Preliminary laboratory investigations into the attenuation of compressional and shear waves on near-surface marine sediments

The attenuation of compressional and shear waves ( Q _p and Q _s) has been studied by several authors but most of these investigations were performed on deep buried reservoir sandstones in order to distinguish between gas and condensate reservoirs and water-saturated sandstones. We present a preliminary investigation into the use of seismic wave attenuation as a measure of the geotechnical parameters of the near-surface marine sediments, a little-studied geological setting. A 6.9 m-long gravity core was taken from the continental slope of the Barents Sea at a water depth of 2227 m. The core was primarily composed of brown to olive-grey clayey mud, having a high content of foraminifers and being locally bioturbated. The values of Q _p and Q _s were determined using the rise-time method at 19 and 18 different points of the core, respectively, and they were correlated with geotechnical parameters such as wet bulk density, porosity, water content, shear strength and C/P ratio (the ratio of shear strength to overburden pressure). The calculated correlation coefficients for all correlations ranged from −0.39 to 0.41, suggesting that the attenuation characteristics of seismic waves could not be used to derive geotechnical parameters of marine sediments. However, with such a small data set it is difficult to determine clearly whether attenuation is primarily a frequency-dependent parameter and consequently not related to sediment properties, or whether the limited number of data points is the main factor responsible for the low correlation coefficients observed. Moreover, several different methods are available for the computation of the quality factor Q , and the rise-time method may not be the most appropriate means of determining the attenuation on near-surface marine sediments.     

Modelling the seismic attributes of overpressured siliciclastic rocks, with a genetic annealing (GAN) algorithm

ABSTRACT A genetic annealing (GAN) algorithm is used to derive an empirical model which predicts compressional-wave velocity values for overpressured siliciclastic rocks. The algorithm involves non-linear random searching and mutation techniques and its annealing component imposes a very strict control over the rate of convergence of the search. This technique provides an alternative to the standard calculations involving the effective stress coefficient ( n ). The pore pressure is introduced into the model as an explicit variable and as part of an overpressure coefficient, ( P _p/ P _c) − the ratio of pore to confining pressure. Empirical model-derived data and known laboratory data are compared and their differences are shown to be within statistically acceptable error limits. The empirical equation fits all under- and overpressured data simultaneously, irrespective of pore fluid pressure level, with the same parameters. It is used to predict seismic velocities very accurately for extreme levels of overpressure, starting from normally pressured experimental data. The model highlights the effect of pore pressure on the compressional-wave velocity of fully saturated samples with different clay contents. It can be used when the experimental data available are sparse and particularly when a prediction of material behaviour is necessary at specific pore fluid pressure and depth conditions.     

低孔隙度泥页岩应力依赖的各向异性裂纹演化特性研究

本文在实验室对所获取的东营地区层理发育的低孔隙度页岩和泥岩的各向异性裂纹演化特性进行了研究,获得了各向同性条件下泥页岩的力学与超声波响应特性,分析了应力幅度对于页岩声波速度和各向异性的影响.主要结论包括:(1)泥页岩在循环载荷下存在滞后效应,表明其经历了去压实或油气产生导致的超压;(2)泥岩和页岩具有不同程度的各向异性,随着各向同性压力的增高微裂隙逐渐闭合,样品的各向异性程度减弱;(3)分析了岩石韧度和裂纹损伤参数随压力的变化特征,相比泥岩,页岩各向异性程度更高,随压力变化更明显,其裂纹导致的附加各向异性更强;(4)分析了各向异性岩石的动态弹性模量特征,由于软裂隙空间的闭合,动态弹性模量在低压条件下都随着围压的增加有硬化趋势.     

Relationship between P- and S-wave velocities and geological properties of near-surface sediments of the continental slope of the Barents Sea

Seismic velocities ( V _p and V _s) of compressional (P-) and shear (S-) waves are important parameters for the characterization of marine sediments with respect to their sedimentological and geotechnical properties. P- and S-wave velocity data of near-surface marine sediments (upper 9 m) of the continental slope of the Barents Sea are analysed and correlated to sedimentological and geotechnical properties. The results show that the S-wave velocity is much more sensitive to changes in lithology and mechanical properties than the P-wave velocity, which is characterized by a narrow range of values. The correlation coefficients between S-wave velocity and silt and clay content, wet bulk density, porosity, water content and shear strength are higher than 0.5 while the correlation coefficients of P-wave velocity and the same parameters are always lower than 0.4. Although the relationship between V _s and clay content has been widely described, the data show that V _s is better correlated with silt content than with clay content for the sediments of the area investigated. However, they show different trends. While V _s increases with increasing clay content, it decreases with increasing silt content.     

Non-equilibrium compaction and abnormal pore-fluid pressures: effects on rock properties1

Knowledge of pore pressure using seismic data will help in planning the drilling process to control potentially dangerous abnormal pressures. Various physical processes cause anomalous pressures on an underground fluid. Non-equilibrium compaction is a significant process of overpressure generation. This occurs when the sedimentation rate is so rapid that the pore fluids do not have a chance to 'escape' from the pore space.
The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.
We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot's theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes.     

Aligned vertical fractures, HTI reservoir symmetry and Thomsen seismic anisotropy parameters for polar media

Certain crack-influence parameters of Sayers and Kachanov are shown to be directly related to Thomsen's weak-anisotropy seismic parameters for fractured reservoirs when the crack/fracture density is small enough. These results are then applied to the problem of seismic wave propagation in polar reservoirs, i.e., those anisotropic reservoirs having two axes that are equivalent but distinct from the third axis), especially for horizontal transversely isotropic seismic wave symmetry due to the presence of aligned vertical fractures and resulting in azimuthal seismic wave symmetry at the Earth's surface. The approach presented suggests one method of inverting for fracture density from wave speed data. A significant fraction of the technical effort in the paper is devoted to showing how to predict the angular location of the true peak (or trough) of the quasi-SV-wave for polar media and especially how this peak is related to another angle that is very easy to compute. The axis of symmetry is always treated here as the x ₃-axis for either vertical transversely isotropic symmetry (due, for example, to horizontal cracks), or horizontal transversely isotropic symmetry (due to aligned vertical cracks). Then, the meaning of the stiffnesses is derived from the fracture analysis in the same way for vertical transversely isotropic and horizontal transversely isotropic media, but for horizontal transverse isotropy the wave speeds relative to the Earth's surface are shifted by  90^o  in the plane perpendicular to the aligned vertical fractures. Skempton's poroelastic coefficient B is used as a general means of quantifying the effects of fluids inside the fractures. Explicit Biot-Gassmann-consistent formulas for Thomsen's parameters are also obtained for either drained or undrained fractures resulting in either vertical transversely isotropic or horizontal transversely isotropic symmetry of the reservoir.     

碳酸盐岩跨频段岩石物理测量与理论建模——不同孔隙结构对碳酸盐岩频散与衰减的影响研究

碳酸盐岩孔隙结构类型复杂多样,当地震波经过含有不同孔隙结构的流体饱和岩石后往往会产生不同的波频散和衰减特征,这使得根据波的不同响应特征来推断碳酸盐岩的孔隙结构类型,甚至孔隙流体性质信息成为可能.本文针对白云岩、灰岩以及人工碳酸盐岩样品开展了跨频段（超声+低频）实验测量和理论建模,探索碳酸盐岩的孔隙结构类型和孔隙流体对模量频散和衰减的影响机制.首先根据铸体薄片、扫描电镜的图像对碳酸盐岩样品进行了孔隙结构类型分析,并将样品主要分为裂缝型、裂缝-孔隙型、孔洞型三类,然后测量了相应样品完全饱和流体后在不同围压下的模量频散与衰减.在完全饱和甘油并处于低围压时,裂缝型与孔洞型样品均出现一个衰减峰,分别位于1 Hz与100 Hz附近,而裂缝-孔隙型样品则具有两个衰减峰,一个在1 Hz附近,另一个在100 Hz附近.裂缝型样品（裂缝主导）的衰减峰相比孔洞型样品（中等刚度孔隙主导）对应的衰减峰在低围压下幅度更大,且对围压变化更敏感.在测量数据的基础上,建立了考虑纵横比分布的软孔隙和中等刚度孔隙的喷射流模型,认为该模型能一定程度上解释裂缝型、裂缝-孔隙型、孔洞型三种类型碳酸盐岩在测量频带的频散.以上研究加深了对不同孔隙类型主导的碳酸盐岩储层地震响应特征的认识,对储层预测工作的进一步精细化具有重要意义.     

A laboratory study of seismic velocity and attenuation anisotropy in near-surface sedimentary rocks

The laboratory ultrasonic pulse‐echo method was used to collect accurate P‐ and S‐wave velocity (±0.3%) and attenuation (±10%) data at differential pressures of 5–50 MPa on water‐saturated core samples of sandstone, limestone and siltstone that were cut parallel and perpendicular to the vertical borehole axis. The results, when expressed in terms of the P‐ and S‐wave velocity and attenuation anisotropy parameters for weakly transversely isotropic media (ɛ, γ, ɛ_Q, γ_Q) show complex variations with pressure and lithology. In general, attenuation anisotropy is stronger and more sensitive to pressure changes than velocity anisotropy, regardless of lithology. Anisotropy is greatest (over 20% for velocity, over 70% for attenuation) in rocks with visible clay/organic matter laminations in hand specimens. Pressure sensitivities are attributed to the opening of microcracks with decreasing pressure. Changes in magnitude of velocity and attenuation anisotropy with effective pressure show similar trends, although they can show different signs (positive or negative values of ɛ, ɛ_Q, γ, γ_Q). We conclude that attenuation anisotropy in particular could prove useful to seismic monitoring of reservoir pressure changes if frequency‐dependent effects can be quantified and modelled.     

The seismic response to overpressure: a modelling study based on laboratory, well and seismic data

We investigate the seismic detectability of an overpressured reservoir in the North Sea by computing synthetic seismograms for different pore-pressure conditions. The modelling procedure requires the construction of a geological model from seismic, well and laboratory data. Seismic inversion and AVO techniques are used to obtain the P-wave velocity with higher reliability than conventional velocity analysis. From laboratory experiments, we obtain the wave velocities of the reservoir units versus confining and pore pressures. Laboratory experiments yield an estimate of the relationship between wave velocities and effective pressure under in situ conditions. These measurements provide the basis for calibrating the pressure model. Overpressures are caused by different mechanisms. We do not consider processes such as gas generation and diagenesis, which imply changes in phase composition, but focus on the effects of pure pore-pressure variations. The results indicate that changes in pore pressure can be detected with seismic methods under circumstances such as those of moderately deep North Sea reservoirs.     

龙马溪组页岩微观结构、地震岩石物理特征与建模

龙马溪组页岩是目前国内页岩气勘探的主要层位之一.由于岩石物理实验结果具有区域性,龙马溪组页岩的岩石特征与其地震弹性性质的响应规律需要开展相关的实验和理论研究工作予以明确.本研究基于系统的微观结构观察(扫描电镜和CT成像技术)和岩石物理实验来分析龙马溪组页岩样品地震弹性性质的变化规律,并依据微观结构特征建立相应的地震岩石物理表征模型.研究结果表明,石英含量对龙马溪组页岩的孔隙度以及有机碳(TOC)含量具有一定的控制作用,TOC和黄铁矿主要赋存于孔隙中;岩石骨架组成亦受控于石英或粘土含量,在石英含量大于40%(对应粘土含量小于30%)时,以石英、粘土共同作为岩石骨架,而粘土含量大于30%时,则以粘土作为岩石的骨架.因此,岩石骨架组成矿物、TOC含量、孔隙度共同制约龙马溪组页岩的地震弹性性质,富有机质储层岩石通常表现出低泊松比、低阻抗和低杨氏模量的特征,但由于支撑矿物的转换,某些富有机质页岩亦可表现为高阻抗特征.粘土矿物的定向排列仍然是造成页岩样品表现出各向异性的主要原因,各向异性参数与粘土含量具有指数关系.基于龙马溪组页岩的岩性特征及微观结构特征,可以利用自洽模型(SCA)、微分等效模量模型(DEM)和Backus平均模型的有效组合较为准确地建立龙马溪组页岩的地震岩石物理模型,实验结果和测井数据验证了模型的准确性.研究结果可为龙马溪组页岩气储层的测井解释和地震"甜点"预测提供依据.     

Poisson's ratio at high pore pressure

Laboratory investigations suggest that a precise relationship exists between Poisson's ratio, pore pressure and fluid type. Values of Poisson's ratio for dry samples are significantly smaller than those for fluid-saturated samples. The values are anomalously high for high pore pressure, with the possibility of differentiating between gas-saturated, brine-saturated and oil-saturated porous rocks.
The present study considers two overpressure models, based on oil/gas conversion and disequilibrium compaction, to obtain Poisson's ratio versus differential pressure (confining pressure minus pore pressure). The model results are in good agreement with experiments. Poisson's ratio is approximately constant at high differential pressures and increases (decreases) for saturated (dry) rocks at low differential pressures. Fluid type can be determined at all differential pressures from Poisson's ratio. The analysis is extended to the anisotropic case by computing the three Poisson's ratios of a transversely isotropic rock versus differential pressure. While one of them is practically independent of effective pressure, the others increase with increasing pore pressure. Experiments performed on cores under different pressure conditions, and calibration of the models with these data, provide a tool for inverting pore pressure from seismic data.     

宁夏地区Lg波衰减及场地响应特征

本文采用2008—2017年宁夏及邻区内15个数字地震台站记录的131次地震的波形资料,基于地震波衰减与场地响应联合反演方法,分析频率介于1—7 Hz之间的Lg波衰减及场地响应。采用2.2—3.6 km/s的速度窗截取了1 069条Lg波,计算得到Lg波各分量的地震波衰减品质因子Q（ f ）与频率f之间的关系。结果显示:Lg波垂直、东西及南北向各分量的Q₀分别为237.1,201.8及245.9;Q（ f ）对f的依赖性指数分别为0.44,0.52及0.44,该结果与全球其它地震活跃地区的相应研究结果相一致。对Q（ f ）在时间域的分析结果表明,研究时段内该地区地壳介质的衰减属性并未改变,15个台站的最大场地响应幅值不大于6。      

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low‐shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional‐wave velocity is strongly correlated with the shear‐wave velocity in this suite of rocks. The ratio V_P/V_S varies significantly with change of both pore‐fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot‐flow and squirt‐flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt‐flow of fluid between the pores of various geometries. The contribution of the Biot‐flow loss mechanism to the total loss is negligible. The compressional‐wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low‐shale, high‐porosity sandstone reservoirs.     

Ultrasonic wave propagation in dry and brine-saturated sandstones as a function of effective stress: laboratory measurements and modelling1

Compressional and shear-wave velocities have been measured and a novel approach using digital processing employed to study wave attenuation for brine- and gas- saturated sandstones, over a range of effective stresses from 5 to 60 MPa. Also measured were the complex conductivity in the brine-saturated state and permeability in the gas-saturated state over the same range of stresses as for the velocity measurements. Broadband ultrasonic pulses of P- and orthogonally polarized S-waves in the frequency range 0.3–0.8 MHz are transmitted through the specimen to be characterized for comparison with a reference (aluminium) having low attenuation. The attenuation is calculated in terms of the quality factor Q from the Fourier spectral ratios, using the frequency spectral ratios technique. The corrections necessary for the effects of diffraction due to the finite size of the ultrasonic transducers have been carried out for the case of measurements under lower confining stress. To interpret the laboratory measured velocity and attenuation data under the physical conditions of this study and to estimate the effects of pore structure, numerical modelling of velocities and attenuation as functions of the confining stress have been performed, based on the MIT model. Theoretical models based on several hypothesized attenuation mechanisms are considered in relation to laboratory data of the effects of confining pressure, fluid saturation and pore structure on attenuation. Numerical calculations using these models with the experimental data indicate that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for dry and brine-saturated sandstones at low effective stresses for the frequencies tested. However, for brine-saturated sandstones at moderately high effective stresses, fluid flow could play a more important role in ultrasonic S-wave attenuation, depending on the pore structure of the sample.     

Elastic constants and velocity surfaces of indurated anisotropic shales

The velocities of two Devonian-Mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation. Both samples were found to be transversely isotropic at elevated pressures with the main symmetry axis perpendicular to bedding. The elastic constants of the shales were used to calculate phase and group velocity surfaces as a function of angle to the bedding normal. Multiple velocity measurements in non-symmetry directions, not undertaken in previously published studies of shales, have been used to confirm features observed on calculated velocity surfaces. It is demonstrated that velocities measured in non-symmetry directions are phase velocities. Group velocities were found to be significantly lower than the corresponding phase velocities of the shales due to their high anisotropies. Shear wave splitting was found to be negligible for propagation directions within approximately 30° of the bedding normals.     

云南高黎贡山典型板岩地震波各向异性研究

板岩作为一种浅变质岩在我国有着广泛的分布,对其地震波速度的研究将有助于对这类过渡性岩石的有效区分,对于浅层地壳的各向异性研究也具有重要意义.本文对采自云南丙中洛地区的板岩样品进行了地震波速度的室内实验研究,其中部分实验是在加拿大Dalhousie High Pressure Laboratory完成.实验获得了板岩在围压10~600 MPa条件下、不同构造主方向（X,Y和Z）上的地震波速度,在围压600 MPa时,X、Y、Z三个方向的P波速度分别为6.58、6.46、5.91 km/s,平均速度为6.30 km/s,S波平均速度约为3.62 km/s,V_P/V_S=1.74;并初步分析了板岩地震波速度、横波分裂及其波速各向异性随着围压的变化规律,发现所测量的板岩在较低围压（<150 MPa）时波速的各向异性随围压升高而迅速减小,主要是由于其内部微裂隙的定向排列引起的,而随着围压的继续增加（>150 MPa时）微裂隙基本闭合,黑云母、阳起石等片状矿物的定向排列成为其地震波各向异性的主导诱因,此时（围压为600 MPa）V_P、V_S的各向异性分别稳定在13%、16%左右.本研究所获取的基础实验数据及所探讨的板岩地震波性质将为确定地壳上部显微裂隙的优选定向、浅层地壳的各向异性分析、地球物理模型条件约束等提供基础.     

Attenuation of P- and S-waves in limestones

Ultrasonic compressional- and shear-wave attenuation measurements have been made on 40, centimetre-sized samples of water- and oil-saturated oolitic limestones at 50 MPa effective hydrostatic pressure (confining pressure minus pore-fluid pressure) at frequencies of about 0.85 MHz and 0.7 MHz respectively, using the pulse-echo method. The mineralogy, porosity, permeability and the distribution of the pore types of each sample were determined using a combination of optical and scanning electron microscopy, a helium porosimeter and a nitrogen permeameter. The limestones contain a complex porosity system consisting of interparticle macropores (dimensions up to 300 microns) and micropores (dimensions 5–10 microns) within the ooids, the calcite cement and the mud matrix. Ultrasonic attenuation reaches a maximum value in those limestones in which the dual porosity system is most fully developed, indicating that the squirt-flow mechanism, which has previously been shown to occur in shaley sandstones, also operates in the limestones. It is argued that the larger-scale dual porosity systems present in limestones in situ could similarly cause seismic attenuation at the frequencies of field seismic surveys through the operation of the squirt-flow mechanism.     

Pressure effects on the joint elastic‐electrical properties of reservoir sandstones

We conducted a laboratory study of the joint elastic‐electrical properties of sixty‐three brine‐saturated sandstone samples to assess the likely impact of differential pressure (confining minus pore fluid pressures) in the range 8–60 MPa on the joint interpretation of marine seismic and controlled‐source electromagnetic survey data. The samples showed a wide range of petrophysical properties representative of most sandstone reservoirs. We found that a regression equation comprising both a constant and an exponential part gave a good fit to the pressure dependence of all five measured geophysical parameters (ultrasonic P‐ and S‐wave velocity, attenuation and electrical resistivity). Electrical resistivity was more pressure‐sensitive in clay‐rich sandstones with higher concentrations of low aspect ratio pores and micropores than in clean sandstones. Attenuation was more pressure‐sensitive in clean sandstones with large open pores (macropores) than in clay‐rich sandstones. Pore shape did not show any influence on the pressure sensitivity of elastic velocity. As differential pressure increases, the effect of the low aspect ratio pores and micropores on electrical resistivity becomes stronger than the effect of the macropores on attenuation. Further analysis of correlations among the five parameters as a function of pressure revealed potentially diagnostic relationships for geopressure prediction in reservoir sandstones.     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推导出准压缩波qP、准剪切波qSV和纯剪切波SH的复速度、相速度、能量速度以及品质因子的解析表达式.对模型的正确性进行了数值验证,并分析了qP,qSV和SH波在介质中的传播特性.数值试验结果表明:本模型能够实现理想的恒定Q行为,表现了品质因子和速度的各向异性特征,显示出黏弹性增强将导致能量速度和相速度的频散曲线变化剧烈;速度和衰减各向异性参数与传播角度之间的耦合效应对qP,qSV和SH波的速度和能量影响明显;qP,qSV和SH波的频散曲线和波前面随着衰减各向异性强度的改变发生显著变化,其中耦合在一起的qP和qSV波变化趋势相同,而SH波与它们呈现相反的变化规律.本研究为从常Q模型角度分析地震波在衰减各向异性黏弹性介质中的传播特征奠定了理论基础.