Obliquely incident wave propagation across rock joints with virtual wave source method

Due to the presence of joints, waves are greatly attenuated when propagating across rock masses. Zhu et al. (2011) (Normally incident wave propagation across a joint set with virtual wave source method. J. Appl. Geophys.73, 283–288.) studied normally incident wave propagation across a joint set with the virtual wave source method (VWSM). The introduced VWSM has merits in some aspects, especially the capability of separating differently arriving transmitted waves. However, normal wave incidence is only the special case for wave incidence with arbitrary incident angles. Obliquely incident wave propagation across a joint set is more complicated than normally incident wave propagation due to wave transformation at the joints. As a continuation of the previous paper, this work is extended to analytically study obliquely incident wave propagation across joints with VWSM. Complete theoretical reflection and transmission coefficients across single joint described by displacement discontinuity model are derived through plane wave analysis. The superposition of P wave and S wave is for the first time mathematically expressed and studied. The VWSM is verified through comparison with the propagation matrix method. Through extensive parametric studies on wave transmission across single and multiple parallel joints, it is shown that transmitted wave energy is mainly constrained in the transmitted wave of the same type as the incident wave. And with increasing joint stiffness, the transmission coefficients across single joint increases except those whose wave type is different from the incident wave. The amplitude of superposed transmitted wave for P wave incidence increases with incident angle, which is coincident with field observations. Both joint spacing and number of joints have significant effects on transmission coefficients. We find that when joint spacing is sufficiently large, the transmission coefficient is no longer a constant as the normally incident wave propagation case (Zhu et al., 2011). And when joints are very closely spaced, wave attenuation depends little on the number of joints, which is different from the conclusions from equivalent medium method.     

应力波作用下节理面前后电磁辐射强度的变化

从压电体中的压电本构方程出发,得到了含石英等压电介质岩体在应力波作用下产生的电场值的关系表达式．电磁辐射强度随电阻率增大而增大,随传播距离发生衰减．对于电阻率较大导电性能较差的岩石来说,压电电荷的贡献是足够引起重视的．利用所得到的表达式对实际地震电磁信号幅值进行了估算,所得结果与实测结果吻合．依据所得到的电场值的表达式及应力波在节理面处的透射解,获得了垂直入射应力波作用下产生的电磁波在线性变形节理面前后的强度关系．研究了节理参数、岩体电性参数以及入射波频率对节理面前后电磁辐射强度的影响．结果表明,电磁辐射的强度随节理初始刚度增大而增大;对于节理面两侧岩体性质不同的情形,从理论上讲,电磁辐射强度随单个参数的变化是明确的,但在多种参数的综合影响下,电磁辐射强度变化情况相对比较复杂．本文的理论计算结果与其它众多学者得出的实验结果一致．      

Fission of a weakly nonlinear interfacial solitary wave at a step

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.     

广州地磁台转换函数的长期变化和季节变化

本文全面系统地研究了1960——1987年广州地磁台转换函数的变化.结果表明:(1)季节变化的特点是夏季幅度大,冬季幅度小,具有12和6个月的主要周期成份;长期变化则表现以每年0.0025的速率下降.转换函数 B 的长期变化和季节变化不明显;(2)由转换函数 A,B 求出的帕金森矢量的方向明显地受海洋的影响,反映了海洋效应;(3)转换函数 A,B 的逐月值与地磁活动相关,而年均值与地磁活动无关.A 的年均值无明显的11年或22年周期.长期变化可能主要受地球内部电性结构的影响.      

Response of transient rock uplift and base level knickpoints to erosional efficiency contrasts in bedrock streams

Knickpoints in bedrock streams are often interpreted as transient features generated by a change in boundary conditions. It is typically assumed that knickpoints propagate upstream with constant vertical velocities, though this relies on a stream being in erosional steady state (erosion rate equals rock uplift rate) prior to the knickpoint's formation. Recent modeling and field studies suggest that along-stream contrasts in rock erodibility perturb streams from erosional steady state. To evaluate how contrasts in rock erodibility might impact knickpoint interpretations, we test parameter space (rock erodibility, rock contact dip angle, change in rock uplift rate) in a one-dimensional (1D) bedrock stream model that has variable rock erodibility and produces a knickpoint with a sudden change in rock uplift rate. Upstream of a rock contact, the vertical velocity of a knickpoint generated by a change in rock uplift rate is strongly correlated with how the rock contact has previously perturbed erosion rates. These knickpoints increase vertical velocity upon propagating upstream of a hard over soft contact and decrease vertical velocity upon propagating upstream of a soft over hard contact. However, interactions with other transient perturbations produced by rock contacts make for nuances in knickpoint behavior. Rock contacts also influence the geometry of knickpoints, which can become particularly difficult to identify upstream of soft over hard rock contacts. Using our simulations, we demonstrate how a contact's along-stream horizontal migration rate and cross-contact change in rock strength control how much an upstream reach is perturbed from erosional steady state. When simulations include multiple contacts, the knickpoint is particularly prone to colliding with other transient perturbations and can even disappear altogether if rock contact dips are sufficiently shallow. Caution should be taken when analyzing stream profiles in areas with significant changes in rock strength, especially when rock contact dip angles are near the stream's slope.     

THE INFLUENCE OF AN ASYMMETRY IN THE SEQUENCE ROCK/COAL/ROCK ON THE PROPAGATION OF RAYLEIGH SEAM WAVES*

Small offsets in hard coal seams can be detected with the aid of seam (channel) waves. Transmission and reflection of seam waves depend, among other parameters, upon the symmetry properties of the sequence rock/coal/rock. Two typical unsymmetrical sequences are found in European coal deposits: (i) coal seams with roof and floor of differing acoustic impedance and (ii) coal seams interlayered with rock and soil. Two-dimensional analog models with appropriate impedance contrasts are used to study the effect of the unsymmetrical layers upon the propagation of Rayleigh seam waves. Data analysis is based upon amplitude measurements both parallel and perpendicular to the layers and dispersion curves. The effect of unsymmetrical roof (rock 1) and floor (rock 2) was studied with models containing homogeneous coal seams. Leaky mode wave groups with phase velocities (c_R) in the range between the SV-wave velocities (β_{r1, 2}) of the two rock materials, i.e. β_r1≥c_R > β_r2, form a characteristic part of the Rayleigh seam wave signal. Using Knott's energy coefficient calculations it is shown that in that range energy leakage into the surrounding rock by refracted SV-waves is restricted to only one of the two interfaces, namely coal/rock 2. At the other interface, coal/rock 1, all waves are totally reflected. Thus, the high amplitudes of these leaky mode wave groups are explained by “quasi-normal mode” features. The influence of a dirt bed on wave propagation was studied in models where the roof and the floor have the same elastic properties. The maximum thickness of the dirt bed did not exceed 20% of the total seam thickness. The effect of the bed's location within the seam was also investigated. For all recorded normal-mode wave groups either the total seam or the coal layers could be regarded as wave guides. This was shown by the fact that the phases could be associated with the phase velocity dispersion curves calculated for the symmetrical sequence rock/coal/rock. These curves are relevant under the condition that the thickness of the coal layer assumed under the calculation coincides with the thickness of the effective wave guide of the respective wave groups. Wave groups guided in the total seam are not influenced by either the thickness or the position of the dirt bed. On the other hand, for wave groups guided in the coal layers, the quotient of signal amplitudes in the coal layers is influenced by the position of the dirt bed.     

Asymmetry in the time-lapse seismic response to injection and depletion

Large changes in seismic reflection amplitude have been observed around injectors, and result from the decrease in elastic‐wave velocity due to the increase in pore pressure in the reservoir. In contrast, the velocity change resulting from the decrease in pore pressure in depleting reservoirs is observed to be smaller in magnitude. Elastic‐wave velocities in sandstones vary with stress due to the presence of stress‐sensitive grain boundaries within the rock. Grain‐boundary stiffness increases non‐linearly with increasing compressive stress, due to increased contact between opposing faces of the boundary. This results in a change in velocity due to a decrease in pore pressure that is smaller than the change in velocity caused by an increase in pore pressure, in agreement with time‐lapse seismic observations. The decrease in porosity resulting from depletion is not fully recovered upon re‐pressurization, and this leads to an additional steepening of the velocity vs. effective stress curve for injection relative to depletion. This difference is enhanced by any breakage of cement or weakening of grain contacts that may occur during depletion and by the reopening or formation of fractures or joints and dilation of grain boundaries that may occur during injection.     

Effects of Contact Geometry of Faults on Transmission Waves

—?In order to clarify the effects of contact geometry of faults on transmission waves, we have performed a series of experiments in which P and S waves with known wavelength were transmitted through an artificial fault. A pair of piezo-electric transducers (PZT) with various resonant frequency were used for the transmitter and the receiver. Parallel grooves were cut on disk surfaces and two disks were placed face to face with the grooves on one disk being perpendicular to those on the other disk. This yields evenly spaced square contacts on the fault. We regard the square contacts as asperity contacts, the size and the height of which were controlled by changing the width and the depth of the grooves. We found that the transmissivity of the waves is solely determined by the ratio of the groove depth/width to wavelength. The shallower and the narrower the groove depth and width are, the larger the amplitude of first arrival is for both P and S waves. When the groove depth is shallower than a quarter of wavelength, the effect of groove depth is negligible; deeper grooves significantly reduce the amplitude. We have made a mathematical model based on the stiffness of fault. By comparing the model calculations with the observation we found that the model has a limit at which the prediction by the model deviates from the data. The deviation occurs when the ratio of the groove depth/width to wavelength becomes 0.25. We refer to the wavelength as the critical wavelength. When the wavelength is larger than the critical wavelength, the observed data can be well explained by the model. Above this threshold, the model no longer fits the data. In this range, the amplitude of transmitted waves is found to be proportional to the real contact area. Although it is a kind of paradox that the amplitude, not the energy, is proportional to the real contact area, it is possibly explained by taking a non-uniform distribution of stress on the surface of the receiver PZT into account.     

各向同性薄层反射理论地震图

本文在各向同性介质假设下,计算了薄层顶、底反射P波和PS波的理论地震图.理论模拟发现薄层的反射P波与PS波是一复合波,包括层内的多次透射和反射转换波型,且具有类似单一界面反射的、脉冲式的波形特征.两类薄层反射整体振幅随着薄层厚度的降低而缩小;在地震子波主频40 Hz条件下,2 m左右厚度的薄层反射相比单一界面反射具有等同的振幅水平.1 m以下极薄层仅有弱反射甚至无反射;薄层反射复合波振幅与炮检距的关系依然成立,但不惟一;单界面反射AVO原理、方法不适用于薄层反射解释与反演.     

Time-dependent friction and the mechanics of stick-slip

Time-dependent increase of static friction is characteristic of rock friction undera variety of experimental circumstances. Data presented here show an analogous velocity-dependent effect. A theor of friction is proposed that establishes a common basis for static and sliding friction. Creep at points of contact causes increases in friction that are proportional to the logarithm of the time that the population of points of contact exist. For static friction that time is the time of stationary contact. For sliding friction the time of contact is determined by the critical displacement required to change the population of contacts and the slip velocity. An analysis of a one-dimensional spring and slider system shows that experimental observations establishing the transition from stable sliding to stick-slip to be a function of normal stress, stiffness and surface finish are a consequence of time-dependent friction.     

INVESTIGATION OF THE SEISMIC RESPONSE OF CYCLICALLY LAYERED CARBONIFEROUS ROCK BY MEANS OF SYNTHETIC SEISMOGRAMS *

Seismic exploration for coal as well as basic scientific research indicate the existence of unsolved problems. These problems arise partly because the requirements are different from those in exploration for gas and oil and are partly due to the geological situation. The medium to be investigated is composed of cyclically changing layers with extremely high velocity and density contrast. Furthermore, the structure of the carboniferous rock is highly fractured and folded. This leads to difficulties in interpreting the seismic response of carboniferous rock. To overcome these difficulties synthetic seismograms are a useful tool. Calculating synthetic seismograms the carboniferous rock has been modelled as a sequence of seams and rock. The following results have been obtained

• (i) A single seam gives rise to a distinct reflection signal even for a thickness of 1/50 of the wavelenght.
• (ii) Individual reflections are not visible from a sequence of layers containing a great number of seams and interfaces. Due to constructive interference only a few high amplitudes appear. These high amplitudes are labelled “interference reflections”.
• (iii) With increasing travel time the interference reflections are mainly composed of short lag multiples such that the primary reflections have no significant influence.
• (iv) The sequence of seams acts on the reflected seismic signal as a high pass filter and on the transmitted signal as a low pass filter. The cut-off frequencies are determined by the average seam thickness, and the steepness of the slopes increases with increasing number of seams.
• (v) The interference reflections can be used for determining the geological structure at least for the upper part of the sequence.

     

Unsaturated water flow across soil aggregate contacts

Unsaturated water flow through soil aggregates is controlled by the contacts between aggregates. The contacts are highly conductive when wet and become bottle-necks for flow when drained. We postulate that the hydraulic conductivity of the contacts is in first place determined by the water-filled contact area. The objective of this study was to measure and model the water-filled contact area and to relate it to the conductivity of a series of aggregates. We performed microscopic tomography of an aggregate pair equilibrated at different water potentials. By means of image analysis and a morphological pore network model, the water-filled contact area was calculated. We found that the aggregate surface is rough and the contact region contains macropores which are rapidly drained. As a consequence the water-filled contact area dramatically decreases as the water potential is diminished. We modeled this process by describing the aggregates as spheres covered by much smaller spheres representing the roughness. The water-filled contact was analytically calculated from this model. Knowing the water-filled contact area we up-scale the hydraulic conductivity of a series of aggregates. This is calculated as the harmonic mean of the contact and aggregate conductivities. The contact conductivity is calculated from the water-filled contact area. Near saturation the conductivity of a series of aggregates is close to the conductivity of a single aggregate, and, when further drained, it rapidly decreases as the water-filled contact area. The model matches the experimental data well.     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.     

A thin-layer interface model for wave propagation through filled rock joints

The present study essentially employs a thin-layer interface model for filled rock joints to analyze wave propagation across the jointed rock masses. The thin-layer interface model treats the rough-surfaced joint and the filling material as a continuum medium with a finite thickness. The filling medium is sandwiched between the adjacent rock materials. By back analysis, the relation between the normal stress and the closure of the filled joint are derived, where the effect of joint deformation process on the wave propagation through the joint is analyzed. Analytical solutions and laboratory tests are compared to evaluate the validity of the thin-layer interface model for filled rock joints with linear and nonlinear mechanical properties. The advantages and the disadvantages of the present approach are also discussed.     

全波形反演在缝洞型储层速度建模中的应用

速度是地震偏移成像准确与否的关键所在.全波形反演综合利用地震波场运动学和动力学信息,能够得到相比传统速度建模方法更高频的成分.全波形反演的理论比较成熟,但实际应用成功的例子相对较少,特别是对于陆上地震资料.塔里木盆地地震地质条件复杂,为了实现缝洞型储层的准确成像,本文开展了针对目标靶区的全波形反演精细速度建场研究.采用一种时间域分层多尺度全波形反演流程:首先通过层析成像建立初始速度模型;其次利用折射波反演浅层速度模型;最后利用反射波反演中深层速度模型.偏移成像结果表明基于全波形反演的速度建模技术能有效改善火成岩下伏构造的成像精度,显示了全波形反演在常规陆上采集资料的应用潜力.     

Analytical and numerical study of P-wave attenuation in rock shelter layer

The protection of underground structures against dynamic loadings has long been a topic of great interest in defense engineering. This paper focuses on the far-field blast-wave propagation and attenuation in rock shelter layer with an inclusion or filled medium. First, the effect of single inclusion on wave attenuation is explored analytically assuming that the interfaces between rock and the inclusion are completely consolidated. The formulae for the strength of total transmitted stress- and velocity-wave after the inclusion are subsequently presented. At last, numerical studies on the attenuation of one-dimensional P-wave in rock embedded with artificial cavity, steel plate and natural joint are carried out. The attenuation rules for various scenarios are discussed in detail in this paper which can provide useful guidelines to the design of intelligent defense structures.     

Coupled finite element and discrete element method for underground blast in faulted rock masses

This paper focuses on the propagation and dynamic effects of blast waves in faulted rock masses. A coupled method combining UDEC and LS-DYNA is presented whereby the explosion process is simulated by LS-DYNA while the wave propagation and its dynamic effects in rock masses with faults are modeled by UDEC. The blast-induced crack evolution and failure zone distribution in faulted rock masses are explored using the proposed coupled method. The relationship between rock failure and fault parameters such as dip, stiffness and friction are also investigated. The results indicate that the coupled method is feasible and effective for evaluating explosion in discontinuous rock system and the existence of faults exerts significant influence on the pattern of rock masses failure.     

Influence of water saturation on horizontal and vertical motion at a porous soil interface induced by incident P wave

This paper describes a study on the influence of water saturation on horizontal and vertical motion at the interface between porous soil and rock formation due to an incident P wave. The soil is modeled as a partially water-saturated porous material with a small amount of air inclusions, while the underlying rock is approximately regarded as an ordinary one-phase solid. Theoretical formulation is developed for the computation of motion amplitudes in both horizontal and vertical components, which are considered as functions of the degree of saturation, the angle of incidence as well as the frequency. Numerical results are provided to illustrate the effect of saturation on displacement amplitudes in both components and their ratios. The results show that even a slight decrease of complete saturation may lead to a substantial change in the motion amplitudes in both horizontal and vertical components. In general, partial saturation may cause lower horizontal-to-vertical ratios over the entire range of incident angles except the normal incidence, implying the potential importance of saturation effects in the interpretation of field observations.     

A data collection and analysis system for research on rock fracturing

We have made a data collection and analysis system for recording microcracks in rock to study the three dimensional pattern of fracture and the dynamic properties of rock during pressurization. This system, with 8 channel data detection, records in real-time, from the initial microcracks to the final vibration waveform excited by the master fracture. The detected data are recorded digitally at the hard disk of an IBM computer (or 286, 386 personal computer) as well as transmitted to disk. The sampling rate for each channel is 10 MHz. Collecting every acoustic emission events in the loaded rock sample with 8 channels by this system, mathematically modelling the AE event travel time, and taking the coordinates of the AE event hypocenter and the three components of P wave velocity as unknown parameters, we set up a set of residual equations for joint inversion, so that the three dimensional localization of AE event hypocenters can be completed under variable velocities, which will lay foundations for the research on rock fracture clearly. The Chinese version of this paper appeared in the Chinese edition ofActa Seismological Sinica,13, 489–495, 1991. The design and development of the system, and the experiments are sponsored by the Chinese Joint Seismological Science Foundation.