基于粒子群优化算法的叠前角道集子波反演

本文探讨了粒子群优化(PSO)算法在叠前地震角道集子波反演中的应用.在基本最优PSO算法的基础上,提出了对粒子更新速度进行平滑滤波的改进最优粒子群算法.由于代表子波的粒子的维数较大,如果粒子的各维元素相互独立,将导致粒子速度更新紊乱,影响搜索速度.通过对粒子速度进行三点均值滤波,加强了单个粒子各维元素的相互联系,并防止了粒子速度逃逸,使粒子更快地向有利于最优解的位置收敛.该方法应用于叠前角道集子波的反演中,取得了较好的子波反演效果,证明了本文方法的有效性.     

Rainfall data simulation by hidden Markov model and discrete wavelet transformation

In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of deterministic and stochastic models (towards possible representation of both deterministic and stochastic properties) has not hitherto been proposed. An attempt is made in this study to simulate daily rainfall data by utilizing discrete wavelet transformation and hidden Markov model. We use a deterministic model to obtain large-scale data, and a stochastic model to simulate the wavelet tree coefficients. The simulated daily rainfall is obtained by inverse transformation. We then compare the accumulated simulated and accumulated observed data from the Chao Phraya Basin in Thailand. Because of the stochastic nature at the small scale, the simulated daily rainfall on a point to point comparison show deviations with the observed data. However the accumulated simulated data do show some level of agreement with the observed data.     

A probabilistic/deterministic approach for the prediction of the sediment transport rate

In this paper we present a probabilistic/deterministic model for the evaluation of the sediment transport rate in a stream. Starting from Einstein’s theory, the approach was obtained by trying to overcome some of the intrinsic limitations. The approach is based on two distinct probability functions, one relevant to the detachment of grains and the second relevant to the length of particle jumps. The sediment transport rate is obtained by integrating the distribution of the ranges of the particle jumps multiplied by the average particle velocity. The relationship for the average ranges of particle jumps is an opportune combination of the Einstein and Yalin expressions. The final formulation was calibrated by means of a large number of experimental data and also by comparison with some of the most widely-used empirical formulas. The results show a better agreement between theory and experiments than do the other theories analyzed.     

Measurement of interstation phase velocity by wavelet transformation

In this paper,we present wavelet transformation method to measure interstation phase velocity. We use Morlet wavelet function as mother wavelet to filter two seismograms at various period of interest,and correlate the wavelet filtered seismograms to form cross-correlogram. If both wavelet filtered signals are in phase at that period,the phase of the cross-correlogram is a minimum. Using 3-spline interpolation to transform cross-correlation matrix to a phase velocity verse period image,it is convenient for u...     

Joint AVO inversion, wavelet estimation and noise-level estimation using a spatially coupled hierarchical Bayesian model

The main objective of the AVO inversion is to obtain posterior distributions for P-wave velocity, S-wave velocity and density from specified prior distributions, seismic data and well-log data. The inversion problem also involves estimation of a seismic wavelet and the seismic-noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well-log data. The posterior distribution is explored by Markov-chain Monte-Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic-noise model resulted in about 10% lower uncertainties for the P-wave velocity, S-wave velocity and density compared with a white-noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.     

Inverse kinematic problem for a random gradient medium in geometric optics approximation

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.     

Review of vibroseis data acquisition and processing for better amplitudes: adjusting the sweep and deconvolving for the time-derivative of the true groundforce

The goal of vibroseis data acquisition and processing is to produce seismic reflection data with a known spatially-invariant wavelet, preferably zero phase, such that any variations in the data can be attributed to variations in geology. In current practice the vibrator control system is designed to make the estimated groundforce equal to the sweep and the resulting particle velocity data are cross-correlated with the sweep. Since the downgoing far-field particle velocity signal is proportional to the time-derivative of the groundforce, it makes more sense to cross-correlate with the time-derivative of the sweep. It also follows that the ideal amplitude spectrum of the groundforce should be inversely proportional to frequency. Because of non-linearities in the vibrator, bending of the baseplate and variable coupling of the baseplate to the ground, the true groundforce is not equal to the pre-determined sweep and varies not only from vibrator point to vibrator point but also from sweep to sweep at each vibrator point. To achieve the goal of a spatially-invariant wavelet, these variations should be removed by signature deconvolution, converting the wavelet to a much shorter zero-phase wavelet but with the same bandwidth and signal-to-noise ratio as the original data. This can be done only if the true groundforce is known. The principle may be applied to an array of vibrators by employing pulse coding techniques and separating responses to individual vibrators in the frequency domain. Various approaches to improve the estimate of the true groundforce have been proposed or are under development; current methods are at best approximate.     

非稳态地震记录时变子波估计

地震子波估计是地震资料处理和解释中的一个关键问题,子波估计的可靠性会直接影响反褶积和反演的准确度.现有的子波估计方法分为确定型和统计型两种类型,本文通过结合这两类方法,利用确定型的谱分析法和统计型的偏度最大化方法,分别提取时变子波的振幅和相位信息,得到估计的时变子波.这种方法不需要对子波进行任何时不变或相位等的假设,具有对时变相位的估计能力.进而利用估计时变子波进行非稳态反褶积,提高地震记录的保真度,为精细储层预测和描述提供高质量的剖面.理论模型试算验证了方法的可行性,通过实际地震资料的处理应用,表明该方法能有效地提取出子波时变信息.     

基于小波分析的水位观测气压效应研究

为研究水位气压效应的主要特征, 采用广西南宁石埠、 九塘两个台站的水位、 气压观测资料, 利用小波分析、 交叉小波分析、 小波相干分析方法在时间-频率空间内对二者的周期特征以及二者的相关特征进行了分析。 结果表明: 水位观测数据的显著周期为7.8~14.7 h, 气压观测数据的显著周期为7.8~14.7 h和17.5~27.8 h; 水位和气压存在7.8~14.7 h尺度的共振周期; 水位和气压在较宽的周期尺度上存在着显著的相关性, 且水位和气压的相关系数随周期和时间变化, 二者的相对相位角也因周期的不同而存在差异。     

Break through the limits of vibroseis data quality

The vibroseis method has become the principal data acquisition method in land seismic exploration. It seems that this method has been extended to its limits as the search for energy resources continues. Many practical issues arising from field operations have remained theoretically unexplained, for example, variations in wavelet arrival time, inaccurate wavelet estimation and harmonics in the wavelet itself. The focus of this paper is the proposal of a new model, which is referred to as the vibrator‐coupled ground model, to simulate the filtering effects of a complex coupling system consisting of the coupling between the baseplate and the ground as well as the coupling between the captured ground mass near the vibrator baseplate and the surrounding earth. With this vibrator‐coupled ground model many of the practical issues mentioned above were reasonably addressed. Furthermore, it was demonstrated from experimental tests that both the pilot sweep and the weighted‐sum groundforce, when filtered by the vibrator‐coupled ground model, are proportional to the far‐field particle velocity whereas the unfiltered signals are not. The harmonics on the filtered weighted‐sum groundforce successfully maintain a proportional relationship with the harmonics seen in the far‐field signal.     

Estimation of the seismic wavelet through homomorphic deconvolution and well log data: application on well-to-seismic tie procedure

Wavelet estimation and well-tie procedures are important tasks in seismic processing and interpretation. Deconvolutional statistical methods to estimate the proper wavelet, in general, are based on the assumptions of the classical convolutional model, which implies a random process reflectivity and a minimum-phase wavelet. The homomorphic deconvolution, however, does not take these premises into account. In this work, we propose an approach to estimate the seismic wavelet using the advantages of the homomorphic deconvolution and the deterministic estimation of the wavelet, which uses both seismic and well log data. The feasibility of this approach is verified on well-to-seismic tie from a real data set from Viking Graben Field, North Sea, Norway. The results show that the wavelet estimated through this methodology produced a higher quality well tie when compared to methods of estimation of the wavelet that consider the classical assumptions of the convolutional model.     

Discrete wavelet‐based trend identification in hydrologic time series

Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

一种新的地震子波提取与层速度反演方法

粒子群优化算法是近十年发展起来的一种基于群智能的非线性全局最优化新方法.本文详细介绍了粒子群优化算法的基本原理,并将其应用到子波提取与层速度反演中.通过模拟数值算例,从不同角度研究了粒子群优化算法的可行性及其效率问题.试算结果表明,粒子群优化算法在不同分辨率、不同信噪比、不同相位子波合成的地震记录反演中效果明显.     

偏移成像中的垂直分辨率

Kirchhoff真振幅偏移研究表明,偏移对地震子波具有拉伸作用,拉伸程度与地震波速度、反射角和地层倾角有关.子波拉伸将改变子波宽度(子波延续长度),对垂直分辨率有重要影响.本文通过对衰减Sinc子波的实际计算,分析了地震波速度、反射角和地层倾角分别与子波宽度的关系.从分析来看,陡倾角和大反射角（大炮检距）造成偏移成像垂直分辨率严重下降.高主频子波对各参数均有较低敏感度.     

TUNING EFFECTS,LITHOLOGICAL EFFECTS AND DEPOSITIONAL EFFECTS IN THE SEISMIC RESPONSE OF GAS RESERVOIRS*

Synergism of 3-D seismic data, wavelet processing, colour display and interactive interpretation has been exploited in the study of a Gulf of Mexico gas reservoir. Seismic amplitude has been used as a measure of the proportion of a sand/shale reservoir capable of producing gas. This has led to the mapping of net producible thickness of gas sand. The tuning phenomena resulting from geometric effects alone were studied in detail, and tuning curves of various levels of sophistication were used as the basis for amplitude editing. Statistical tuning curves were derived by interactive cross-plotting and deterministic curves by wavelet extraction. Multiple wavelet side lobes cause multiple maxima in the tuning curve. Depositional effects and intrareservoir communication have also been studied by interactive cross-plotting.     

Fast free surface multiples attenuation workflow for three-dimensional ocean bottom seismic data

Water multiples can be very strong and contaminate the primary reflections. This can cause problems in the processing flow and the interpretation of the subsurface image. Hence, multiples suppression is an important part of the preprocessing flow. We present a fast workflow for attenuation of free surface related multiples for 2D and 3D ocean bottom seismic data based on the wave equation approach. Included in the workflow are: 1. Calibration of the pressure and vertical velocity components by using wavefield splitting. 2. Data interpolation by using offset projection. 3. Fast Radon transform by using fast fractional Fourier transform. Advantages of this workflow are that it is fast, efficient and the only requirements are the recording of both pressure and vertical particle components at some point below the source in the water column.     

Acoustic directional snapshot wavefield decomposition

Up–down wavefield decomposition is effectuated by a scaled addition or subtraction of the pressure and vertical particle velocity, generally on horizontal or vertical surfaces, and works well for data given on such surfaces. The method, however, is not applicable to decomposing a wavefield when it is given at one instance in time, i.e. on snapshots. Such situations occur when a wavefield is modelled with methods like finite-difference techniques, for the purpose of, for example, reverse time migration, where the entire wavefield is determined per time instance. We present an alternative decomposition method that is exact when working on snapshots of an acoustic wavefield in a homogeneous medium, but can easily be approximated to heterogeneous media, and allows the wavefield to be decomposed in arbitrary directions. Such a directional snapshot wavefield decomposition is achieved by recasting the acoustic system in terms of the time derivative of the pressure and the vertical particle velocity, as opposed to the vertical derivative in up–down decomposition for data given on a horizontal surface. As in up–down decomposition of data given at a horizontal surface, the system can be eigenvalue decomposed and the inverse of the eigenvector matrix decomposes the wavefield snapshot into fields of opposite directions, including up–down decomposition. As the vertical particle velocity can be rotated at will, this allows for decomposition of the wavefield into any spatial direction; even spatially varying directions are possible. We show the power and effectiveness of the method by synthetic examples and models of increasing complexity.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental investigation of the velocity of a sand cloud blowing over a sandy surface

The velocity of a wind‐blown sand cloud is important for studying its kinetic energy, related erosion, and control measures. PDA (particle dynamics analyser) measurement technology is used in a wind tunnel to study the probability distribution of particle velocity, variations with height of the mean velocity and particle turbulence in a sand cloud blowing over a sandy surface. The results suggest that the probability distribution of the particle velocity in a blowing sand cloud is stochastic. The probability distribution of the downwind velocity complies with a Gaussian function, while that of the vertical velocity is greatly complicated by grain impact with the bed and particle–particle collisions in the air. The probability distribution of the vertical velocity of ?ne particles (0·1–0·3 mm sands) can be expressed as a Lorentzian function while that of coarse particles (0·3–0·6 mm sands) cannot be expressed by a simple distribution function. The mean downwind velocity is generally one or two orders greater than the mean vertical velocity, but the particle turbulence in the vertical direction is at least two orders greater than that in the downwind direction. In general, the mean downwind velocity increases with height and free‐stream wind velocity, but decreases with grain size. The variation with height of the mean downwind velocity can be expressed by a power function. The particle turbulence of a blowing sand cloud in the downwind direction decreases with height. The variations with height of the mean velocity and particle turbulence in the vertical direction are very complex. It can be concluded that the velocity of a sand cloud blowing over a sandy surface is mainly in?uenced by wind velocity, grain impact with the bed and particle–particle collisions in the air. Wind velocity is the primary factor in?uencing the downwind velocity of a blowing sand cloud, while the grain impact with the bed and particle–particle collisions in the air are the primary factors responsible for the vertical velocity. Copyright © 2004 John Wiley & Sons, Ltd.     

POST-CRITICAL WAVELET ESTIMATION AND DECONVOLUTION1

Using synthetic data, it is demonstrated that the amplitude spectra of post-critical plane-wave components are stable and equal to the amplitude spectrum of the input wavelet (critical reflection theorem). Our analysis and physical explanation of the theorem are based only on amplitude versus offset arguments. The stability of the spectra in the post-critical region is directly related to a high amplitude post-critical reflection that dominates the trace in the slant-stack domain. The validity of the theorem for both the acoustic and elastic cases, its assumptions and limitations, are also examined with emphasis on applications for processing seismic reflection data. Based on the theorem, a deterministic procedure is developed (assuming minimum-phase properties) for wavelet estimation and subsequent deconvolution. We call this method Post-critical Deconvolution, which emphasizes reliance on post-critical reflection data. The performance of the method is shown with real data and the results are compared to those obtained with conventional deconvolution techniques.