Tomographic inversion of near-surface <Emphasis Type="Italic">Q</Emphasis> factor by combining surface and cross-hole seismic surveys

The estimation of the quality factor Q plays a fundamental role in enhancing seismic resolution via absorption compensation in the near-surface layer. We present a new geometry that can be used to acquire field data by combining surface and cross-hole surveys to decrease the effect of geophone coupling on Q estimation. In this study, we drilled number of receiver holes around the source hole, each hole has different depth and each geophone is placed geophones into the bottom of each receiver hole to avoid the effect of geophone coupling with the borehole wall on Q estimation in conventional cross-hole seismic surveys. We also propose a novel tomographic inversion of the Q factor without the effect of the source signature, and examine its stability and reliability using synthetic data. We estimate the Q factors of the near-surface layer in two different frequency bands using field data acquired in the Dagang Oilfield. The results show that seismic absorption in the near-surface layer is much greater than that in the subsurface strata. Thus, it is of critical practical importance to enhance the seismic solution by compensating for near-surface absorption. In addition, we derive different Q factors from two frequency bands, which can be treated, to some extent, as evidence of a frequency-dependent Q.     

Construction of constant-<Emphasis Type="Italic">Q</Emphasis> viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

裂缝诱导双相HTI介质地震波场错格伪谱法模拟与波场特征分析

裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征.     

Attenuation of seismic waves of very low frequency

The quality factor of the free oscillations of the earth is calculated from the observed time rate of decay of the energy. Records of the I.P.G.P. long-period data acquisition system are used, after a process enhancing a chosen mode, so that the scatter in the Q results is reduced. Determination of attenuation is made for the spheroidal and torsional fundamental modes and two torsional higher modes.The attenuation of seismic waves is determined from the decay of energy of standing-wave patterns with time, and from the damping of travelling waves with distance, using the surface mantle waves recorded at a single I.P.G.P. long-period seismic station after each great circle path (Gaulon, 1971).     

Features of Radiation and Propagation of Seismic Waves in the Northern Caucasus: Manifestations in Regional Coda

Based on the Anapa (ANN) seismic station records of ~40 earthquakes (M_W > 3.9) that occurred within ~300 km of the station since 2002 up to the present time, the source parameters and quality factor of the Earth’s crust (Q(f)) and upper mantle are estimated for the S-waves in the 1–8 Hz frequency band. The regional coda analysis techniques which allow separating the effects associated with seismic source (source effects) and with the propagation path of seismic waves (path effects) are employed. The Q-factor estimates are obtained in the form Q(f) = 90 × f 0.7 for the epicentral distances r < 120 km and in the form Q(f) = 90 × f1.0 for r > 120 km. The established Q(f) and source parameters are close to the estimates for Central Japan, which is probably due to the similar tectonic structure of the regions. The shapes of the source parameters are found to be independent of the magnitude of the earthquakes in the magnitude range 3.9–5.6; however, the radiation of the high-frequency components (f > 4–5 Hz) is enhanced with the depth of the source (down to h ~ 60 km). The estimates Q(f) of the quality factor determined from the records by the Sochi, Anapa, and Kislovodsk seismic stations allowed a more accurate determination of the seismic moments and magnitudes of the Caucasian earthquakes. The studies will be continued for obtaining the Q(f) estimates, geometrical spreading functions, and frequency-dependent amplification of seismic waves in the Earth’s crust in the other regions of the Northern Caucasus.     

Time-domain forward and inverse modeling of lossy soils with frequency-independent Q for near-surface applications

In this paper, we are concerned with a full-waveform-based methodology that allows the simultaneous imaging of the soil's stiffness and attenuating properties, using solely the soil's surficial response to probing waves.To date, field observations of small-strain wave attenuation in geomaterials at moderate spatial scales suggest that a commonly used metric of intrinsic and apparent attenuation, the seismic quality factor Q, is frequency-independent for a wide part of the frequency spectrum, including the frequency range of interest to seismic applications. We discuss first the forward simulation of waves in near-surface soil deposits directly in the time-domain using simplified models that adequately approximate nearly frequency-independent Q. To this end, we first review various attenuation models that aim at reproducing the frequency-independent Q behavior, and conclude, supported by site analyses, that, even though a generalized Maxwell body with eight Maxwell elements in parallel (GMB8) provides the best fit to frequency-independent Q, we favor a version of it with fewer parameters (GMB2), in order to reduce modeling complexity, while still retaining good agreement with the GMB8 model.We report on forward site analyses that lend credence to the choice of the GMB2 simplified model. We, then, use the GMB2 constitutive relation in the context of full-waveform inversion, and report on numerical experiments that lead to the imaging of the soil's properties in heterogeneous semi-infinite domains.     

基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟

本文建立了无分裂复频移卷积完全匹配层(CFS-CPML)吸收边界条件,利用交错网格下的高精度有限差分格式对黏弹性介质中的勒夫波场进行了数值模拟;分析了松弛机制个数对品质因子拟合精度的影响,验证了CFS-CPML边界条件对大角度掠射波的吸收效果．数值结果表明:本文方法所使用的5个松弛机制和空间4阶差分精度,即可在保证计算效率的前提下满足目前理论研究的需要;随着品质因子的减小,频散特征曲线的相速度逐渐向增高的方向偏离理论频散特征曲线的相速度,且各模式的高频能量也随之减弱．本文结果可为发展高精度的面波反演方法提供必要的理论依据．      

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)}.     

Q of the crust beneath southwestern Honshu,Japan, derived from explosion seismic waves

The specific quality factor Q of the crust was derived from explosion seismic waves by measuring the change of spectrum ratio with distance from the source. The spectrum for two wave groups, which are supposed to be transmitted entirely in the upper crust and transmitted primarily in the lower crust, respectively, were used. The source function could be represented by a simple function with one parameter. The value of Q and the parameter were determined simultaneously by the least-squares method. The same Q value was obtained for the upper and the lower crust and was estimated to be in the range Q = 1000–2000.     

普洱大寨深井噪声压制效果及井孔附近波场特征研究

基于2011年建立的云南普洱大寨深井台站,开展了噪声压制及附近波场特征研究.通过计算该台站的噪声功率谱概率密度函数,显示该井下台站对1 Hz以上的高频噪声具有明显的压制效果, 最高能降低40 dB,其降噪能力优于其它井下台阵,推断与该台站附近的场地条件有关.基于地表与井下地震记录的差异,应用正则化反卷积干涉方法进一步研究该台站附近的波场特征.以地表记录为参考,对井下记录进行反卷积,获取两台站之间的格林函数,直接识别出了原始记录上无法区分的上行入射波与下行地表反射波,然后利用两震相的到时差建立了一个浅层地震波速度模型,与理论模拟的结果一致.研究结果表明,相对于地表观测,井下台站在压制噪声和近地表地震波传播特征研究等方面具有很大的优势,同时该研究对其它地区开展深井观测具有参考意义.      

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.     

Synthetic Seismograms for a Layered Earth Geological Model Using the Absorption and Dispersion Phenomena

—An algorithm has been developed to compute the dispersive and dissipative seismic response using FUTTERMAN’S (1962) third attenuation-dispersion relationship. In the computation, frequency-dependent velocity and quality factor Q have been used but in the case of the nondispersive synthetic seismogram, frequency-independent velocity has been used. The model’s parameters are density, phase velocity, quality factors and thicknesses of the layers. Dispersive and nondispersive synthetic seismograms have been computed with and without absorption for a layered earth geological model. Fast Fourier transform (FFT) technique has been adopted for converting the frequency domain response into the time domain. The frequency spacing, Δf = 0.976?Hz, has been considered to avoid the aliasing effect. The results have revealed changes in the reflected waveforms in the frequency domain as well as in the time domain for absorption and dispersion cases. It is also concluded that dispersion reduces the arrival time and this effect is increasing with the travel time. The effect of constant Q on the seismic response has also been studied.     

Variation of <Emphasis Type="Italic">Q</Emphasis> value before and after the 1999 Xiuyan,Liaoning Province, <Emphasis Type="Italic">M</Emphasis>=5.4 earthquake on the basis of analysis on attenuation dispersion of P waves

A method for determining medium quality factor is developed on the basis of analyzing the attenuation dispersion of the arrived first period P wave. In order to enhance signal to noise ratio, improve the resolution in measurement and reduce systematic error we applied the data resampling technique. The group velocity delay of P wave was derived by using an improved multi-filtering method. Based on a linear viscoelastic relaxation model we deduced the medium quality factor Q _m, and associated error with 95% confidence level. Applying the method to the seismic record of the Xiuyan M=5.4 earthquake sequences we obtained the following result: (1) High Q _m started to appear from Nov. 9, 1999. The events giving the deduced high Q _m value clustered in a region with their epicenter distances being between 32 and 46 km to the Yingkou station. This Q _m versus distance observation obviously deviates from the normal trend of Q _m linearly increasing with distance. (2) The average Q _m before the 29 Dec. 1999 M=5.4 earthquake is 460, while the average Q _m between the M=5.4 event and the 12 Jan. 2000 M=5.1 earthquake is 391, and the average Q _m after the M=5.1 event is 204.     

Construction of constant-Q viscoelastic mode with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor （Q） and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

Comparison of the attenuation properties for two different areas in eastern Anatolia,Turkey

In this study, the attenuation properties of the crust and the quality factor of S wave in eastern Anatolia (Turkey) were determined by local earthquakes for two different areas, Oltu and Erzurum. Seismic wave attenuation can be changed with high pressure or structural effects. Therefore, we argued that the estimation of attenuation coefficient in seismic active zones in Eastern Anatolia is a very useful tool to determine seismic activities. It uses regional waveform data set from two stations, OLT and ERZ, for 95 events that occurred in these regions between 2001 and 2005. The attenuation has been determined using the Chobra–Alexeev model based on the epicenter distance–amplitude relations. This model allows for investigation of the effects of variations in attenuation properties for different areas. We introduced a new magnitude formula for these areas using the amplitude normalization methods for reference values M_L=4, so as to correct effects of the magnitudes. We also determined velocity of seismic waves. The average attenuation coefficient (α), average quality factor (Q_s) and P and S waves velocities were obtained with normalized amplitude values for Erzurum (ERZ) and Oltu (OLT) as 0.0135 km⁻¹, 37, 6.20 km/s and 3.38 km/s and 0.0151, 34, 6.13 and 3.48.     

Characteristics of seismic wave attenuation in the crust and upper mantle of the Northern Caucasus

The quality factor Q as a function of frequency in an S wave range of 1–8 Hz is estimated from records of ～60 earthquakes (M _w > 3.9 and source depths of 1–60 km) obtained at the Sochi seismic station at epicentral distances of less than ～300 km. Methods of Q estimation used in the paper were developed in works by Aki, Rautian, and others; they are based on the suppression of source-related and local effects in S wave spectra with the help of coda waves measured at a fixed time from the first arrival. To compensate for directivity effects, averaging was performed over the set of events whose sources were located in a wide range of back azimuths. The geometric divergence is represented as a three-segment function: 1/R, 1, and 1/√R at epicentral distances of 1/50–1/70 to 50–70 km, 50–70 to 130–150 km, and greater than 130–150 km, respectively. The geometric divergences in this model yielded the following estimates of the quality factor: Q(f) ～ 80f ^0.9 with a base of 35–280 km and Q(f) ～ 110f ^0.8 with a base of 60–280 km. The resulting combinations of the propagation path effects (Q and the geometric divergence) can be used for predicting strong motion parameters in the Northern Caucasus.     

Inferred attenuation from site effect-correctedT phases recorded on the island of Hawaii

Coda site amplification factors are used to eliminate the site effect from records of three circum-PacificT phases recorded by the Hawaiian Volcano Observatory (HVO) network on the island of Hawaii. ObservedT-phase amplitudes across the island generally decrease with increasing distance from the conversion point where acoustic waves in the SOFAR channel become seismic waves propagating through the crust. However, the decay of the observedT-phase signal across the island is not regular in regions of dense station coverage, in particular, the Kilauea caldera region. We divide the maximum observedT-phase amplitudes at a given station by the coda site amplification factor obtained for the same station and frequency band (3.0Hz); the distribution of these amplitudes reveals a smooth pattern over the entire island. The distance over which the site effect-correctedT-phase amplitude decreases by one-half, combined with the apparent velocity of propagation ofT phases across the island, allows for an approximate determination of near-surfaceQ over much of the island of Hawaii. We found a region of lowQ in the Kilauea summit area (Q≈30) and east rift zone (Q≈60) with considerably higherQ in the Kaoiki and northern portions of the island (Q≈150 to 200). The lowQ values obtained in the Kilauea summit region and east rift zone are significantly lower than estimates of codaQ in the same region, suggestingT phases may be sampling the earth's near-surface properties.     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.