Multiwell study of seismic attenuation at the CO2CRC Otway project geosequestration site: Comparison of amplitude decay,centroid frequency shift and 1D waveform inversion methods

At the CO2CRC Otway geosequestration site, the abundance of borehole seismic and logging data provides a unique opportunity to compare techniques of Q (measure of attenuation) estimation and validate their reliability. Specifically, we test conventional time-domain amplitude decay and spectral-domain centroid frequency shift methods versus the 1D waveform inversion constrained by well logs on a set of zero-offset vertical seismic profiles. The amplitude decay and centroid frequency shift methods of Q estimation assume that a seismic pulse propagates in a homogeneous medium and ignore the interference of the propagating wave with short-period multiples. The waveform inversion explicitly models multiple scattering and interference on a stack of thin layers using high-resolution data from sonic and density logs. This allows for stable Q estimation in small depth windows (in this study, 150 m), and separation of the frequency-dependent layer-induced scattering from intrinsic absorption. Besides, the inversion takes into account band-limited nature of seismic data, and thus, it is less dependent on the operating frequency bandwidth than on the other methods. However, all considered methods of Q estimation are unreliable in the intervals where subsurface significantly deviates from 1D geometry. At the Otway site, the attenuation estimates are distorted by sub-vertical faults close to the boreholes. Analysis of repeated vertical seismic profiles reveals that 15 kt injection of the CO₂-rich fluid into a thin saline aquifer at 1.5 km depth does not induce detectable absorption of P-waves at generated frequencies 5–150 Hz, most likely because the CO₂ plume in the monitoring well is thin, <15 m. At the Otway research site, strong attenuation Q ≈ 30–50 is observed only in shaly formations (Skull Creek Mudstone, Belfast Mudstone). Layer-induced scattering attenuation is negligible except for a few intervals, namely 500–650 m from the surface, and near the injection interval, at around 1400–1550 m, where Q_scat ≈ 50–65.     

地层衰减对地震波速度逆散射反演的影响研究

在利用地震波数据进行地球物理反演时,地层对地震波的吸收衰减效应会对地层物性参数的准确反演产生较大的影响,因此利用黏弹性声波方程进行反演更符合实际情形.本文在考虑地层衰减效应进行频率空间域正演模拟的基础上,提出基于黏弹性声波方程的频率域逆散射反演算法并对地震波传播速度进行反演重建,在反演过程中分别用地震波传播复速度和实速度来表征是否考虑地层吸收衰减效应.基于反演参数总变差的正则化处理使反演更加稳定,在反演中将低频反演速度模型作为高频反演的背景模型进行逐频反演,由于单频反演过程中背景模型保持不变,故该方法不需要在每次迭代中重新构造正演算子,具有较高的反演效率;此外本文在反演过程中采用了基于MPI的并行计算策略,进一步提高了反演计算的效率.在二维算例中分别对是否考虑地层吸收衰减效应进行了地震波速度反演,反演结果表明考虑衰减效应可以得到与真实模型更加接近的速度分布结果,相反则无法得到正确的地震波速度重建结果.本文算法对复杂地质模型中浅层可以反演得到分辨率较高的速度模型,为其他地震数据处理提供比较准确的速度信息,在地层深部由于地震波能量衰减导致反演分辨率不太理想.     

Caustics in a periodically layered transversely isotropic medium with vertical symmetry axis

Wave propagation in a finely layered medium is a very important topic in seismic modelling and inversion. Here we analyse non‐vertical wave propagation in a periodically layered transversely isotropic (VTI) medium and show that the evanescent (attenuation) zones in the frequency‐horizontal slowness domain result in caustics in the group velocity domain. These caustics, which may appear for both the quasi‐compressional (qP) and quasi‐shear (qSV) wave surfaces are frequency dependent but display weak dependence at low frequencies. The caustics computed for a specific frequency differ from those observed at the low‐ and high‐frequency limits. We illustrate these caustics with a few numerical examples and snapshots computed for both qP‐ and qSV‐wave types.     

Double parameterized regularization inversion method for migration velocity analysis in transversely isotropic media with a vertical symmetry axis

Simultaneous estimation of velocity gradients and anisotropic parameters from seismic reflection data is one of the main challenges in transversely isotropic media with a vertical symmetry axis migration velocity analysis. In migration velocity analysis, we usually construct the objective function using the l₂ norm along with a linear conjugate gradient scheme to solve the inversion problem. Nevertheless, for seismic data this inversion scheme is not stable and may not converge in finite time. In order to ensure the uniform convergence of parameter inversion and improve the efficiency of migration velocity analysis, this paper develops a double parameterized regularization model and gives the corresponding algorithms. The model is based on the combination of the l₂ norm and the non‐smooth l₁ norm. For solving such an inversion problem, the quasi‐Newton method is utilized to make the iterative process stable, which can ensure the positive definiteness of the Hessian matrix. Numerical simulation indicates that this method allows fast convergence to the true model and simultaneously generates inversion results with a higher accuracy. Therefore, our proposed method is very promising for practical migration velocity analysis in anisotropic media.     

Inverse analysis of weak and strong motion downhole array data from the Mw7.0 Sanriku-Minami earthquake

A hybrid optimization scheme, comprising a genetic algorithm in series with a local least-squares fit operator, is used for the inversion of weak and strong motion downhole array data obtained by the Kik-Net Strong Motion Network during the M_w7.0 Sanriku-Minami Earthquake. Inversion of low-amplitude waveforms is first employed for the estimation of low-strain dynamic soil properties at five stations. Successively, the frequency-dependent equivalent linear algorithm is used to predict the mainshock site response at these stations, by subjecting the best-fit elastic profiles to the downhole-recorded strong motion. Finally, inversion of the mainshock empirical site response is employed to extract the equivalent linear dynamic soil properties at the same locations. The inversion algorithm is shown to provide robust estimates of the linear and equivalent linear impedance profiles, while the attenuation structures are strongly affected by scattering effects in the near-surficial heterogeneous layers. The forward and inversely estimated equivalent linear shear wave velocity structures are found to be in very good agreement, illustrating that inversion of strong motion site response data may be used for the approximate assessment of nonlinear effects experienced by soil formations during strong motion events.     

Use of spectral acceleration data for determination of three-dimensional attenuation structure in the Pithoragarh region of Kumaon Himalaya

Three-dimensional attenuation structures are related to the subsurface heterogeneities present in the earth crust. An algorithm for estimation of three-dimensional attenuation structure in the part of Garhwal Himalaya, India has been presented by Joshi (Curr Sci 90:581–585, 2006b; Nat Hazards 43:129–146, 2007). In continuation of our earlier approach, we have presented a method in which strong motion data have been used to estimate frequency-dependent three-dimensional attenuation structure of the region. The border district of Pithoragarh in the Higher Himalaya, India, lies in the central seismic gap region of Himalaya. This region falls in the seismic zones IV and V of the seismic zoning map of India. A dense network consisting of eight accelerographs has been installed in this region. This network has recorded several local events. An algorithm based on inversion of strong motion digital data is developed in this paper to estimate attenuation structure at different frequencies using the data recorded by this network. Twenty strong motion records observed at five stations have been used to estimate the site amplification factors using inversion algorithm defined in this paper. Site effects obtained from inversion has been compared with that obtained using Nakamura (1988) and Lermo et al. (Bull Seis Soc Am 83:1574–1594, 1993) approach. The obtained site amplification term has been used for correcting spectral acceleration data at different stations. The corrected spectral acceleration data have been used as an input to the developed algorithm to avoid effect of near-site soil amplification term. The attenuation structure is estimated by dividing the entire area in several three-dimensional block of different frequency-dependent shear wave quality factor Q _β (f). The input to this algorithm is the spectral acceleration of S phase of the corrected accelerogram. The outcome of the algorithm is given in terms of attenuation coefficient and source acceleration spectra. In the present study, this region has been divided into 25 rectangular blocks with thickness of 10 km and surface dimension of 12.5 × 12.1 km, respectively. Present study gives three-dimensional attenuation model of the region which can be used for both hazard estimation and simulation of strong ground motion.     

Attenuation,source parameters and site effects in the Irpinia–Basilicata region (southern Apennines,Italy)

We derive S-wave attenuation characteristics, earthquake source parameters and site amplification functions at seismic stations used for earthquake early warning in the Irpinia–Basilicata region, using non-parametric spectral inversion of seismograms from 49 local events with M _L = 1.5–3.1. We obtain relatively low Q values (Q ₀ = 28 at a frequency of 1 Hz) in conjunction with a strong frequency-dependence (close to linear). The source spectra can be satisfactorily modeled using the omega-square model, with stress drops ranging between 0.01–2 MPa, and in the narrow magnitude range available for analysis, the source spectra seem to scale self-similarly. The local magnitude M _L shows a linear correlation with moment magnitude M _W, however with a systematic underestimation by about 0.5-magnitude units. The results obtained in this work provide important insights into the ground-motion characteristics that are required for appropriate seismic hazard assessment and are of practical relevance for a suite of applications, such as the calibration of ground-motion prediction equations or the correction for site amplification in earthquake early warning and rapid calculation of shake-maps for seismic emergency management.     

基于多射线联合反演的速度无关叠前地震数据Q值估计

描述地震波衰减特征的品质因子Q对地震数据处理和油藏描述非常重要,在地震勘探领域,Q值一般通过垂直地震剖面(VSP)数据或地面地震数据得到.由于叠前地面地震数据具有复杂的射线路径且存在噪声、调谐干涉效应等影响,从叠前地震数据中准确估计Q值相对困难.本文以地震波射线传播为基础,根据同相轴局部斜率和射线参数的映射关系,将多射线波形频谱同时带入谱比法联合反演估计Q值,提出了基于多射线联合反演的速度无关叠前Q值估计方法.该方法通过局部斜率属性避开了速度对Q值估计的影响,局部斜率携带地震波传播的速度信息,具有相同局部斜率的地震反射波具有相同的传播射线参数.同相轴局部斜率是地震数据域的属性,而速度是模型域的参数,在估计Q值中采用数据域的属性参数可以直接应用于数据的联合反演,而不需要通过速度对其做进一步的转化,从而提高了Q值估计的精度.同时,本方法采用预测映射(predictive mapping)技术将非零炮检距反射信息映射到零炮检距处,从而获得零偏移距走时对应的Q值.模拟和实际算例验证了本文方法的有效性.     

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.     

Estimation of frequency dependent coda wave attenuation structure at the vicinity of Cairo Metropolitan Area

Estimation of seismic wave attenuation in the shallow crust in terms of coda wave Q structure previously investigated in the vicinity of Cairo Metropolitan Area was improved using seismograms of local earthquakes recorded by the Egyptian National Seismic Network. The seismic wave attenuation was measured from the time decay of coda wave amplitudes on narrow bandpass filtered seismograms based on the single scattering theory. The frequency bands of interest are from 1.5 to 18 Hz. In general, the values obtained for various events recorded at El-Fayoum and Wadi Hagul stations are very similar for all frequency bands. A regional attenuation law Q _c = 85.66 f ^0.79 was obtained.     

Attenuation of coda waves in northern Greece

The single scattering model has been applied for the estimation of codaQ values for local earthquakes that occurred in northern Greece during the period 1983–1989 and recorded by the telemetered network of the Geophysical Laboratory of the University of Thessaloniki. CodaQ estimations were made for four frequency bands centered at 1.5 Hz, 3.0 Hz, 6.0 Hz and 12.0 Hz and for the lapse time windows 10–20 sec, 15–30 sec, 20–45 sec, 30–60 sec and 50–100 sec. The codaQ values obtained show a clear frequency dependence of the formQ _c =Q ₀ f ⁿ , whileQ ₀ andn depend on the lapse time window.Q ₀ was found equal to 33 andn equal to 1.01 for the time window of 10 to 20 sec, while for the other windowsQ ₀ increased from 60 to 129, withn being stable, close to 0.75. This lapse time dependence is interpreted as due to a depth dependent attenuation. The high attenuation and the strong frequency dependence found are characteristic of an area with high seismicity, in agreement with studies in other seismic regions.     

Post-stack impedance blocky inversion based on analytic solution of viscous acoustic wave equation

The conventional impedance inversion method ignores the attenuation effect, transmission loss and inter-layer multiple waves; the smooth-like regularization approach makes the corresponding impedance solution excessively smooth. Both fundamentally limit the resolution of impedance result and lead to the inadequate ability of boundary characterization. Therefore, a post-stack impedance blocky inversion method based on the analytic solution of viscous acoustic equation is proposed. Based on the derived recursive formula of reflections, the 1D viscous acoustic wave equation is solved analytically to obtain zero-offset full-wave field response. Applying chain rule, the analytical expression of the Fréchet derivative is derived for gradient-descent non-linear inversion. Combined with smooth constraints, the blocky constraints can be introduced into the Bayesian inference framework to obtain stable and well-defined inversion results. According to the above theory, we firstly use model data to analyse the influence of incompleteness of forward method on seismic response, and further verify the effectiveness of the proposed method. Then the Q-value sensitivity analysis of seismic trace is carried out to reduce the difficulty of Q-value estimation. Finally, the real data from Lower Congo Basin in West Africa indicate that the proposed approach provide the high-resolution and well-defined impedance result. As a supplement and development of linear impedance inversion method, the non-linear viscous inversion could recover more realistic and reliable impedance profiles.     

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。     

The design of visco‐acoustic weighted L1‐error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L ₁ ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L ₁ ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L ₄ ‐norm and L_∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L ₁ ‐error method enhances the resolution and results in practically stable images.     

Wigner-Ville分布及其在地震衰减估计中的应用

地震信号的衰减一般是在频域内利用信号功率谱的统计性质进行表征。但是,传统的基于傅立叶变换的功率谱估计方法的分辨率较低,使得衰减估计的精度较低。Wigner-Ville分布是一种重要的Cohen类时频分布,它具有一系列的优良性质,如时频边缘分布性质、好的时频聚集性等。这些性质对信号的时频分析具有重要意义。因此,Wigner-Ville分布为地震信号的衰减估计提供了新的手段。本文首先介绍了Wigner-Ville分布以及能够减少或消除交叉项影响的平滑Wigner-Ville分布,然后,提出了一种基于Wigner-Ville分布的衰减估计方法。在这一方法中,利用Wigner-Ville分布得到的瞬时能量谱中高频段的能量下降速率度量衰减。将这一方法应用到塔中地区奥陶系礁滩相碳酸盐岩储层预测,结果表明,基于Wigner-Ville分布的衰减能够有效地检测出礁滩相带和泻湖区域之间衰减特性的差异。     

An empirical attenuation relationship for Northwestern Turkey ground motion using a random effects approach

Using a random effects model that takes into consideration the correlation of data recorded by a single seismic event, a database consisting of 195 recordings from 17 recent events is employed to develop empirical attenuation relationships for the geometric mean of horizontal peak ground acceleration and 5-percent damped spectral acceleration (S_a). The recordings employed are obtained from strong motion stations operating in Northwestern Turkey and resulted from events that include the Kocaeli (M_w=7.4) and the Düzce (M_w=7.1) earthquakes and their aftershocks as well as other events. By studying differences in standard errors, the random effects model is compared with a fixed effects model that does not account for distinctions between intra- and inter-event variability. Effects of local site conditions are included in the empirical relationships developed. The dependence on frequency of the various model parameters is also studied. Frequency-dependent attenuation coefficients for the proposed random effects models developed are summarized in tables to facilitate their use.     

Determination of Q β(f) in Different Parts of Kumaon Himalaya from the Inversion of Spectral Acceleration Data

This paper presents the results of a modified two-step inversion algorithm approach to find S wave quality factor Q _β(f) given by Joshi (Bull Seis Soc Am 96:2165–2180, 2006). Seismic moment is calculated from the source displacement spectra of the S wave using both horizontal components. Average value of seismic moment computed from two horizontal components recorded at several stations is used as an input to the first part of inversion together with the spectra of S phase in the acceleration record. Several values of the corner frequency have been selected iteratively and are used as inputs to the inversion algorithm. Solution corresponding to minimum root mean square error (RMSE) is used for obtaining the final estimate of Q _β(f) relation. The estimates of seismic moment, corner frequency and Q _β(f) from the first part of inversion are further used for obtaining the residual of theoretical and observed source spectra which are treated as site amplification terms. The acceleration record corrected for the site amplification term is used for determination of seismic moment from source spectra by using Q _β(f) obtained from first part of inversion. Corrected acceleration record and new estimate of seismic moment are used as inputs to the second part of the inversion scheme which is similar to the first part except for use of input data. The final outcome from this part of inversion is a new Q _β(f) relation together with known values of seismic moment and corner frequency of each input. The process of two-step inversion is repeated for this new estimate of seismic moment and goes on until minimum RMSE is obtained which gives final estimate of Q _β(f) at each station and corner frequency of input events. The Pithoragarh district in the state of Uttarakhand in India lies in the border region of India and Nepal and is part of the seismically active Kumaon Himalaya zone. A network of eight strong motion recorders has been installed in this region since March, 2006. In this study we have analyzed data from 18 local events recorded between March, 2006 and October, 2010 at various stations. These events have been located using HYPO71 and data has been used to obtain frequency-dependent shear-wave attenuation. The Q _β(f) at each station is calculated by using both the north-south (NS) and east-west (EW) components of acceleration records as inputs to the developed inversion algorithm. The average Q _β(f) values obtained from Q _β(f) values at different stations from both NS and EW components have been used to compute a regional average relationship for the Pithoragarh region of Kumaon Himalaya of form Q _β(f)?=?(29?±?1.2)f ^{(1.1 ± 0.06)}.     

The estimation of spectra from time‐frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.     

Iterated extended Kalman filter method for time-lapse seismic full-waveform inversion

Time-lapse seismic data is useful for identifying fluid movement and pressure and saturation changes in a petroleum reservoir and for monitoring of CO₂ injection. The focus of this paper is estimation of time-lapse changes with uncertainty quantification using full-waveform inversion. The purpose of also estimating the uncertainty in the inverted parameters is to be able to use the inverted seismic data quantitatively for updating reservoir models with ensemble-based methods. We perform Bayesian inversion of seismic waveform data in the frequency domain by combining an iterated extended Kalman filter with an explicit representation of the sensitivity matrix in terms of Green functions (acoustic approximation). Using this method, we test different strategies for inversion of the time-lapse seismic data with uncertainty. We compare the results from a sequential strategy (making a prior from the monitor survey using the inverted baseline survey) with a double difference strategy (inverting the difference between the monitor and baseline data). We apply the methods to a subset of the Marmousi2 P-velocity model. Both strategies performed well and relatively good estimates of the monitor velocities and the time-lapse differences were obtained. For the estimated time-lapse differences, the double difference strategy gave the lowest errors.     

An inversion of site response and Lg attenuation using Lg waveform

Based on spectral ratio method, a joint inversion method was used to obtain parameters of Lg wave attenuation and site response. The inversion method allows simple and direct (two-parameter) determination of Lg wave attenua- tion and site response from sparse spectral data, which are not affected by radiation pattern factor and different response of same instrument after geometrical spreading. The method was used successfully for estimating site re- sponse of stations of Zhejiang Seismic Network and measuring Lg wave attenuation. The study is based on 20 earth- quakes occurred in northeast of Taiwan with magnitude MS5.0~6.7 and 960 seismic wave records from 16 stations in Zhejiang area from 2002 to 2005. The parameters of site response and Lg attenuation were calculated with a fre- quency interval of 0.2 Hz in the range of 0.5 Hz to 10 Hz. Lg wave attenuation coefficient corresponding to U-D, E-W and N-S components are γ ( f )=0.00175 f 0.43485, γ ( f )=0.00145f 0.48467 and γ ( f )=0.0021f 0.41241, respectively. It is found that the site response is component-independent. It is also found that the site response of QIY station is significant above the frequency of 1.5 Hz, and that the site response of NIB station is low for most frequency