Local Determination of Weak Anisotropy Parameters from qP-wave Slowness and Particle Motion Measurements

— We propose an algorithm for local evaluation of weak anisotropy (WA) parameters from measurements of slowness vector components and/or of particle motions of q P waves at individual receivers in a borehole in a multi-azimuthal multiple-source offset VSP experiment. As a byproduct the algorithm yields approximate angular variation of q P-wave phase velocity. The formulae are derived under assumption of weak but arbitrary anisotropy and lateral inhomogeneity of the medium. The algorithm is thus independent of structural complexities between the source and the receiver. If complete slowness vector is determinable from observed data, then the information about polarization can be used as an independent additional constraint. If only the component of the slowness along the borehole can be determined from observations (which is mostly the case), the inversion without information about polarization is impossible. We present several systems of equations which can be used when different numbers of components of the slowness vector are available. The SVD algorithm is used to solve an overdetermined system of linear equations for WA parameters for two test examples of synthetic multi-azimuthal multiple-source offset VSP data. The system of equations results from approximate first-order perturbation equations for the slowness and polarization vectors of the q P wave. Analysis of singular values and of variances of WA parameters is used for the estimation of chances to recover the sought parameters. Effects of varying number of profiles with sources and of noise added to “observed” data are illustrated. An important observation is that although, due to insufficient data, we often cannot recover all individual WA parameters with sufficient accuracy, angular phase velocity variation can be recovered rather well.     

倾斜地层中的井孔声场研究

研究声波在倾斜充液井孔中的传播对于声波测井数据处理和解释具有重要意义.应用三维交错网格有限差分方法模拟了处于倾斜各向同性分层地层中的井孔声场.首先,针对均匀地层中单极子声源在裸眼井中激发的声场,将有限差分的结果和实轴积分法的结果进行对比验证.然后,采用单极子和偶极子两种声源,针对地层分界面和井轴间的不同倾角,计算了相应的声场分布和井轴上的接收波形.数值计算的结果表明,当声源处于倾斜分界面以下,即处于快速（下方）地层,接收器处于倾斜分界面以上（慢速）地层时,随着地层倾斜角度的加大,测得的慢度值从接近上方慢速地层值逐渐减小直至接近下方快速地层的值.任何源距情况下测得的首波慢度均小于上方地层实际的纵波慢度.并且,慢度与源距的关系曲线随源距的加大逐渐平缓.用偶极子声源激发得到的横波慢度与纵波结果相同,并表现得比纵波对倾角的改变更敏感.上述结论在本文中用声场快照和利用合成接收波列的慢度计算得以清楚显示,并且用射线声学理论验证.     

VERTICAL SEISMIC PROFILING—SEPARATION OF P- AND S-WAVES*

In vertical seismic profile's (VSP's) shot with a large source offset, rays from shot to receiver can have large angles of incidence. Shear waves generated by the source and by conversions at interfaces are likely to be recorded by both the vertical and the horizontal geophones. Varying angles of incidence may give strong variations in the recorded amplitudes. Separation of P- and SV-waves and recovery of their full amplitudes are important for proper processing and interpretation of the data. A P-S separation filter for three-component offset VSP data is presented which performs this operation. The separation filter is applied in the k-f domain and needs an estimate of the P- and S-velocities along the borehole as input. Implementation and stability aspects of the filter are considered. The filter was tested on an 1800 m offset VSP and appeared to be robust. Large velocity variations along the borehole could be handled and results were superior to those obtained by velocity filtering.     

The Bishkek vertical array (BIVA): acquiring strong motion data in Kyrgyzstan and first results

We present results from a vertical array of accelerometers that was recently installed in Bishkek (Kyrgyzstan) with the long-term aim of recording strong motion data. Taking advantage of recordings of a Mb 4.7 earthquake that occurred 40 km from the array site during the installation phase, we provide results of some preliminary data analysis. First, estimates of the S-wave velocity and Qs structure are deduced by the inversion of the deconvolved wavefield between the sensors in the borehole. Furthermore, the application of the nonstationary ray decomposition Kinoshita (Earth Planets Space 61:1297-1312, 2009) allowed at least three reflectors in the shallow velocity structure below the array to be identified. The complex nature of the wavefield (with up-going, down-going waves, and converted phases) due to the coarse, unconsolidated subsoil structure is highlighted by means of numerical simulations of ground motion.     

非对称圆弧片状声源在井旁地层中产生的声场

提出了一种可用于随钻三维反射声波成像测井的圆弧片状声源,推导了该声源声学性质在波数-频率域内的数学描述,并利用实轴积分的方法对该声源在井旁地层中产生的声场进行求解,考察了声源的线度、频率等因素对该声源向地层中辐射的声场的影响.研究结果表明,特定尺寸和特定频率下的圆弧片状声源产生的纵波场的水平和垂直指向性图中仅具有一个明显的主瓣,且主瓣三分贝角宽较窄,方位分辨率较高,指向性良好,适用于随钻三维反射成像测井;SV波场和SH波场的指向性图中存在两个或者多个角瓣,SV波场在垂直于井轴方向上辐射的能量为0,另外在井中发射和接收的反射SH波场和SV波场会相互干扰,所以难以利用SV波场和SH波场进行三维反射声波成像;声源的线度和频率等因素对其辐射声场影响较大,考虑到激励效率和方位分辨率等因素,对于本文描述的井孔模型,选择圆周角在75°和90°之间, 主频为12 kHz左右的声源是合适的.     

Comment on “Slowness-azimuth corrections of teleseismic events for IMS primary arrays in China” by Hao and Zheng

Knowledge about backazimuth and slowness deviations at seismic arrays can be used as a tool to study subsurface lateral heterogeneity and improve the ability to locate events. Recently, Hao and Zheng (J Seismol 13:437–448, 2009) estimated the backazimuth and slowness deviations for teleseismic P waves recorded by the HILR array and the LZDM array using f–k analysis. They attributed the significant deviations at the LZDM array to dipping structures beneath the array. However, another possible factor, namely the altitude variations of array elements, was not taken into consideration during the slowness estimation process. For the LZDM array, the maximum altitude difference is ~15% of the array aperture and not negligible. In this study, we made some numerical experiments to investigate the difference between the estimated and theoretical slowness vectors when ignoring the altitude difference. The results reveal that remarkable artificial slowness shift is produced. Assuming a P-wave velocity of 5.4 km/s immediately beneath the array, the magnitude of slowness shift increases from 1.4 to 2.2 s/° when the theoretical slowness decreases from 16 to 4 s/°. For a 10° emergence angle, the backazimuth deviation reaches nearly 40°, and the relative slowness deviation can be greater than 60%. It is also shown that ignoring the altitude difference gives rise to a northeastward slowness shift, opposite to the southwestward shift proposed by Hao and Zheng, suggesting that they have heavily underestimated the slowness residuals at the LZDM array. Note that the elevation of one of the array stations is much lower than others. Avoiding the use of this station, the elevation variation range of array stations decreases by nearly one half, and the artificial backazimuth and slowness deviations decrease by more than one half.     

EXTENDED MARINE ARRAYS VERSUS SIMULATED EXTENDED ARRAYS*

Two factors are responsible for the fact that an extended marine source array performs better than a point source: 1. a higher degree of transmission of the radiated seismic energy through the water-sediment interface providing a better penetration; 2. filtering effects. The higher degree of transmission is due to: (a) the directivity of extended sources, (b) the lower reflection coefficient at the water-sediment interface for seismic waves radiated from an extended source array than for spherical seismic waves radiated from a point source, (c) the lower amplitude decay of the pulses from an extended source than from a point source. In addition, signature characteristic of an extended source array and Fresnel zone of waves generated by such a source differ from those corresponding to a point source. The propagating wavelet radiated from a point source array may not be, in a sedimentary sequence below the sea-floor, the linear combination of wavelets emitted from point sources. In such cases, there is a noticeable difference between the performance of a field-implemented source array and that of the corresponding simulated source array. The performances of the field-implemented and simulated extended receiver arrays can be identical if the recording system is adequate and the processing technique appropriate.     

径向分层TI孔隙介质井孔中激发的模式波的数值研究

横向各向同性介质是地层中普遍存在的一种各向异性介质.本文对径向分层TI孔隙介质包围井孔中激发的斯通利波和弯曲波的传播特性进行了理论计算,发现模式波在低频时更多的是反应原状地层的信息,而随着频率的增加侵入带参数逐渐起控制作用;Biot理论描述的地层衰减比速度更容易受井壁附近地层参数的影响.利用灵敏度曲线定量研究了不同频率下地层各个参数对相速度和衰减系数的贡献大小,主要结果显示模式波的衰减受水平渗透率影响明显,而垂直渗透率的变化对模式波几乎无影响;斯通利波对水平向传播的横波速度比弯曲波的灵敏度高.从单极子和偶极子声源在井孔中激发的全波波形也可发现,声波测井仪器较宽的声源频带和合适的源距设置有利于对不同径向深度上的地层声学参数进行成像.     

MIGRATION OF MIXED-MODE VSP WAVEFIELDS1

Two-dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode-conversions in both downgoing and upgoing wavefields. Migration of mixed-mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave-types (P-wave and SV-wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three-component downhole geophone assembly. The wavemode filter partitions wave-types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced. Much of the energy arriving at the receivers is P-wave which has followed the P-wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV-wave imaging, a common mode-code is P-wave from source to reflector and SV-wave from reflector to geophone. Migration of such data calls for back-propagation of the geophone array wavefield, at SV-wave velocity, to the point in the subsurface where it is time-coincident with the forward propagated downwave, at P-wave velocity.     

Source/receiver array directivity effects on marine seismic attenuation measurements

Attenuation of seismic waves, quantified by the seismic quality factor Q, holds important information for seismic interpretation, due to its sensitivity to rock and fluid properties. A recently published study of Q, based on surface seismic reflection data, used a modified spectral ratio approach (QVO), but both source and receiver responses were treated as isotropic, based on simple raypath arguments. Here, this assumption has been tested by computing apparent attenuation generated by frequency-dependent directivity of typical marine source and receiver arrays and acquisition geometries. Synthetic wavelet spectra were computed for reflected rays, summed over the first Fresnel zone, from the base of a single interval, 50–3000 m thick and velocity 2000 m/s, overlying a 2200 m/s half-space, and for offsets of 71–2071 m. The source and receiver geometry were those of an actual survey. The modelled spectra are clearly affected by directivity, most strongly because of surface ghosts. In general, the strong high-frequency component, produced by the array design, leads to apparently negative attenuation in individual reflection events, though this is dependent on offset and target depth. For shallow targets (less than 400–500 ms two-way traveltime (TWT) depth), apparent Q-values as extreme as ?50 to ?100 were obtained. For deeper target depths, the directivity effect is far smaller. The implications of the model study were tested on real data. QVO was applied to 20 true-spectrum-processed CMPs, in a shallow (405–730 ms TWT) and a deeper (1000–1300 ms TWT) interval, firstly using a measured far-field source signature (effectively isotropic), and secondly using computed directivity effects instead. Mean interval Q^?1-values for the deeper interval, 0.029 ± 0.011 and 0.027 ± 0.018 for conventional and directional processing, respectively, suggested no directivity influence on attenuation estimation. For the shallow interval (despite poor spectral signal-to-noise ratios and hence scattered attenuation estimates), directional processing removed directivity-generated irregularities from the spectral ratios, resulting in an improvement from Q^?1_int = ?0.036 ± 0.130 to a realistic Q^?1_int = 0.012 ± 0.030: different at 94% confidence level. Equivalent Q-values are: for the deeper interval, 35 and 37 for conventional and directional processing, respectively, and ?28 and 86 for the shallow interval. These results support the conclusions of the model studies, i.e. that source/receiver directivity has a negligible effect except for shallow targets (e.g. TWT depth ≤ 500 ms) imaged with conventional acquisition geometry. In such cases directivity corrections to spectra are strongly recommended.     

利用qP波慢度和偏振矢量计算 弱各向异性介质参数

提出了一种使用慢度矢量分量和偏振矢量计算变井源距垂直地震剖面(walkaway VSP)钻孔中接收点附近介质弱各向异性(WA)参数的方法. 假定介质是任意弱各向异性介质, 从一般公式中得到了只有一条观测剖面情况下的反演公式. 如果知道了慢度矢量的垂直分量和偏振矢量, 可以通过反演得到与剖面和钻孔所在平面相关的WA参数, 反演过程不用进行射线追踪, 与上覆介质无关. 用合成数据检验了公式和方法的正确性, 并把它们应用于在爪哇海地区得到的一条变井源距垂直地震剖面的弱各向异性参数反演中.      

Detection of regional phases of seismic body waves using an array of three-component sensors

A small-aperture seismic array consisting of seven three-component seismometers carried out continuous measurements of regional seismicity in a selected area of the Nizhni Novgorod nuclear power plant during four months of 2013. Automatic signal detection using beamforming was applied separately for each motion component. Two horizontal components were transformed into radial and transverse components for the given values of the velocity and azimuth of the plane wave front. We have investigated the dependence of the coherence of microseismic noise on frequency, azimuth, and slowness, as well as determining the level of cross-correlation between signals on separate channels in order to estimate expected improvement in the signal-to-noise ratio, which is crucial for signal detection. Most signals detected by the seismic array from regional sources are associated with quarry blasts. Using repetitive explosions at seven quarries, we have quantitatively estimated and compared the increase in detection efficiency of regional seismic phases using a three-component small aperture seismic array and a subarray of vertical sensors. Horizontal sensors showed a higher efficiency in the detection of transverse waves, while the subarray of vertical sensors missed S-waves from certain events. For one of the nearby quarries, the vertical subarray missed up to 25% of events (5 of 20). The results of the investigation point to the need for the use of three-component seismic arrays for the study of regional seismicity.     

Locating Small Aftershocks Using a Small-Aperture Temporary Seismic Array

In this paper, we developed a specialized method to locate small aftershocks using a small-aperture temporary seismic array. The array location technique uses the first P arrival times to determine the horizontal slowness vector of the incoming P wave, then combines it with S–P times to determine the event location. In order to reduce the influence of lateral velocity variation on the location determinations, we generated slowness corrections using events well-located by the permanent broadband network as calibration events, then we applied the corrections to the estimated slownesses. Applications of slowness corrections significantly improved event locations. This method can be a useful tool to locate events recorded by temporary fault-zone arrays in the near field but unlocated by the regional permanent seismic network. As a test, we first applied this method to 64 well-located aftershocks of the 1992 Landers, California, earthquake, recorded by both the Caltech/USGS Southern California Seismic Network and a small-aperture, temporary seismic array. The average horizontal and vertical separations between our locations and the well-determined catalogue locations are 1.35 and 1.75 km, respectively. We then applied this method to 132 unlocated aftershocks recorded only by the temporary seismic array. The locations show a clear tendency to follow the surface traces of the mainshock rupture.     

A modelling study of open-hole single-well seismic imaging

Single-well, or uni-well, imaging uses an acoustic source and an array of receivers located in the same borehole to image local geological structure. Due to the intrinsic attenuation of the formation it is likely that a source emitting frequencies in the typical cross-well range would be necessary to illuminate structure at distances above 100 m from the borehole. At these frequencies a significant proportion of the source energy is converted into tube-waves which are, for the purpose of these surveys, noise. This paper reports the results of a modelling study designed to assess the feasibility of using existing cross-well hardware, i.e. a piezo-electric source and hydrophone array, modified to run in a single borehole, to perform single-well surveys. In particular we study the case of an open borehole in a gas-filled, low-permeability sandstone reservoir. Our results suggest that the amplitudes of the tube-wave reverberations generated by calliper variations are such that reflections of interest arriving in the time window after the first tube-wave arrival will not be visible. However, reflections may be visible in the time window preceding the first tube-wave arrival provided tube waves from previous shots are not still present and the long source–receiver offsets required to make observations in this window can be incorporated into the tool design.     

Importance of borehole deviation surveys for monitoring of hydraulic fracturing treatments

During seismic monitoring of hydraulic fracturing treatment, it is very common to ignore the deviations of the monitoring or treatment wells from their assumed positions. For example, a well is assumed to be perfectly vertical, but in fact, it deviates from verticality. This can lead to significant errors in the observed azimuth and other parameters of the monitored fracture‐system geometry derived from microseismic event locations. For common hydraulic fracturing geometries, a 2° deviation uncertainty on the positions of the monitoring or treatment well survey can cause a more than 20° uncertainty of the inverted fracture azimuths. Furthermore, if the positions of both the injection point and the receiver array are not known accurately and the velocity model is adjusted to locate perforations on the assumed positions, several‐millisecond discrepancies between measured and modeled SH‐P traveltime differences may appear along the receiver array. These traveltime discrepancies may then be misinterpreted as an effect of anisotropy, and the use of such anisotropic model may lead to the mislocation of the detected fracture system. The uncertainty of the relative positions between the monitoring and treatment wells can have a cumulative, nonlinear effect on inverted fracture parameters. We show that incorporation of borehole deviation surveys allows reasonably accurate positioning of the microseismic events. In this study, we concentrate on the effects of horizontal uncertainties of receiver and perforation positions. Understanding them is sufficient for treatment of vertical wells, and also necessary for horizontal wells.     

CROSS-BOREHOLE OBSERVATION OF MODE CONVERSION FROM BOREHOLE STONELEY WAVES TO CHANNEL WAVES AT A COAL LAYER1

Conversion of borehole Stoneley waves to channel waves was observed in data from a seismic cross-borehole experiment conducted between wellbores penetrating a thin coal layer at 2022 m depth, near Rifle, Colorado. Traveltime moveout observations show that borehole Stoneley waves underwent partial conversion to channel waves at the coal layer. The channel waves were detected directly in an adjacent borehole 35 m away at receiver positions within the coal. Stoneley waves, subsequently produced by partial conversion of channel waves, were also detected at receiver positions located up to 50 m above and below the coal layer in the adjacent borehole. We infer the channel wave to be the first-higher Rayleigh mode by comparing the observed group velocity with theoretically derived dispersion curves. Identifying the conversion between borehole and stratigraphically guided waves is significant because coal penetrated by multiple wells may be detected without placing a transmitter or receiver in the coal itself.     

Rupture Process of the 1995 Antofagasta Subduction Earthquake (Mw = 8.1)

—A finite-source rupture model of the July 30, 1995, M _w = 8.1 Antofagasta (Northern Chile) subduction earthquake is developed using body and surface waves that span periods from 20 to 290s. A long-period (150–290s) surface-wave spectral inversion technique is applied to estimate the average finite-fault source properties. Deconvolutions of broadband body waves using theoretical Green’s functions, and deconvolutions of broadband fundamental mode surface waves using empirical Green’s functions provided by a large aftershock, yield effective source time functions containing periods from 20 to 200s for many directivity parameters. The source time functions are used in an inverse radon transform to image a one-dimensional spatial model of the moment rate history. The event produced a predominantly unilateral southward rupture, yielding strong directivity effects on all seismic waves with periods less than a few hundred seconds. The aftershock information, spectral analysis, and moment rate distribution indicate a rupture length of 180–200km, with the largest slip concentrated in the first 120km, a rupture azimuth of 205°± 10° along the Chilean coastline, and a rupture duration of 60–68s with a corresponding average rupture velocity of 3.0–3.2km/s. The overall rupture character is quite smooth, accentuating the directivity effects and reducing the shaking intensity, however there are three regions with enhanced moment rate distributed along the rupture zone near the epicenter, 50 to 80km south of the epicenter, and 110 to 140km south of the epicenter.     

Source parameters of central California earthquakes on February 24 and September 4, 1972

The directivity function method is combined with an earthquake sequence study to obtain the reliable estimates of rupture area and rupture velocity of two right-lateral strike-slip earthquakes occurring along the San Andreas fault zone in central California. By utilizing a significant difference in velocity structure on both sides of the main fault, a modified version of the directivity function is formulated and applied to near-field SH waves. On assuming aftershock areas following their step-wise increase with time as rupture areas, an extensive systematic search for the best fit between the observed and theoretical directivity functions is made for a combination of both source parameters. The rupture at the February 24, 1972 earthquake (M_L = 5.0) propagated unilaterally with an average velocity of about 2.3 km/sec. It produced a rectangular area, the horizontal and vertical lengths being about 5 and 2 km, respectively. The rupture at the September 4, 1972 earthquake (M_L = 4.6) was of bilateral, yielding a nearly square rupture area of which side length is about 2 km. The rupture velocity of this earthquake, though some ambiguities resulting from a lower quality of the observed directivity function, is estimated at 1.9 km/sec or less. A difference in average rupture velocity between both earthquakes might imply its dependence on the ambient tectonic environment such as represented by local stress and humidity. By taking into account a post-earthquake creep increase of about 3.0–3.5 cm observed at a creepmeter station situated over the focus of the February 24, 1972 earthquake, its stress drop and seismic moment are estimated at about 10 bar and 10²³ dyn · cm, respectively. The above procedure has a broad applicability for recovering reliable estimates of source parameters, especially when it is combined with a synthetic approach.     

Study on the simulation of acoustic logging measurements in horizontal and deviated wells

The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain (FDTD) combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order (i.e., in the near-field scenarios), the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat's principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.     

Velocity Model of Western Volgo-Uralia from Receiver Functions

The results of studying the deep structure of the Earth’s crust and upper mantle in the central part of the Russian platform from receiver functions are presented. The records of teleseismic waves by the Monakovo small-aperture seismic array in the region of the northwestern slope of the Tokmovskii Arch of the Volga–Kama anteclise are used. The modification of the P-receiver function method (Vinnik, 1977) suggested in (Sanina et al., 2014) for analyzing the receiver functions in the regions with a complexly structured upper part of the section and the presence of a thick sedimentary cover is applied. The method is based on separating the high- and low-frequency components of the seismic record and successive reconstruction of the V-s velocity section in the upper part of the crust, which is performed first and, next, the entire deep section of the crust and the mantle down to a depth of ~300 km. The positions of the seismic conversion boundaries in the crust and upper mantle beneath the Monakovo array are determined. The upper mantle velocity section constructed based on the observations at the Mikhnevo array (Sanina et al., 2014) is compared with the world data on the ancient Precambrian platform.