P-wave Propagation Research Articles

The importance of accurate time-integration in the numerical modelling of P-wave propagation

The numerical dissipation characteristics of the Newmark and generalised-α time-integration schemes are investigated for P-wave propagation in a fully saturated level-ground sand deposit, where higher frequencies than those for S-waves are of concern. The study focuses on resonance, which has been shown to be of utmost importance for triggering liquefaction due to P-waves alone. The generalised-α scheme performs well, provided that the time-step has been carefully selected. Conversely, the dissipative Newmark method can excessively damp the response, changing radically the computed results. This implies that a computationally prohibiting small time-step would be required for Newmark to provide an accurate solution.

Temperature effect on microstructure and P-wave propagation in Linyi sandstone

In order to study the effect of high temperature on the sandstone, scanning electron microscope (SEM) experiments and primary wave (P-wave) velocity tests have been carried out on sandstone specimens heated to different temperature. The results showed that: (1) the mass loss rate increases exponentially with the increase of temperature and reaches 2.97% at 900°C; (2) the P-wave velocity change rate increases exponentially with the increase of temperature while there is some fluctuation before 500°C; (3) the damage threshold temperature of sandstone samples is 300°C and the limit temperature is 900°C; (4) there is a good linear relationship between the mass loss rate and the P-wave velocity change rate, and the correlation coefficient (R) of the fitting line is 0.989; (5) the damage caused by high temperature can be reflected better by the mass loss rate than P-wave velocity change rate. The results obtained in this paper will be good for predicting the properties of sandstone when exposed to high temperature.

Controls and implications of anisotropy across a strain gradient within granodiorite, Serifos, Greece

Microtextural analyses including electron backscatter diffraction (EBSD), anisotropy of magnetic susceptibility (AMS) and the anisotropy of anhysteretic remanent magnetization (AARM) have been applied across a shear zone within a Miocene granodioritic intrusion on Serifos island, Western Cyclades, Greece. The shear zone records progressive deformation through a ductile to brittle transition. One of the consequences of anisotropic crust is the variation in seismic wave velocity with the direction of propagation, which is largely controlled by the crystallographic preferred orientation (CPO) of anisotropic minerals such as micas and feldspars. CPO data was collected using EBSD and seismic properties were calculated using Voigt-Reuss-Hill averaging of the single minerals' elastic stiffness tensor. The magnetic fabric is used to characterize weakly defined tectonic fabric, thus complementing the CPO data. The structure of rocks exhibiting weak magmatic fabric, as defined by magnetic anisotropy and CPO, appears to reflect the elliptical shape of the pluton. The SW-directed kinematics of the Western Cyclades produced an ENE-striking, SSE dipping low-angle shear zone in the granodiorite that imparted a signature onto the magnetic data of foliated and mylonitic samples, creating a composite fabric from the magmatic emplacement fabric and the top-to-SW directed shear. As for the seismic properties, P-wave anisotropy reaches 11.8% and is consistently controlled by the CPO of plagioclase feldspar, with the direction of fast P-wave propagation subperpendicular to foliation and the direction of slow P-wave propagation subparallel to foliation. The magnetic fabric, coupled with the tectonic fabric inferred from CPO data, gives unique insight into the character of anisotropic minerals in a syntectonic intrusion. This is especially useful for weakly strained rocks where the lineation and foliation (given by the magnetic fabric) can be related to the seismic anisotropy derived from the CPO data. Given the anisotropy caused by the preferred orientation fabrics of major rock-forming minerals, the microstructural analysis of anisotropic minerals is fundamental for incorporating seismic anisotropy into large-scale geophysical models.

Relation between ultrasound measurements and phase evolution in accelerated cementitious matrices

This paper focuses on the characterization of setting and hardening of accelerated cementitious matrices by ultrasound propagation velocity, correlating these processes with chemical parameters and the phase evolution obtained by in situ XRD. Evolution of temperature and determination of setting times complemented this analysis. The technique employed provided a continuous monitoring of the setting and hardening of the hydrating matrix and was susceptible to changes in accelerator reactivity and phase composition. Results showed that ettringite formed by accelerator reaction improves the solid-phase interconnectivity and increases initial ultrasound velocity. P-wave propagation during the acceleration period is directly proportional to alite and C3A degrees of hydration. The influence of AFm phases to increase ultrasound velocity is stronger than ettringite and C-S-H. Based on an extensive statistical analysis, multivariate linear regressions were established between ultrasound velocity and the main chemical properties influencing its evolution, leading to a better comprehension of how these parameters are related.

Velocity model building and imaging in the presence of shallow gas

Multiple shallow layers of low saturation gas charged sands cause poor seismic imaging and hamper exploitation of many oil and gas discoveries in SE Asia. These gas ‘clouds’ are characterized by bright high amplitude reflectors of low P-wave velocity beneath which the seismic reflections have delayed P-wave travel times, reduced bandwidth, reduced reflected and transmitted amplitudes and associated phase distortion (Figure 1). All gas clouds are not equal, the appearance of gas clouds varies worldwide and within regions. A single gas-charged sand may sometimes have almost no effect on P-wave propagation; a shallow region of limited spatial extent may sometimes be undershot resulting in an interpretable image or multiple shallow layers can result in complete ‘wipeout’ of the final image. We believe that both anelastic losses and multiple scattering phenomena (indicated by rays on Figure 1) contribute to weak reflected energy beneath the gas-charged sands. A similar problem in the North Sea led to the development of multi-component seabed seismic solutions utilizing converted waves to penetrate beneath the gas (Berg et al., 1994). These solutions have been successfully applied to the largest of the Malaysian producing fields and are the PETRONAS preferred technical solution (e.g. Radzi et al., 2015). As with many problems, a mixture of acquisition and processing related solutions produces the optimal result but sometimes processing alone can produce a cost-effective result. Despite cost reductions and technical advances, converted wave imaging is still expensive, difficult and time consuming. In this paper we attempt to build an efficient and accurate workflow for velocity model building of P-wave data in order to best exploit the latest imaging algorithms. We use a mixture of synthetic and real data examples from offshore Malaysia to illustrate this difficult and unresolved problem.

Modeling attenuation and dispersion of acoustic waves in porous media containing immiscible non viscous fluids

Este artículo reporta resultados de la propagación de ondas P en medios porosos, simulada solucionando en diferencias finitas las ecuaciones generalizadas de Biot. En modelos saturados se observó que cuando avanza la onda, la amplitud máxima del espectro se desplaza hacia frecuencias menores, y que esta amplitud máxima y su frecuencia están directamente relacionadas. Además, que el factor de calidad disminuye con la porosidad y la saturación. Por ende, la atenuación aumenta con la porosidad, la saturación y la frecuencia pero tiende asintóticamente a un valor constante. Se observó que la fase de la onda cambia linealmente con la frecuencia a una rata de cambio que aumenta linealmente con el tiempo de viaje. Esta rata aumenta con la saturación pero disminuye ligeramente con la porosidad. Este trabajo ignora la divergencia esférica y la retro dispersión, concentrándose en la atenuación intrínseca causada por la fricción, en particular entre líquido y partículas sólidas.

Stress dependence of elastic P-wave velocity and amplitude in coal specimens under varied loading conditions

Experiments allowed finding regular patterns in propagation of elastic P-waves in specimens of black coal exposed to uniaxial compression and triaxial compression by von Karman. It is shown that in case of uniaxial compression, the largest information content is ensured by translucence in perpendicular to bedding and loading axis of coal specimens. Such translucence exhibits four stages of deformation of a specimen. The information content of translucence under triaxial compression reduces with the increase in the constrained pressure that prevents from disintegration of a coal specimen. Four deformation stages are best identified with the constrained pressure of 2.5 MPa, while only stages of specimen consolidation and failure are traced at the pressure of 10 MPa.

Stress Wave Propagation Across a Rock Mass with Two Non-parallel Joints

A rock mass includes a number of joints, which govern the mechanical behavior of the rock mass and greatly affect stress wave propagation. Generally, joints do not parallel with each other, resulting in multiple wave reflections between joints and complex wave propagation process in rock masses. The present study presents an approach to analyze stress wave propagation through a rock mass with two non-parallel joints when the angle between the two joints is <10°. For incident P-wave impinging on this kind of rock mass, multiple reflections take place between the two joints. Meanwhile, transmitted waves are generated and propagate successively away from the joints. The mathematical expressions for P-wave propagation across the two joints are established in time domain by analyzing the wave field in the rock mass. By comparing with the result from numerical simulation, the new approach is proved to be effective to analyze wave propagation across two non-parallel joints, where the influence of joint tips on wave propagation is neglected. Parametric studies show that the joint stiffness, joint angle and frequency of incident wave have different effects on transmission and reflection coefficients.

Experimental study of the stress effect on attenuation of normally incident P-wave through coal

The purpose of this study is to experimentally investigate the stress effect on normally incident P-wave attenuation through coal specimens. Laboratory tests were carried out using a Split Hopkinson pressure bar (SHPB) system, and a modified method was proposed to determine the quality factor (Q) of P-waves through coal specimens. Larger quality factor denotes less energy attenuated during P-wave propagating through coal. Experimental results indicate that the quality factor and stress (σ) within coal specimens are positively correlated. The P-wave propagation through coal specimens causes crack closure at the beginning of the coal fracture process in SHPB tests, an innovative model was thus proposed to describe the relationship between the crack closure length and the dynamic stress induced by P-wave. Finally, the stress effect on P-wave attenuation through coal was quantitatively represented by a power function Q=a(c–bσ)−6, and the material constants a, b, and c were determined as 1.227, 1.314, and 0.005, respectively. The results obtained in this study would be helpful for engineers to estimate seismic energy attenuation and coal mass instability in coal mines.

Evaluating use of resonant column in flexural mode for dynamic characterization of Bangalore sand

The resonant column method is a well-established medium-frequency wave propagation technique for the dynamic characterization of soils. This study presents an evaluation of Young׳s modulus of a quartzitic sand derived from flexural resonant column tests. The results are compared with extender elements, which are embedded in the same apparatus and apply high-frequency P-wave propagation, as well as a published model in the literature derived from longitudinal resonant column experiments. The comparison of the elastic Young׳s modulus values was satisfactory. The material damping derived from the free-vibration decay method had higher values in flexural mode than torsional mode. And, with an increase in confinement, a faster reduction in material damping associated with S-wave propagation was observed. The results of the study are promising for the standardization of the flexural mode of vibration in the classical torsional resonant column device which can provide invaluable insight into the behavior of state and effective stress-dependent materials.

Numerical Simulation of P-Wave Propagation in Rock Mass with Granular Material-Filled Fractures Using Hybrid Continuum-Discrete Element Method

In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.

P-wave propagation in dry rocks under controlled temperature and humidity

P-wave propagation in dry rocks under controlled temperature and humidity

Propagation and attenuation of P-waves in patchy saturated porous media

We establish a patchy saturation model and derive the seismic wave equations for patchy saturated porous media on the basis of Biot’s equations and Johnson’s bulk modulus. We solve the equations, obtain the attenuation coefficients, and analyze the characteristics of wave attenuation in the seismic frequency range. The results suggest that seismic waves show attenuation and dispersion in partially saturated rocks in the low frequency range. With frequency increasing, attenuation increases. The attenuation of P-waves of the second kind is more pronounced in agreement with Biot’s theory. We also study the effect of porosity, saturation, and inner sphere radius on the attenuation of the P-waves of the first kind and find that attenuation increases with increasing frequency and porosity, and decreases with increasing frequency and degree of saturation. As for the inner sphere radius, wave attenuation is initially increasing with increasing frequency and inner sphere radius less than half the outer radius. Subsequently, wave attenuation decreases with increasing frequency and inner sphere radius is higher than half the outer sphere radius.

Cnoidal waves in solids

Cnoidal waves are nonlinear and exact periodic stationary waves, well known in the shallow water theory of fluid mechanics. In this study we retrieve such periodic stationary wave solutions as singularities of the problem of homogeneous volumetric deformation of a rate-dependent, heterogeneous solid material. In accordance to the classical Hill stationary wave localization instability, which provides velocity gradient discontinuities in shear failure, cnoidal waves are dilational and compactional manifestations of volumetric localization along lines of stress discontinuities. They therefore emerge along the volumetric component of the classical slip line field theory, with their regular distance being a tell tale indication of rate-dependent volumetric deformation. We discuss applications for the dominant mode of I1 compaction in geomaterials where distinct cnoidal wave instabilities appear as localisation features in compaction. We also discuss the case of localisation features in a classical (J2 plastic) material where a small but important cnoidal contribution may trigger equidistant bands of localisation known as Lüders lines. We therefore postulate that cnoidal waves constitute fundamental material instabilities stemming from the propagation of elasto-plastic P-waves.

Parametric Study on Cylindrical P-Wave Propagation

Considering the energy variation, cylindrical P-wave propagation across a linear elastic rock joint is analyzed. Then parametric studies are carried out to investigate the effects of the wave source distance,the joint stiffness and the incident waveforms on wave propagation across a jointed rock mass.

Analytical Study of Cylindrical P-Wave Propagation across Jointed Rock Masses

According to the displacement discontinuity method and the conservation of momentum at the wave fronts, analysis for cylindrical P-wave propagation across a linear elastic rock joint is carried out. Considering the energy variation for wave propagation in one medium, the wave propagation equation was derived and expressed in an iterative form. The transmission and reflection coefficients are then obtained from the equation. By verification, the results agree very well with those from the existing results.

Simulation of the effect of stress-induced anisotropy on borehole compressional wave propagation

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This can lead to an incorrect estimation of formation elastic properties measured from sonic logs. Previous work has focused on estimating the elastic properties of the formation surrounding a borehole under anisotropic stress loading. We studied the effect of borehole stress concentration on sonic logging in a moderately consolidated Berea sandstone using a two-step approach. First, we used an iterative approach, which combines a rock-physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole subjected to an anisotropic stress loading. Second, we used the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response of the borehole. Although we neglected the effects of rock failure and stress-induced crack opening, our modeling results provided important insights into the characteristics of borehole P-wave propagation when anisotropic in situ stresses are present. Our simulation results were consistent with the published laboratory measurements, which indicate that azimuthal variation of the P-wave velocity around a borehole subjected to uniaxial loading is not a simple cosine function. However, on field scale, the azimuthal variation in P-wave velocity might not be apparent at conventional logging frequencies. We found that the low-velocity region along the wellbore acts as an acoustic focusing zone that substantially enhances the P-wave amplitude, whereas the high-velocity region caused by the stress concentration near the borehole results in a significantly reduced P-wave amplitude. This results in strong azimuthal variation of P-wave amplitude, which may be used to infer the in situ stress state.

Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems

The original numerical manifold method (NMM) employs an implicit time integration scheme to achieve higher computational accuracy, but its efficiency is relatively low, especially when the open–close iterations of contact are involved. To improve its computational efficiency, a modified version of the NMM based on an explicit time integration algorithm is proposed in this study. The lumped mass matrix, internal force and damping vectors are derived for the proposed explicit scheme. A calibration study on P-wave propagation along a rock bar is conducted to investigate the efficiency and accuracy of the developed explicit numerical manifold method (ENMM) for wave propagation problems. Various considerations in the numerical simulations are discussed, and parametric studies are carried out to obtain an insight into the influencing factors on the efficiency and accuracy of wave propagation. To further verify the capability of the proposed ENMM, dynamic stability assessment for a fractured rock slope under seismic effect is analysed. It is shown that, compared to the original NMM, the computational efficiency of the proposed ENMM can be significantly improved.

Simulation of the hydration kinetics and elastic moduli of cement mortars by microstructural modelling

The ability of the VCCTL microstructural model to predict the hydration kinetics and elastic moduli of cement materials was tested by coupling a series of computer simulations and laboratory experiments, using different cements. The novel aspects of this study included the fact that the simulated hydration kinetics were benchmarked using real-time measurements of the early-age phase composition during hydration by in situ X-ray diffraction. Elastic moduli are measured both by strain gauges (static approach) and by P-wave propagation (dynamic approach). Compressive strengths were measured by loading mortar prisms until rupture. Virtual samples were generated by VCCTL, using particle size distribution and phase composition as input. The hydration kinetics and elastic moduli were simulated and the numerical results were compared with the experimental observations. The compressive strength of the virtual mortars were obtained from the elastic moduli, using a power-law relation. Experimentally measured and simulated time-dependence of the major cement clinker phases and hydration product phases typically agreed to within 5%. Also, refinement of the input values of the intrinsic elastic moduli of the various phases enabled predictions of effective moduli, at different ages and different water-to-cement mass ratios, that are within the 10% uncertainty in the measured values. These results suggest that the VCCTL model can be successfully used as a predictive tool, which can reproduce the early age hydration kinetics, elastic moduli and mechanical strength of cement-based materials, using different mix designs.

Microstructures and seismic properties of south Patagonian mantle xenoliths (Gobernador Gregores and Pali Aike)

The subcontinental lithospheric mantle evolves through time due to tectonic events and processes as static recrystallization and melt percolation. To constrain the extent of these processes in the South Patagonian subcontinental mantle lithosphere we performed a microstructural and Electron Backscattered Diffraction (EBSD) study of a suite of 35 peridotite xenoliths brought to the surface by Plio-Pleistocene alkaline volcanic rocks from Gobernador Gregores and Pali Aike. All samples show a well-developed olivine and pyroxene crystallographic preferred orientation (CPO), consistent with deformation by dislocation creep with dominant activation of [100]{0kl} in olivine. The coarse granular or tabular textures and the low density of intracrystalline deformation features indicate that deformation was followed by annealing under static conditions. The xenoliths also show microstructural evidence of multiple episodes of reactive melt percolation. Neither annealing nor melt percolation erased the olivine CPO, which has [010]-fiber, [100]-fiber and orthorhombic patterns in Pali Aike xenoliths and essentially [010]-fiber and orthorhombic patterns in Gobernador Gregores xenoliths. Seismic properties calculated based on the CPO and modal compositions are, however, rather homogeneous, with fast S-wave polarization and P-wave propagation parallel to the [100] olivine axis. The variation in the olivine CPO solely changes the minimum S-wave birefringence direction, which is normal to the foliation for axial-[010] olivine CPO. Average samples for the two localities, obtained by adding up the individual samples CPO data in a common reference frame, show, however, a 'normal' upper mantle anisotropy with a maximum S-wave birrenfringence of ca. 5% at high angle to the both the maximum [010] and [100] axes concentrations, that is in the foliation, but normal to the lineation, and a minimum birefringence at low angle to the [100] maximum, that is parallel to the lineation.