WAVELET ESTIMATION USING THE MULTITAPER METHOD1

An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well-control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum-phase assumption. The construction of the minimum-phase wavelet is critically dependent on the decay of the spectrum at the low-frequency end. Traditional methods of cross-spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side-lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low-frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side-lobe leakage causes poor estimates of the low-frequency decay, resulting in degraded wavelet estimates. Thomson's multitaper method of cross-spectral estimation which suffers little from side-lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low-frequency roll-off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll-off is only about 36 dB/oct. Thus the multitaper method gives a low-frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi-taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.     

WAVELET DECONVOLUTION USING A SOURCE SCALING LAW*

We present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source-receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase. We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non-minimum-phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.     

用参考台技术计算大地电磁张量阻抗

Gaubau等人于1978年提出的参考台技术,从理论上完全消除了计算张量阻抗时所具有的偏倚误差。但在实际测量中,参考台的距离多大才合适,尚无定论。本文所给的实例,采取了固定主测台、移动参考台的方法。结果表明,参考台距离从20 km变到40 km不会给测量结果带来明显的变化。     

用参考台技术计算大地电磁张量阻抗

Gaubau等人于1978年提出的参考台技术,从理论上完全消除了计算张量阻抗时所具有的偏倚误差。但在实际测量中,参考台的距离多大才合适,尚无定论。本文所给的实例,采取了固定主测台、移动参考台的方法。结果表明,参考台距离从20 km变到40 km不会给测量结果带来明显的变化。     

INTERPRETATION OF MAGNETIC ANOMALIES USING SPECTRAL ESTIMATION TECHNIQUES*

The depth of causative bodies may be derived from the power spectrum of their magnetic anomalies. After a short review of the theoretical basis of the method, several examples of its application to synthetic cases are shown. Disturbing effects due to improper choice of the sampling interval and to anomalies only partially contained in the examined segment of the profile are studied. The spectral method is then applied to real cases; the tapering of the anomalies, the application of non-linear filters and the effects of anomaly superpositions are investigated. In conclusion, an appraisal of the method and of its possible practical impact has been given.     

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.     

A COMPARISON BETWEEN WIENER FILTERING,KALMAN FILTERING,AND DETERMINISTIC LEAST SQUARES ESTIMATION*

The least squares estimation procedures used in different disciplines can be classified in four categories:

• a. Wiener filtering,
• b. b. Autoregressive estimation,
• c. c. Kalman filtering,
• d. d. Recursive least squares estimation.

The recursive least squares estimator is the time average form of the Kalman filter. Likewise, the autoregressive estimator is the time average form of the Wiener filter. Both the Kalman and the Wiener filters use ensemble averages and can basically be constructed without having a particular measurement realisation available. It follows that seismic deconvolution should be based either on autoregression theory or on recursive least squares estimation theory rather than on the normally used Wiener or Kalman theory. A consequence of this change is the need to apply significance tests on the filter coefficients. The recursive least squares estimation theory is particularly suitable for solving the time variant deconvolution problem.     

A PULSE COMPRESSION TECHNIQUE USING COHERENT LIGHT*

Seismic methods of the Vibroseis type require a cross-correlation between received and transmitted signals. This process is now carried out with computers with convolvers but was first analogically realized. When the amount of data to be processed becomes very important as for marine seismic, it might be worth considering the principle described in this article. Dynamic range determination and synthetic examples are shown.     

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array. In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array. Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.     

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.     

用波速层析成像方法提高储层横向预测精度

以数值模拟方法为基础，考察了反射地震层析成像技术对油气储层波速横向检测的效果，然后用渤海油田的地震资料进行了实用试验．对数值模拟结果和实际数据的试验结果进行了分析与评价，认为油气勘探中的反射地震资料具有地震射线近似垂直分布的特点，适合用反射地震层析成像技术进行目标层横向非均匀性检测．     

用波速层析成像方法提高储层横向预测精度

以数值模拟方法为基础,考察了反射地震层析成像技术对油气储层波速横向检测的效果,然后用渤海油田的地震资料进行了实用试验．对数值模拟结果和实际数据的试验结果进行了分析与评价,认为油气勘探中的反射地震资料具有地震射线近似垂直分布的特点,适合用反射地震层析成像技术进行目标层横向非均匀性检测．     

基于相关系数的海底大地电磁阻抗Robust估算方法

对于海洋的特殊环境，常规的阻抗估算方法往往不能很好地估算海底大地电磁的阻 抗张量，本文提出了基于相关归一Robust方法. 以相关系数为参数对阻抗张量元素进行归一，据相关系数值的变化修正Robust的权系数. 模拟和实测数据的计算表明，相关归一Robust法比其他常规方法更能有效地抑制干扰. 噪声强度小于30%时常规方法和新方法都能有效 地估算阻抗张量；噪声强度大于50%时，常规方法估算误差明显偏大，新方法误差要小得多，反映出该方法有较强抗干扰的能力.     

小波变换在识别储层流体性质中的应用

根据小波变换的特点提出一种识别储层流体的新方法. 本文假设测井所得的信号为地层微观孔隙结构、地层流体性质及岩性和岩相等各部分的综合贡献之和，不同的储层中小波分析的能量谱特征不同，因而通过对已知储层模型进行小波能量谱分析，可得到各种储层的特征能量谱，根据这些储层特征能量谱就可以对待划分的储层段进行储层流体性质判别.     

ESTIMATION OF SPECTRUM AND CROSS-SPECTRUM OF AEROMAGNETIC FIELD USING FAST DIGITAL FOURIER TRANSFORM (FDFT) TECHNIQUES*

An efficient method of computing spectrum and cross-spectrum of large scale aero-magnetic field (or of any other two-dimensional field) has been developed and programmed for a digital computer. The method uses fast Fourier transform techniques. Briefly, the method is as follows: a digitized aeromagnetic map is divided into a number of rectangular blocks. Fourier transforms of these blocks are computed using a two-dimensional fast Fourier transform method. Finally, the amplitude of the Fourier transforms is averaged to give the desired spectrum. Computation of cross-spectrum follows the same lines. In fact, the same programme may be used to a compute the spectrum as well as cross-spectrum. The method has a number of computational advantages, in particular it reduces greatly computational time and storage requirements. The programme has been tested on synthetic data as well as on real aeromagnetic data. It took less than 30 seconds on an IBM 360/50 computer to compute the spectrum of an aeromagnetic map covering an area of approximately 4500 square miles.     

利用多分辨率小波网络进行地震资料反演

在讨论小波网络理论方法的基础上,研究了利用地震纪录小波多尺度分解属性资料进行虚井声波时差反演的技术方法。分析了利用地震信号进行小波分解和网络学习、训练的理论方法。研究中发现:对于相邻的地震道,较小一段的相似性比整个地震道的相似性要好。据此,利用小波时-频分析技术方法,可以把相邻道的信息外推到其它地震道上。通过以上综合研究及对实际资料进行反演计算、分析,认为小波网络与人工神经网络相比其网络结构要容易选定,并且收敛速度快。同时,利用地震资料分段时-频分析的相似性较好和小波网络学习、训练及记忆能力较强的特点,可以较好地把井旁道的高、低频信息转换到相邻道上。这样在提高分辨率的同时,又增加了反演结果的真实可靠性     

ESTIMATION OF THE PRIMARY SEISMIC PULSE *

A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, α_j is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and n_j is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.     

MAXIMUM-LIKELIHOOD ESTIMATION OF SEISMIC IMPULSE RESPONSES*

A seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus a moving average noise process (colored noise). Multiple reflections and reverberations are assumed to be removed from the trace by conventional means. The method of maximum likelihood (ML) is used to estimate the reflection coefficients and the unknown noise parameters. If the reflection coefficients are known from well logs, the seismic pulse and the noise parameters can be estimated. The maximum likelihood estimation problem is reduced to a nonlinear least-squares problem. When the further assumption is made that the noise is white, the method of maximum likelihood is equivalent to the method of least squares (LS). In that case the sampling rate should be chosen approximately equal to the Nyquist rate of the trace. Statistical and numerical properties of the ML- and the LS-estimates are discussed briefly. Synthetic data examples demonstrate that the ML-method gives better resolution and improved numerical stability compared to the LS-method. A real data example shows the ML- and LS-method applied to stacked seismic data. The results are compared with reflection coefficients obtained from well log data.     

A STATISTICAL APPROACH TO THE EXTRACTION OF THE SEISMIC PROPAGATING WAVELET*

A model of the seismic trace is generally given as a convolution between the propagating wavelet and the reflectivity series of the earth and normally it is assumed that a white noise is added to the trace. The knowledge of the propagating wavelet is the basic point to estimate the reflectivity series from the seismic trace. In this paper a statistical method of wavelet extraction from several seismic traces, assuming the wavelet to be unique, is discussed. This method allows one to obtain the propagating wavelet without any classical limitative assumptions on the phase spectrum. Furthermore, a phase unwrapping method is suggested and some statistical properties of the phase spectrum of the reflectivity traces are examined.