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.     

Velocity dispersion in fractured rocks in a wide frequency range

Experimental measurements of fracture-induced seismic waves velocity variations at frequencies ~ 1 kHz, ~ 40 kHz and ~ 1 MHz were performed directly in the field at the rocky outcrop and in the laboratory on specific rock samples collected from the outcrops. The peridotite–lherzolite outcrop appeared macroscopically uniform and contained three systems of visible parallel sub-vertical fractures. This rock has substantial bulk density and higher than average value of seismic wave velocity. The presence of fracture systems gives rise to its velocity anisotropy. The seismic waves passing through the rock fractures are subject to velocity dispersion and frequency dependent attenuation. Our data, obtained from field and laboratory measurements, were compared with theoretical model predictions. In this model we successfully used displacement discontinuity approach. For the velocity dispersion evaluation we used multi-frequency measurements. The a priori observation of orientations and densities of fracture sets allowed evaluation of their stiffness. Our approach revealed that the first arrivals of seismic waves can be used for evaluation of P-wave group velocities, the specific case, in which we expect anomalous velocity dispersion. Our observations contribute to the issue of up-scaling of well-log derived velocities in fractured rock to the scale of standard seismic exploration frequencies.     

Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data

Knowledge about the spatial distribution of the fracture density and the azimuthal fracture orientation can greatly help in optimizing production from fractured reservoirs. Frequency-dependent seismic velocity and attenuation anisotropy data contain information about the fractures present in the reservoir. In this study, we use the measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuths to infer information about the multiple fracture sets present in the reservoir. We consider a reservoir model with two sets of vertical fractures characterized by unknown azimuthal fracture orientations and fracture densities. Frequency-dependent seismic velocity and attenuation anisotropy data is computed using the effective viscoelastic stiffness tensor and solving the Christoffel equation. A Bayesian inversion method is then applied to measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuth to estimate the azimuthal fracture orientations and the fracture densities, as well as their uncertainties. Our numerical examples suggest that velocity anisotropy data alone cannot recover the unknown fracture parameters. However, an improved estimation of the unknown fracture parameters can be obtained by joint inversion of velocity and attenuation anisotropy data.     

不同尺度裂缝对弹性波速度和各向异性影响的实验研究

裂缝广泛分布于地球介质中并且具有多尺度的特点,裂缝尺度对于油气勘探和开发有着重要的意义.本文制作了一组含不同长度裂缝的人工岩样,其中三块含裂缝岩样中的裂缝直径分别为2 mm、3 mm和4 mm,裂缝的厚度都约为0.06 mm,裂缝密度大致相同(分别为4.8%、4.86%和4.86%).在岩样含水的条件下测试不同方向上的纵横波速度,实验结果表明,虽然三块裂缝岩样中的裂缝密度大致相同,但是含不同直径裂缝岩样的纵横波速度存在差异.在各个方向上,含数量众多的小尺度裂缝的岩样中纵横波速度都明显低于含少量的大尺度裂缝的岩样中纵横波速度.尤其是对纵波速度和SV波速度,在不同尺度裂缝岩样中的差异更明显.在含数量多的小尺度裂缝的岩样中纵波各向异性和横波各向异性最高,而含少量的大尺度的裂缝的岩样中的纵波各向异性和横波各向异性较低.实验测量结果与Hudson理论模型预测结果进行了对比分析,结果发现Hudson理论考虑到了裂缝尺度对纵波速度和纵波各向异性的影响,但是忽略了其对横波速度和横波各向异性的影响.     

Forced imbibition into a limestone: measuring P‐wave velocity and water saturation dependence on injection rate

Quantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.     

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green’s function for wavefield propagation and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operator-root one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency-dependent shear-wave splitting modeling and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications.     

基于各向异性分析的微地震震源矢量场重建和裂缝解释

针对微地震裂缝解释的复杂性,从震源矢量场的重建开始研究,在研究VTI介质速度模型各向异性条件下的走时和透射系数的变化特征基础上,形成了各向异性条件下的群、相速度及透射系数的计算方法.针对多级检波器水平分量朝向的多向性特点,提出了多级检波器水平分量的偏振分析方法,得到了完整的水平特征矢量,克服了单级检波器水平分量偏振分析构建特征矢量信息不全的问题,形成了高精度微地震事件定位方法,实现各向异性VTI介质速度模型的高斯束微地震格林函数正演模拟.利用格林函数模拟场、观测记录场,从构建完整场研究入手,重建震源矢量场.根据重建的震源矢量场,提出了裂缝解释的全新的系列方法,包括单条裂缝、裂缝网络的解释方法.通过实际资料的测试分析,验证了研究技术的实用性.     

Field trial of seismic recording using distributed acoustic sensing with broadside sensitive fibre‐optic cables

Distributed acoustic sensing is an emerging technology using fibre‐optic cables to detect acoustic disturbances such as flow noise and seismic signals. The technology has been applied successfully in hydraulic fracture monitoring and vertical seismic profiling. One of the limitations of distributed acoustic sensing for seismic recording is that the conventional straight fibres do not have broadside sensitivity and therefore cannot be used in configurations where the raypaths are essentially orthogonal to the fibre‐optic cable, such as seismic reflection methods from the surface. The helically wound cable was designed to have broadside sensitivity. In this paper, a field trial is described to validate in a qualitative sense the theoretically predicted angle‐dependent response of a helically wound cable. P‐waves were measured with a helically wound cable as a function of the angle of incidence in a shallow horizontal borehole and compared with measurements with a co‐located streamer. The results show a similar behaviour as a function of the angle of incidence as the theory. This demonstrates the possibility of using distributed acoustic sensing with a helically wound cable as a seismic detection system with a horizontal cable near the surface. The helically wound cable does not have any active parts and can be made as a slim cable with a diameter of a few centimetres. For that reason, distributed acoustic sensing with a helically wound cable is a potential low‐cost option for permanent seismic monitoring on land.     

Static and dynamic stiffness measurements with Opalinus Clay

In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi-static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low-frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P-wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non-elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.     

Numerical investigation of alternative fracture stiffness measures and their respective scaling behaviours

We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half‐space follow a self‐affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub‐fractures of smaller dimensions are extracted. The self‐affine distribution implies that the stress‐free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self‐affine fractures itself scales with the length of the fractures.     

Influence of crack distribution of rocks on P‐wave velocity anisotropy – a laboratory and field scale study‡

The purpose of this paper is the comparison of P‐wave velocity and velocity anisotropy, measured at different scales under laboratory and field conditions. A shallow seismic refraction survey with shot/receiver spacing of up to 10 m was carried out on a flat outcrop of lhertzolite in the southern part of the Balmuccia massif. Oriented rock samples were also obtained from the locality. The particular advantage of the laboratory method used is the possibility of measuring velocity in any direction under controlled conditions. Laboratory tests were made on spherical peridotite samples, 50 mm in diameter, by ultrasonic velocity measurements in 132 directions (meridian and parallel networks) under confining stress ranging from atmospheric to 400 MPa. The mean P‐wave velocity of the field and laboratory data differed by between 20–30%. In addition, P‐wave velocity anisotropy of 25% was detected in the field data. Whereas the anisotropy in the laboratory samples in the same orientation as the field surveys was less than 2%. This observed scaling factor is related to the different sampling sizes and the difference in frequencies of applied elastic waves. With an ultrasonic wavelength of 10 mm, laboratory samples represent a continuum. The field velocities and velocity anisotropy reflect the presence of cracks, which the laboratory rock samples do not contain. Three sub‐vertical fracture sets with differing strikes were observed in the field outcrop. Estimates of fracture stiffness from the velocity anisotropy data are consistent with other published values. These results highlight the difficulty of using laboratory velocity estimates to interpret field data.     

波前重建法折射成像及应用研究

根据实际工作需要对传统的地震折射资料解释方法的适用范围进行了讨论,指出了传统折射资料解释方法所存在的问题。采用重建波前的方法进行折射成像,通过改进震源函数,并在反演过程中使用有限差分技术解程函方程,进行波场外推,从根本上解决了传统折射资料解释方法存在的问题,计算精度高,速度快。通过理论模型和实际资料的对比计算和验证,效果良好。     

Damping formulation for nonlinear 1D site response analyses

Measurements and observations of ground shaking during large earthquakes have demonstrated the predominant role of site effects in the response of infrastructure during a seismic event. Despite significant efforts to model the hysteretic response and nonlinearity of soils due to medium and large ground motions, the most widely accepted nonlinear site response methods are not able to represent simultaneously the changes of stiffness and energy dissipation (damping) observed in both laboratory tests and during earthquake events. This paper presents two new soil damping formulations implemented in nonlinear one-dimensional site response analysis for small and large strains. The first formulation introduces an approach to construct a frequency-independent viscous damping matrix which reduces the over-damping at high frequencies, and therefore, the filtering at those frequencies. The second formulation introduces a reduction factor that modifies the extended Masing loading/unloading strain–stress relationship to match measured modulus reduction and damping curves simultaneously over a wide range of shear strains. A set of examples are introduced to illustrate the effect of using the two proposed formulations, separately and simultaneously, in nonlinear site response analyses.     

Accurate estimation of acoustic impedance based on spectral inversion

Acoustic impedance is one of the best attributes for seismic interpretation and reservoir characterisation. We present an approach for estimating acoustic impedance accurately from a band‐limited and noisy seismic data. The approach is composed of two stages: inverting for reflectivity from seismic data and then estimating impedance from the reflectivity inverted in the first stage. For the first stage, we achieve a two‐step spectral inversion that locates the positions of reflection coefficients in the first step and determines the amplitudes of the reflection coefficients in the second step under the constraints of the positions located in the first step. For the second stage, we construct an iterative impedance estimation algorithm based on reflectivity. In each iteration, the iterative impedance estimation algorithm estimates the absolute acoustic impedance based on an initial acoustic impedance model that is given by summing the high‐frequency component of acoustic impedance estimated at the last iteration and a low‐frequency component determined in advance using other data. The known low‐frequency component is used to restrict the acoustic impedance variation tendency in each iteration. Examples using one‐ and two‐dimensional synthetic and field seismic data show that the approach is flexible and superior to the conventional spectral inversion and recursive inversion methods for generating more accurate acoustic impedance models.     

A groundwater recharge field study: site characterization and initial results

A field study site was installed in east‐central Pennsylvania to examine processes controlling groundwater recharge. It was instrumented to monitor climatic inputs, soil water dynamics and groundwater response. Characterization of the layered fractured bedrock underlying the site by rock coring, seismic surveys and interval packer testing showed consistencies between layer depths, fracture frequencies, seismic velocities and hydraulic conductivities. Monthly summaries of rainfall and percolate over two years showed that percolate rates were generally high and closely related to precipitation during the dormant season. During the growing season, however, the relationship became erratic with large variabilities occurring between individual lysimeter measurements. Eight dormant season rainfall events were examined in detail. Smaller events produced similar responses from 1 m deep percolate lysimeters. Approximately 10–15 mm of rain was required to initiate percolate, with the time delay in response dependent on how long it took this depth to accumulate; 5 to 6 mm of the rain was retained in storage, with the remainder becoming percolate. Larger rains, from 30–110 mm, caused correspondingly larger depths of percolate and larger water table responses, but generally similar patterns of site response. Groundwater at the site was typically about 6 m below the land surface during the dormant season. It responded 1–2 hours after the onset of percolate, and reached its maximum elevation anywhere from 4 to 16 hours after that, even though percolate was still occurring. Based on causative depth of recharge and amount of water level rise in wells, the specific yield of the aquifer was found to be of the order of 0·01. This value is characteristic of fracture geometry rather than matrix properties of the bedrock. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical modelling of interface scattering of seismic wavefield from a random rough interface in an acoustic medium: comparison between 2D and 3D cases

Seismic wavefield scattering from a statistically randomly rough interface in a multilayered piecewise homogeneous medium is studied in 3D. The influence of the surface roughness on the scattered wavefield is analysed numerically by using a finite‐difference operator in the acoustic domain. Since interface scattering in the real practical sense is a 3D physical phenomenon, we show in this work that the scattering response of a randomly rough interface is not the same in 3D situations as in the 2D cases described in some earlier works. For a given interface roughness height in 3D, an interface roughness height at least three times greater is required to produce an equivalent phase scattering effect in 2D situations, for a given correlation length of the interface roughness scale. Based on observations from spectral analysis, we show that scattering results principally in de‐phasing and frequency band‐limiting of the incident wavefront, the frequency band‐limiting properties being comparable to cases reported in the literature for absorption and thin‐layer filtering. The interface scattering phenomenon should be critically considered when using amplitude and phase information from seismic signal during inversion processes.     

Electromechanical phenomena associated with earthquakes

This article reviews the field, laboratory, and theoretical investigations made concerning different electromechanical phenomena associated with earthquakes. It discusses laboratory measurements of electrical resistivity of rocks stressed up to fracture, particular attention being paid to the interpretation of results according to the diffusion-dilatancy theory. This is followed by the discussion of field measurements of electrical characteristics of rocks in seismic areas in connections with seismic activity in these regions. Piezoelectric and electrostrictive phenomena are briefly discussed, and also a theoretical model of electro-elastic effects associated with an earthquake source. The last part concerns electrokinetic phenomena in porous rocks, caused by the diffusion of fluids into the dilatant focal region. The divergence of opinion about the physical models of the earthquake process is emphasized.     

逆断层对致密岩石构造裂缝发育的约束控制

致密岩石(如火山岩和碳酸盐岩)可广泛发育构造裂缝,这类致密岩石的构造裂缝数值建模是构造裂缝地震解释、地震反演和油藏数值模拟的基础.我国西北各盆地普遍发育逆断层,通过在新疆巴楚地区微波塔逆断层和一间房逆断层分别布置实测剖面对野外测量的构造裂缝面密度进行定量分析,发现受逆断层控制的裂缝面密度与逆断层面的曲率呈线性关系;裂缝...     

Dynamic microplasticity manifestation in consolidated sandstone in the acoustical frequency range

Microplasticity manifestations caused by acoustical wave in the frequency range of about 4.5 kHz–7.0 kHz are detected in consolidated artificial sandstone. Equipment was tested by means of comparison of data obtained for a standard material (aluminium) and sandstone. Microplasticity manifestations in acoustic records are present in the form of the ladder‐like changes in the amplitude course. The stress plateaus in the acoustic trace interrupt the amplitude course, transform the wavefront, and shift the arrival time along the time axis. Microplasticity contribution to the acoustic record changes with the increase in the strain amplitude value. The combined elastic–microplastic process conditions the wavefront steepness and its duration. Stress plateaus exert influence on the waveform and, accordingly, on pulse frequency response. These results confirm the earlier data obtained for weakly consolidated rock. This contribution to wave propagation physics can be useful in solving applied problems, as, for instance, the reservoir properties prediction by means of wave attenuation in acoustic logging and seismic prospecting.     

Seismic behavior of a post-tensioned integral bridge including soil–structure interaction (SSI)

Current practice usually pays little attention to the effect of soil–structure interaction (SSI) on seismic analysis and design of bridges. The objective of this research study is to assess the significance of SSI on the modal with geometric stiffness and seismic response of a bridge with integral abutments that has been constructed using a new bridge system technology. Emphasis is placed on integral abutment behavior, since abutments together with piers are the most critical elements in securing the integrity of bridge superstructures during earthquakes. Comparison is made between analytical results and field measurements in order to establish the accuracy of the superstructure–abutment model. Sensitivity studies are conducted to investigate the effects of foundation stiffness on the overall dynamic and seismic response of the new bridge system.