated on synthetic and field data.     

METHOD FOR DETERMINATION OF VELOCITY AND DEPTH FROM SEISMIC REFLECTION DATA1

The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots. The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section. Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming. The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.     

SEISMIC STRATIGRAPHY IN HIGH RESOLUTION SHALLOW MARINE SEISMIC DATA OF THE GEMLIK GULF1

Seismic stratigraphy and sedimentological studies of the Gemlik Gulf in the Sea of Marmara, Turkey, have been carried out. For this purpose, 19 lines totalling 189 km of excellent quality, high-resolution seismic data were recorded. Four major acoustic units were identified in the seismic profiles. Three were sedimentary units: irregular layered, cross-layered and well-layered; and the fourth was an acoustic basement which is probably composed of crystalline volcanic rocks. Some local areas in the Neogene formation contain gas accumulations. The formation of faults in E–W and N–S directions can be explained by the existence of shear stresses in the Gulf. The bathymetric map shows good accommodation with the shore line as does the tectonic map.     

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.     

SOME REMARKS ON NOISE STABILITY IN DYNAMIC INVERSION OF REFLECTION SEISMIC DATA1

The dynamic inversion of reflection seismic data is investigated with reference to the influence of noise on pseudo-impedance logs. Model traces are calculated with 0, 5, 15 and 50% noise, respectively. In solving the inversion problem, the algorithm of Marquardt and Levenberg is used in connection with singular value decomposition (SVD). The results are within a 1% error range so that there was no visible change in the logs. Further signal analysis show that there is no dependence on the phase content of the wavelet used if all other parameters of the model are known.     

FULL WAVE EQUATION DOWNWARD CONTINUATION OF SEISMIC REFLECTION DATA*

A new method for suppressing multiple reflections in seismograms is developed. It is based on a downward continuation procedure which uses the full acoustic wave equation (hyperbolic form) as a downward continuation operator. We demonstrate that the downward continuation of the recorded wave field maps a reflectivity function without multiply reflected events. The method is applied successfully to individual traces of plane-wave decomposed (slant-stacked) synthetic and field data.     

A COMPARISON OF STATISTICAL AND DETERMINISTIC WIENER DECONVOLUTION OF DEEP-TOW SEISMIC DATA*

Wiener ‘spiking’ deconvolution of seismic traces in the absence of a known source wavelet relies upon the use of digital filters, which are optimum in a least-squares error sense only if the wavelet to be deconvolved is minimum phase. In the marine environment in particular this condition is frequently violated, since bubble pulse oscillations result in source signatures which deviate significantly from minimum phase. The degree to which the deconvolution is impaired by such violation is generally difficult to assess, since without a measured source signature there is no optimally deconvolved trace with which the spiked trace may be compared. A recently developed near-bottom seismic profiler used in conjunction with a surface air gun source produces traces which contain the far-field source signature as the first arrival. Knowledge of this characteristic wavelet permits the design of two-sided Wiener spiking and shaping filters which can be used to accurately deconvolve the remainder of the trace. In this paper the performance of such optimum-lag filters is compared with that of the zero-lag (one-sided) operators which can be evaluated from the reflected arrival sequence alone by assuming a minimum phase source wavelet. Results indicate that the use of zero-lag operators on traces containing non-minimum phase wavelets introduces significant quantities of noise energy into the seismic record. Signal to noise ratios may however be preserved or even increased during deconvolution by the use of optimum-lag spiking or shaping filters. A debubbling technique involving matched filtering of the trace with the source wavelet followed by optimum-lag Wiener deconvolution did not give a higher quality result than can be obtained simply by the application of a suitably chosen Wiener shaping filter. However, cross correlation of an optimum-lag spike filtered trace with the known ‘actual output’ of the filter when presented with the source signature is found to enhance signal-to-noise ratio whilst maintaining improved resolution.     

A PREDICTION OF SEDIMENTARY ENVIRONMENT FROM MARINE SEISMIC DATA *

Stratigraphic models are usually oversimplified by petroleum geologists, and the result is that the principles which we use for interpreting geophysical data are also over-simplified or even incorrect. Based on the marine seismic data from the Adriatic Sea, an example of prediction of a rather complex sedimentation model of detrital sediments is shown. On the basis of the stratigraphic interpretation using seismic techniques only for this some very important characteristics are discussed: — paleotopography of the valley and conditions which have given opportunity to map accurately the pre-depositional surface, — seismic signatures of the sedimentary section of the ancient valley in which we have recognized aluvial sequence and marine one. The conclusion is that there is a real opportunity for exploration of stratigraphic traps in this part of the Mediterranean Basin.     

地震资料自适应时变卡尔曼反褶积

应用卡尔曼滤波的一步预测方法,并根据卡尔曼滤波方程适用于时变系统的特点,给出了利用卡尔曼滤波进行地震资料自适应时变反褶积的方法,文中给出了理论和实际资料处理的例子.     

地震资料自适应时变卡尔曼反褶积

应用卡尔曼滤波的一步预测方法,并根据卡尔曼滤波方程适用于时变系统的特点,给出了利用卡尔曼滤波进行地震资料自适应时变反褶积的方法,文中给出了理论和实际资料处理的例子.     

SEISMIC REFLECTION AMPLITUDES1

Seismic amplitude variations with offset contain information about the elastic parameters. Prestack amplitude analysis seeks to extract this information by using the variations of the reflection coefficients as functions of angle of incidence. Normally, an approximate formula is used for the reflection coefficients, and variations with offset of the geometrical spreading and the anelastic attenuation are often ignored. Using angle of incidence as the dependent variable is also computationally inefficient since the data are recorded as a function of offset. Improved approximations have been derived for the elastic reflection and transmission coefficients, the geometrical spreading and the complex travel-time (including anelastic attenuation). For a 1 D medium, these approximations are combined to produce seismic reflection amplitudes (P-wave, S-wave or converted wave) as a Taylor series in the offset coordinate. The coefficients of the Taylor series are computed directly from the parameters of the medium, without using the ray parameter. For primary reflected P-waves, dynamic ray tracing has been used to compute the offset variations of the transmission coefficients, the reflection coefficient, the geometrical spreading and the anelastic attenuation. The offset variation of the transmission factor is small, while the variations in the geometrical spreading, absorption and reflection coefficient are all significant. The new approximations have been used for seismic modelling without ray tracing. The amplitude was approximated by a fourth-order polynomial in offset, the traveltime by the normal square-root approximation and the absorption factor by a similar expression. This approximate modelling was compared to dynamic ray tracing, and the results are the same for zero offset and very close for offsets less than the reflector depth.     

地震资料自适应时变卡尔曼反褶积

应用卡尔曼滤波的一步预测方法,并根据卡尔曼滤波方程适用于时变系统的特点,给出了利用卡尔曼滤波进行地震资料自适应时变反褶积的方法,文中给出了理论和实际资料处理的例子.     

IMAGING CAPABILITY OF CROSS-HOLE SEISMIC REFLECTION SURVEYS1

In seismic migration, it is important to sample a range of dips around the local structural dip at each image point. Meaningful images are obtained only where this condition holds. For cross-hole seismic reflection surveys, the distribution of dips sampled at each image point is controlled principally by the survey geometry, including source and receiver array lengths and their element spacings. Using a real data set as an example, we show how survey geometry can limit imaging capability close to the boreholes and even in the middle of the section between the boreholes. At the processing stage, effective removal of direct waves and accurate estimation of the velocity field are essential for optimizing image quality. For migration, we propose a generalized Berryhill (GB) scheme which is based on the Kirchhoff integral and takes into account both the near-field and far-field terms. This should improve the ability to image close to source and receiver arrays, provided that the element spacing in the nearby array is small enough.     

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.     

由宽角反射地震资料重建壳幔反射结构的相似性剖面

针对人工源宽角地震测深中炮点与接收点稀疏的特点,利用几何散射理论进行壳幔散射体的相似性剖面成像,利用互易性原理计算散射体相似性成像的时间条件,研究基于宽角反射地震资料重建壳幔反射结构的相似性成图方法. 其中,成像点的时间采用快速、高精度的程函方程求解技术. 利用该方法处理东南陆缘区宽角反射剖面实际资料,结果表明,较之壳幔反射结构的CDP成图技术,相似性成图方法具有提高反射同相轴横向连续性的能力.