Joint viscoacoustic waveform inversion with the separated upgoing and downgoing wavefields in zero-offset vertical seismic profile data

The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality-factor Q. The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality-factor is proposed based on the multi-objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the individual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the individual wavefields and improve the convergence of viscoacoustic full-waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality-factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical example validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.     

VERTICAL SEISMIC PROFILING IN COAL*

The intellection of seismic wave propagation in coal measures demands direct observation of the wavefield progression. Two vertical seismic profiles with high spatial and temporal sampling, were recently recorded in the Sydney Basin coalfields as part of an experimental coal seismic program. Static corrections and interval velocities were obtained by an automated system to determine first kicks and pulse rise times. Upgoing and downgoing waves were separated in the f—k-plane using a novel technique of contour slice filtering. The isolated upgoing waves clearly display reflections from the major coal seams within the stratigraphic sequence. The downgoing wave spectra were subjected to attenuation analysis. The deduced specific quality factor Q for Permian coal measure rocks lies in the range 20–70. Similar estimates were obtained in the time domain from measurements of pulse broadening. Synthetic VSP seismograms, computed using an exact recursive formulation, are an indispensable aid to interpretation. They illustrate the filtering effects of coal seams and sequences, and the effects of the contribution of internal and free-surface multiple reflections in the recorded wavetrains.     

基于局部斜率属性的VSP波场分离研究

基于垂直地震剖面(VSP)资料中上、下行波视速度的差异,利用地震剖面同相轴局部斜率属性参数,提出了一种分离上、下行波场的新方法.首先利用Fourier变换初步分离上、下行波场,然后利用平面波分解滤波器(Plane Wave Destruction (PWD) Filter)技术估计初始分离波场的同相轴局部斜率属性参数,在此基础上对VSP原始资料波场分离.该方法是一种时间域最小平方优化分离波场的方法,不存在其他滤波方法阈值滤波器边界的影响,减少了因镶边问题带来的假象.模拟和实际资料处理结果表明,该方法与传统方法相比,分离出的上、下行波噪声假象少,振幅保持好,更好地消除了上、下行波的相互影响.     

WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS. PART I: METHODS USING THE ONE-WAY WAVE EQUATIONS*

Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one-way wave equations. In cases of limited propagation angles and weak inhomogeneities these one-way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub-division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.     

基于两步SVD变换的零偏VSP资料上下行波场分离方法

垂直地震剖面(Vertical Seismic Profiling,VSP)资料处理中波场分离是关键问题之一.随着属性提取技术的发展,新的属性参数(例如Q值)提取技术对波场分离的保真性要求越来越高.本文改进了传统奇异值分解(Singular Value Decomposition,SVD)法,给出了一种对波场的动力学特征具有更好的保真性,可以作为Q值提取的预处理步骤的零偏VSP资料上下行波场分离方法.该方法通过两步奇异值分解变换实现:第一步,排齐下行波同相轴,利用SVD变换压制部分下行波能量;第二步,在剩余波场中排齐上行波同相轴,使用SVD变换提取上行波场.在该方法的实现过程中,压制部分下行波能量后的剩余波场中仍然存在较强的下行波干扰,使得上行波同相轴的排齐比较困难.本文给出了一种通过极大化多道数据线性相关程度(Maximize Coherence,MC)排齐同相轴的算法,在一定程度上解决了低信噪比下排齐同相轴的问题.将本文提出的方法用于合成数据和实际资料的处理,并与传统SVD法的处理结果进行对比,结果表明本文提出的波场分离方法具有良好的保真性,得到波场的质量明显优于传统SVD法.通过对本文方法和传统SVD法处理合成数据得到的下行波场提取Q值,然后进行对比可知,本文方法可以有效提高所提取Q值的准确性,适合作为Q值提取的预处理步骤.     

Marine seismic wavefield measurement to remove sea-surface multiples

We propose a new method for removing sea-surface multiples from marine seismic reflection data in which, in essence, the reflection response of the earth, referred to a plane just above the sea-floor, is computed as the ratio of the plane-wave components of the upgoing wave and the downgoing wave. Using source measurements of the wavefield made during data acquisition, three problems associated with earlier work are solved: (i) the method accommodates source arrays, rather than point sources; (ii) the incident field is removed without simultaneously removing part of the scattered field; and (iii) the minimum-energy criterion to find a wavelet is eliminated. Pressure measurements are made in a horizontal plane in the water. The source can be a conventional array of airguns, but must have both in-line and cross-line symmetry, and its wavefield must be measured and be repeatable from shot to shot. The problem is formulated for multiple shots in a two-dimensional configuration for each receiver, and for multiple receivers in a two-dimensional configuration for each shot. The scattered field is obtained from the measurements by subtracting the incident field, known from measurements at the source. The scattered field response to a single incident plane wave at a single receiver is obtained by transforming the common-receiver gather to the frequency–wavenumber domain, and a single component of this response is obtained by Fourier transforming over all receiver coordinates. Each scattered field component is separated into an upgoing wave and a downgoing wave using the zero-pressure condition at the water-surface. The upgoing wave may then be expressed as a reflection coefficient multiplied by the incident downgoing wave plus a sum of scattered downgoing plane waves, each multiplied by the corresponding reflection coefficient. Keeping the upgoing scattered wave fixed, and using all possible incident plane waves for a given frequency, yields a set of linear simultaneous equations for the reflection coefficients which are solved for each plane wave and for each frequency. To create the shot records that would have been measured if the sea-surface had been absent, each reflection coefficient is multiplied by complex amplitude and phase factors, for source and receiver terms, before the five-dimensional Fourier transformation back to the space–time domain.     

VSP上下行反射波联合成像方法研究

VSP资料上下行波场发育丰富.本文在分析VSP直达波、上行反射波、下行反射波传播路径及其照明范围的基础上,指出了常规VSP波动方程偏移方法缺陷,进而通过修改波场延拓方式,提出了上下行反射波联合成像方法,并在高频近似下分析了该方法的成像原理.该方法不需要进行VSP上下行反射波场分离,能够同时对VSP资料中的一次反射波、自由表面多次波、层间多次波进行成像,比常规成像剖面具有更宽的成像范围和更好的成像效果.该方法能够对下行一次反射波进行成像,从而可以实现常规偏移方法难以处理的高陡倾角构造成像.模拟资料和实际资料处理证明了本文方法的正确性.     

THE SPECTRAL FUNCTION OF A LAYERED SYSTEM AND THE DETERMINATION OF THE WAVEFORMS AT DEPTH*

Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram.     

小波尺度域含气储层地震波衰减特征

黏弹性衰减因子Q的可靠估计可通过Q反褶积来提高地震资料的分辨率并有助于振幅分析. 本文从小波理论出发,结合地震波在黏弹性介质中的传播方程,推导出小波尺度域地震波能量衰减公式. 能量衰减公式具有下列性质：（1）Q值越大,能量衰减得越慢;Q值越小,能量衰减越严重;（2）尺度越小,信号中保留的能量越少;（3）对于脉冲源来说在理想的无衰减介质(即Q趋近于∞)中传播时,信号在不同尺度内的能量相同. 利用尺度能量公式,可从反射地震资料中直接估计品质因子Q（即衰减因子）,也可以提取不同尺度的能量衰减剖面作为储层描述的属性参数,用来进行岩性识别和指示气藏,与经典的谱比法相比,避免了谱比法所面临的双时窗问题以及进行谱估计的窗选择问题. 理论模型试验表明了本文方法的正确性和有效性.     

The influence of errors in the source wavelet on inversion‐based surface‐related multiple attenuation

We investigate the influence of source wavelet errors on inversion‐based, surface‐related multiple attenuation, in order to address how the inverted primary impulse response, estimated primaries, and predicted multiples are affected by the estimated wavelet. In theory, errors in estimated wavelet can lead to errors in the upgoing waves. Because of smoothness and the band‐limitedness characteristics of the estimated wavelet, errors in the upgoing waves are usually not white and random. Theoretical analysis and two synthetic examples demonstrate that (i) when the overall amplitude scalar of the estimated wavelet is underestimated, the inversion of the primary impulse response suffers from instability, which will distort the estimation of primaries, and (ii) when the wavelet is overestimated, the estimated primaries will simply mimic the recorded upgoing waves. Nevertheless, the quality of the estimated primaries in the region above the first‐order, water‐bottom multiples is independent of the estimated wavelet. Synthetic results illustrate that inversion‐based, surface‐related multiple attenuation with a known wavelet is stable, since slight inaccuracy in amplitude spectrum and/or phase spectrum of the given wavelet or the corresponding upgoing waves will not lead to considerable deviation in the waveforms of the inverted results from those of the references. Furthermore, shot‐to‐shot wavelet variations, with maximum amplitude difference of 5% and maximum phase difference of 10°, create just slight artefacts in both the inverted primary impulse response and the estimated primaries. Moreover, the sensitivity test of estimation of primaries by sparse inversion method involving wavelet estimation shows that this method can stably and alternately update the wavelet and the primary impulse response; however, different choices of the initial wavelet can lead to different final inverted results.     

Theory of convective saturation of Langmuir waves during ionospheric modification of a barium cloud

In recent experiments (Djuth, F. T., Sulzer, M. P., Elder, J. H. and Groves, K. M. (1995) Journal of Geophysical Research, 100, 17,347), a parametric decay instability was excited by an ordinarywave HF pump during an ionospheric chemical release from a rocket over Arecibo, PR, which created an artificial ‘barium ionosphere,’ with peak plasma frequency above the pump frequency, and a density gradient with a (short) 5 km scale length. Simultaneous incoherent scattering measurements revealed a strong initial asymmetry in the amplitudes of almost vertically upgoing versus downgoing measured plasma waves. We can account for this asymmetry in terms of linear convective saturation of parametrically unstable plasma waves propagating over a range of altitudes along geometric optics ray paths. Qualitative features of the frequency spectrum of the measured downgoing wave are in agreement with this model, although the theoretically predicted spectrum is narrower than observed. The observed altitude localization of the enhanced spectrum to a few range cells is consistent with the theory.     

Modeling of Wide-Angle Seismic Attributes Using the Gaussian Beam Method

In this study, observed seismic attributes from shot gather 11 of the SAREX experiment are used to derive a preliminary velocity and attenuation model for the northern end of the profile in southern Alberta. Shot gather 11 was selected because of its prominent Pn arrivals and good signal to noise ratio. The 2-D Gaussian beam method was used to perform the modeling of the seismic attributes including travel times, peak envelope amplitudes and pulse instantaneous frequencies for selected phases. The preliminary model was obtained from the seismic attributes from shot gather 11 starting from prior tomographic results. The amplitudes and instantaneous frequencies were used to constrain the velocity and attenuation structure, with the amplitudes being more sensitive to the velocity gradients and the instantaneous frequencies more sensitive to the attenuation structure. The resulting velocity model has a velocity discontinuity between the upper and lower crust, and lower velocity gradients in the upper and lower crust compared to earlier studies. The attenuation model has Q _p ^-1 values between 0.011 and 0.004 in the upper crust, 0.0019 in the lower crust and a laterally variable Q _p ^-1 in the upper mantle. The Q _p ^-1 values are similar to those found in Archean terranes from other studies. Although the results from a single gather are non-unique, the initial model derived here provides a self-consistent starting point for a more complete seismic attribute inversion for the velocity and attenuation structure.     

大陆架科学钻探CSDP-2井的垂直地震剖面测量

南黄海海相地层的地震波场特征和层位标定一直是困扰地震勘探的重要问题.为了近距离、高精度和高分辨率地观测井周围构造特征和岩石性质引起的波场变化,为地震资料的采集、处理与解释提供地震波衰减规律、速度与层位标定等信息,对大陆架科学钻探CSDP-2井实施了近零偏移距垂直地震剖面（VSP）观测.针对海相地层顶部强反射界面地震波穿透难的问题,采用了大容量气枪震源并设计了气枪阵列组合方式,提高了激发地震波的能量,获得了强反射界面之下清晰的PP、PS下行波和上行波信号.采用了三分量偏振合成、组合滤波和波场分离等处理方法,对VSP观测数据进行处理,获得了海相三叠系—志留系的精细的纵波、横波速度结构和地层吸收因子等物性数据,建立了钻井地层、测井、VSP上行波和多道地震剖面对应关系,实现了不同尺度的地质和地球物理属性资料的有效衔接,标定了钻井地质剖面上各深度地质体的地震反射特性,厘定了过井地震剖面上反射同相轴的地质属性.此次观测取得的纵波、横波速度信息,成为建立南黄海海相地层速度模型主要的资料来源,也是地震资料的岩性反演处理不可缺少的信息.     

用于零偏移距VSP资料的自适应波形反演方法研究

提出一种利用零偏移距VSP资料初至下行波(即直达波)反演介质品质因子Q及层速度V等参数的方法, 称为自适应时域波形反演法(ATWI). 为了充分地利用有效信息, 该方法根据实际VSP资料的信噪比及直达波与上行波干涉的程度,自适应最大限度地选取未受干扰的初至波片段,并用该片段构造目标函数; 通过恰当地构造数据加权矩阵提高目标函数对Q值变化的敏感性;为克服非线性反演的病态问题,采用近来发展的乘性正则化方法,并通过约束条件限制待求参数的取值范围;文中推导出了雅可比矩阵各元素的解析表达式,从而减小了反问题的计算量.合成数据反演结果表明,与谱比值法和子波包络峰值瞬时频率法相比较,ATWI法受上行波影响相对较小、抗噪性能更强.实际资料算例进一步证明了ATWI方法的有效性.     

Determining Q of near-surface materials from Rayleigh waves

High-frequency (≥2 Hz) Rayleigh wave phase velocities can be inverted to shear (S)-wave velocities for a layered earth model up to 30 m below the ground surface in many settings. Given S-wave velocity (V_S), compressional (P)-wave velocity (V_P), and Rayleigh wave phase velocities, it is feasible to solve for P-wave quality factor Q_P and S-wave quality factor Q_S in a layered earth model by inverting Rayleigh wave attenuation coefficients. Model results demonstrate the plausibility of inverting Q_S from Rayleigh wave attenuation coefficients. Contributions to the Rayleigh wave attenuation coefficients from Q_P cannot be ignored when Vs/V_P reaches 0.45, which is not uncommon in near-surface settings. It is possible to invert Q_P from Rayleigh wave attenuation coefficients in some geological setting, a concept that differs from the common perception that Rayleigh wave attenuation coefficients are always far less sensitive to Q_P than to Q_S. Sixty-channel surface wave data were acquired in an Arizona desert. For a 10-layer model with a thickness of over 20 m, the data were first inverted to obtain S-wave velocities by the multichannel analysis of surface waves (MASW) method and then quality factors were determined by inverting attenuation coefficients.     

紫坪铺水库诱发地震与构造地震波谱时频特征差异性研究

利用紫坪铺水库2004～2007年记录的实际地震数据,通过比较多种滤波方法,发展出一种既能有效滤除地震数据中本底噪音、又对有效信号损伤较小的比值滤波方法。对去噪后的水库诱发地震和构造地震数据,利用小波变换方法,分别进行时频分析获得两类地震的时频谱,并提取可以反映地震发生前后能量分布和聚集情况的时频属性,最后根据各个属性的响应效果,组合得到新的属性。将时频谱与时频属性相结合,总结归纳紫坪铺水库诱发地震与构造地震波谱时频特征的差异性,为地震监测分析提供基础依据。     

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.     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

利用基于子波估计的频谱校正方法提高Q值估计精度(英文)

用Q值刻画的地震衰减在地震信号处理和解释中具有很广泛的应用。利用反射地震资料进行Q值估计需要解决地震子波和反射系数序列耦合的问题。从反射地震资料中去除反射系数序列的影响,这个过程称为频谱校正。本文提出了一种基于子波估计的求取Q值的方法,进而设计了一个反Q滤波器。该方法利用反射地震资料的高阶统计量进行子波估计,并利用所估计子波实现频谱校正。我们利用合成数据实验给出了质心频移法与频谱比法这两种常用的Q值估计方法在不同参数设置下的性能。人工合成数据和实际数据处理表明,利用本文提出的方法进行频谱校正后,可以得到可靠的Q值估计。经过反Q滤波,地震数据的高频部分得到了有效地恢复。