SHEAR-WAVE VELOCITY ESTIMATION IN POROUS ROCKS: THEORETICAL FORMULATION,PRELIMINARY VERIFICATION AND APPLICATIONS1

Shear-wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude-versus-offset analyses and multicomponent seismic interpretations. Measured shear-wave velocity logs are, however, often unavailable. We developed a general method to predict shear-wave velocity in porous rocks. If reliable compressional-wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear-wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional- and shear-wave velocities for water-saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first-order applicability of the Biot–Gassmann theory to real rocks. We verified these concepts with laboratory measurements and full waveform sonic logs. Shear-wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations.     

Paleomagnetism and tectonics of Karaginsky Island, Bering Sea

Abstract Rocks from Karaginsky accretionary prism (Karaginsky Island, Bering Sea) yield both prefolding (close to original) and postfolding magnetic vectors. The prefolding vectors suggest that the Maastrichtian–Paleocene volcanic–terrigenous sequences of Karaginsky Island formed at approximately 40°N to 50°N ( n = 45, D _G = 325, I _G = 57, K _G = 6, α_95G = 8, F _G = 15.06, D _S = 332, I _S = 63, K _S = 20, α_95S = 4.5, F _S = 0.3297, F _cr = 2.64) and were not originally part of either Eurasia ( F = 19, Δ F = 6.5) or North America ( F = 17, Δ F = 4.4). The geologic blocks rotated insignificantly counterclockwise about the horizontal plane, suggesting that the structure of Karaginsky Island arose without major strike-slip motions. Analysis of secondary magnetizations (for example, n = 28, D _G = 311, I _G = − 50, K _G = 9, α_95G = 8.7, F _G = 2.44; D _S = 293, I _S = − 41, K _S = 5, α_95S = 11, F _S = 12.04, F _cr = 2.65) reveals that the development of this framework involved at least two stages of deformation. During the second stage the sequences must have been tilted to west-northwest and northwest directions at 45–65°. This agrees with the northwest vergence of the structure of Karaginsky Island.     

Velocity anisotropy and attenuation of shale in under- and overpressured conditions

The seismic velocity and attenuation of fully saturated shales were measured for the first time under overpressured conditions, using the ultrasonic reflection technique. Shale cores from naturally overpressured horizons in the North Sea were tested in the laboratory, at confining and pore pressures relevant to in situ conditions.
A single-frequency tone-burst pulse wave was used to determine the seismic wave velocities and quality factors of the shale samples, with errors less than 0.3% and 0.1 dB/cm, respectively, at a frequency of 0.75 MHz. Sample length changes with varying confining and pore pressure were measured and the pore pressure equilibration time was monitored for each sample.
The anisotropy of the seismic attributes ( V _p, V _s, Q _p and Q _s) was determined over a range of differential pressures from 5 to 60 MPa, with respect to the predominant foliation. The ultrasonic velocity data followed a transversely isotropic pattern depending on the direction of wave propagation with respect to the laminations. The Poisson's ratio was found to rise by 5% as the shale material progressed from a normally pressured to an overpressured state. The quality factor ( Q ) characteristics were interpreted in terms of pore geometry and connectivity as well as the directional permeability of the transversely isotropic shale material. The results were converted to bulk and shear loss modulus defects, and a positive bulk loss was observed for waves propagating perpendicular to the lamination plane even above differential pressures of 20 MPa. This indicates different levels of Biot-flow and squirt-flow attenuation mechanisms acting within the shale structure, depending on the wave propagation and vibration directions.     

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.     

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.     

Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.     

Shallow Seismic Velocity Structure of the Betic Cordillera (Southern Spain) from Modelling of Rayleigh Wave Dispersion

A detailed dispersion analysis of Rayleigh waves generated by local earthquakes and occasionally by blasts that occurred in southern Spain, was undertaken to obtain the shear-wave velocity structure of the region at shallow depth. Our database includes seismograms generated by 35 seismic events that were recorded by 15 single-component short-period stations from 1990 to 1995. All these events have focal depths less than 10 km and body-wave magnitudes between 3.0 and 4.0, and they were all recorded at distances between 40 and 300 km from the epicentre. We analysed a total of 90 source-station Rayleigh-wave paths. The collected data were processed by standard digital filtering techniques to obtain Rayleigh-wave group-velocity dispersion measurements. The path-averaged group velocities vary from 1.12 to 2.25 km/s within the 1.0-6.0 s period interval. Then, using a stochastic inversion approach we obtained 1-D shear-wave velocity–depth models across the study area, which were resolved to a depth of circa 5 km. The inverted shear-wave velocities range approximately between 1.0 and 3.8 km/s with a standard deviation range of 0.05–0.16 km/s, and show significant variations from region to region. These results were combined to produce 3-D images via volumetric modelling and data visualization. We present images that show different shear velocity patterns for the Betic Cordillera. Looking at the velocity distribution at various depths and at vertical sections, we discuss of the study area in terms of subsurface structure and S-wave velocity distribution (low velocity channels, basement depth, etc.) at very shallow depths (0–5 km). Our results characterize the region sufficiently and lead to a correlation of shear-wave velocity with the different geological units features.     

Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. The symmetry of a rock with horizontal bedding that contains two or more non-orthogonal sets of vertical fractures may be approximated as monoclinic with a horizontal plane of mirror symmetry. For offsets that are small compared with the depth of the reflector, the azimuthal variation in P-wave AVO gradient for such a medium varies with azimuth as     where φ is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. φ ₂ depends on both the normal compliance B _N and the shear compliance B _T of the fractures and may differ from zero if B _N B _T varies significantly between fracture sets. If B _N B _T is the same for all fractures,     and the principal axes of the azimuthal variation in P-wave AVO for fixed offset are determined by the polarization directions of a vertically propagating shear wave. At larger offsets, terms in     and     are required to describe the azimuthal variation in AVO accurately. φ ₄ and φ ₆ also depend on B _N B _T. For gas-filled open fractures     but a lower value of B _N B _T may result from the presence of a fluid with non-zero bulk modulus.     

Predicting Soil-Water and Soil-Air Transport Properties and Their Effects on Soil-Vapor Extraction Efficiency

Accurate prediction of water and air Iran sport parameters in variably saturated soil is necessary for modeling of soil-vapor extraction (SVE) at soil sites contaminated with volatile organic chemicals (VOCs). An expression for predicting saturated water permeability (k_l,s) in undisturbed soils from the soil total porosity and the field capacity soil-water content was developed by fitting a tortuous-tube fluid flow model to measured water permeability and gas diffusivity data. The new k_l,s expression gave accurate predictions when tested against independent k_l,s data. The k_l,s expression was implemented in the Campbell relative water permeability model to yield a predictive model for water permeability in variably saturated, undisturbed soil. The water permeability model, together with recently developed predictive equations for gas permeability and gas diffusivity, was used in a two-dimensional numerical SVE model that also included non-equilibrium mass transfer of VOC from a separate phase (nonaqueous phase liquid [NAPL]) to the air phase. SVE: calculations showed that gas permeability is likely the most important factor controlling VOC migration and vapor extraction efficiency. Water permeability and gas diffusivity effects became significant at water contents near and above field capacity. The NAPL-air mass transfer coefficient also had large impacts on simulated vapor extraction efficiency. The calculations suggest that realistic SVE models need to include predictive expressions for both conveciive, diffusive. and phase-partitioning processes in natural, undisturbed soils.     

In Situ Electromigration as a Method for Removing Sulfate, Metals, and Other Contaminants from Ground Water

Electromigration is proposed as an in situ method for preconcentrating contaminants in ground water prior to pumping and treating. In earlier investigations by the senior author and co-workers, it was found that Cu in synthetic ground water migrated strongly to a Pt cathode and plated out as metallic copper. In the present study, carbon electrodes were inserted into a laboratory column of fine quartz sand that was saturated with a lower concentration of CuSO₄ solution. A fixed potential of 2.5 V was applied, causing dissolved Cu and SO₄ to accumulate strongly at the cathode and anode, respectively. Only minor plating-out of Cu took place on the carbon electrodes. In addition to the use of carbon electrodes, the present research also investigated the effects of a lower concentration of metal, accumulation of SO₄ adjacent to the anodes, adsorption of Cu on the sand, and competition by moving ground water.
At an imposed voltage of 2.5 V and in the presence of 65 mg/L of dissolved Cu and 96 mg/L of SO₄ (0.001 M CuSO₄ solution), electrolysis of water caused large changes in the pH and speciation of the aqueous components, as well as precipitation of solid Cu-hydroxides. Significant retardation of Cu occurred in the presence of ground water flowing at an average intergranular velocity of 0.2 m/day, but only minor retardation at water velocities of 1.9 and 2.9 m/day.
Sulfate tends to migrate strongly to the anodes, suggesting that in situ electromigration may offer a useful new method for preconcentrating such highly soluble ions as SO₄, NO₃, and CI that are difficult to remove by conventional pump-and-treat methods. A number of potential problems exist that should be addressed in a field test.     

3D near-surface soil response from H/V ambient-noise ratios

The applicability of the horizontal-to-vertical (H/V) ambient-noise spectral ratio for characterizing earthquake site effects caused by near-surface topography and velocity structures was evaluated at sites underlain by thick (i.e. >100 m) sediment deposits near the southern-end of the New Madrid seismic zone in the central United States. Three-component ambient-noise and velocity models derived from seismic (shear-wave) refraction/reflection surveys showed that a relatively horizontal, sharp shear-wave velocity interface in the soil column resulted in an H/V spectral ratio with a single well-defined peak. Observations at sites with more than one sharp shear-wave velocity contrast and horizontally arranged soil layers resulted in at least two well-defined H/V spectral ratio peaks. Furthermore, at sites where there were sharp shear-wave velocity contrasts in nonhorizontal, near-surface soil layers, the H/V spectra exhibited a broad-bandwidth, relatively low-amplitude signal instead of a single well-defined peak.     

The effect of mineralization on the ratio of normal to tangential compliance of fractures

The effect of a fracture on the propagation of seismic waves can be represented in terms of the normal compliance B_N and tangential compliance B_T of the fracture. If   B_N / B_T = 1  for all fractures, the effective elastic stiffness tensor of an isotropic background containing an arbitrary orientation distribution of fractures is orthotropic (i.e., has three orthogonal planes of mirror symmetry) in the long-wave limit. However, deviations from orthotropy may occur if   B_N / B_T   differs significantly from unity and this can cause the principal axes of the P -wave NMO ellipse and of the variation in the PP -reflection amplitude as a function of azimuth, to deviate from the fast and slow polarization direction of a vertically propagating S -wave. Simple models of a fracture in terms of a planar distribution of cracks suggest that   B_N / B_T ≈ 1  for dry fractures. However, naturally occurring fractures often exhibit mineralization in the form of bridges between opposing faces of the fracture. The presence of such bridges leads to significant departures of   B_N / B_T   from unity.     

IN SITU MEASUREMENTS OF SHEAR-WAVE VELOCITY IN SEDIMENTS WITH HIGHER-MODE RAYLEIGH WAVES*

A seismic survey was carried out on a tidal flat in the SW-Netherlands in order to determine shear-wave velocities in sediments by means of higher-mode Rayleigh waves. The dispersion properties of these Rayleigh waves were measured in the 2-D amplitude spectrum–or f, k-spectrum–and resulted in phase velocities for six different modes as a function of frequency (5–30 Hz). These observed phase velocities were inverted for a nine-layer model for the shear-wave velocity to a depth of 50 m.     

Laterally constrained inversion of surface wave data at Najaf city (Iraq)

A case history is reported to outline a possible strategy for the construction of a pseudo-2D model of shear-wave velocity for seismic site response studies. Experimental data have been collected using the Multichannel Analysis of Surface Wave technique (MASW) at six sites in the city of Najaf (Southern Iraq). The sites are aligned along the route of a proposed subway. The dataset has been processed to extract the dispersion curves of each site and then it has been inverted by using a Laterally Constrained Inversion (LCI) algorithm. The initial model for the local search algorithm has been obtained with a preliminary Monte Carlo Inversion (MCI). A priori information from borehole logs and lateral constraints between neighbors 1D models are used to mitigate the non-uniqueness of the solution. The result is a pseudo-2D shear-wave velocity model of the area which is in good agreement with sediment lithology and thicknesses obtained from borehole logs.     

Tomography and velocity structure of the crust and uppermost mantle in southeastern Europe obtained from surface wave analysis

A set of two hundred shear-wave velocity models of the crust and uppermost mantle in southeast Europe is determined by application of a sequence of methods for surface-waves analysis. Group velocities for about 350 paths have been obtained after analysis of more than 600 broadband waveform records. Two-dimensional surface-wave tomography is applied to the group-velocity measurements at selected periods and after regionalisation, two sets of local dispersion curves (for Rayleigh and Love waves) are constructed in the period range 8–40 s. The shear-wave velocity models are derived by applying non-linear iterative inversion of local dispersion curves for grid cells predetermined by the resolving power of data. The period range of observations limits the velocity models to depths of 70 km in accordance to the penetration of the surface waves with a maximum period of 40 s. Maps of the Moho boundary depth, velocity distribution above and below Moho boundary, as well as velocity distribution at different depths are constructed. Well-known geomorphologic units (e.g. the Pannonian basin, southeastern Carpathians, Dinarides, Hellenides, Rodophean massif, Aegean Sea, western Turkey) are delineated in the obtained models. Specific patterns in the velocity models characterise the southeast Carpathians and adjacent areas, coast of Albania, Adriatic coast of southern Italy and the southern coast of the Black Sea. The models obtained in this study for the western Black Sea basin shows the presence of layers with shear-wave velocities of 3.5 km/s–3.7 km/s in the crust and thus do not support the hypothesis of existence of oceanic structure in this region.     

Seismic Velocity and Q Structure of the Middle Eastern Crust and Upper Mantle from Surface-wave Dispersion and Attenuation

—Observed velocities and attenuation of fundamental-mode Rayleigh waves in the period range 7–82 sec were inverted for shear-wave velocity and shear-wave Q structure in the Middle East using a two-station method. Additional information on Q structure variation within each region was obtained by studying amplitude spectra of fundamental-mode and higher-mode Rayleigh waves. We obtained models for the Turkish and Iranian Plateaus (Region 1), areas surrounding and including the Black and Caspian Seas (Region 2), and the Arabian Peninsula (Region 3). The effect of continent-ocean boundaries and mixed paths in Region 2 may lead to unrealistic features in the models obtained there. At lower crustal and upper-mantle depths, shear velocities are similar in all three regions. Shear velocities vary significantly in the uppermost 10 km of the crust, being 3.21, 2.85, and 3.39 km/s for Regions 1, 2, and 3, respectively. Q models obtained from an inversion of interstation attenuation data show that crustal shear-wave Q is highest in Region 3 and lowest in Region 1. Q’s for the upper 10 km of the crust are 63, 71, and 201 for Regions 1, 2, and 3, respectively. Crustal Q’s at 30 km depth for the three regions are about 51, 71, and 134. The lower crustal Q values contrast sharply with results from stable continental regions where shear-wave Q may reach one thousand or more. These low values may indicate that fluids reside in faults, cracks, and permeable rock at lower crustal, as well as upper crustal depths due to convergence and intense deformation at all depths in the Middle Eastern crust.     

Test of rock physics models for prediction of seismic velocities in shallow unconsolidated sands: a well log data case‡

This paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz‐Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point. Using either the Hertz‐Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over‐prediction of the velocities. The P‐velocity is overpredicted by a factor of ～1.5 and the S‐velocity by a factor of ～1.8 for highly porous gas‐sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz‐Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences. The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab‐derived results.     

山东乳山震群剪切波分裂参数的时间演化特征分析

2013年10月1日山东乳山发生M_L3.8地震后, 该地区的地震活动呈现出小震群特征, 且持续至今, 其中2014—2015年先后发生了4次M_L4.1—5.0显著性地震, 造成了较大的社会影响． 本文利用山东数字地震台网中乳山台记录的地震波形资料, 测定了来自乳山震群中224次小地震的剪切波分裂参数． 研究结果表明: 快剪切波的偏振优势方向与山东半岛地区的主压应力方向基本一致; 剪切波分裂时间延迟在这4次显著性地震发生前后均产生明显的变化, 分裂时间延迟平均在震前1个月左右开始出现升高异常, 在震前约12天出现下降异常变化． 这些特征均可作为利用应力进行地震预测的前兆指标．      

SHEAR-WAVE REFLECTION PROFILING FOR NEAR-SURFACE LIGNITE EXPLORATION*

We present the results of a shear-wave reflection experiment and in situ measurements in opencast lignite exploration. Near-surface coal seams have lower shear-wave velocities (～ 200 m/s) and lower densities than sand and clay layers. Due to strong reflection coefficients, a shear-wave reflection survey provides a powerful tool in lignite prospecting. Due to shorter seismic wavelengths shear waves will yield a higher resolution of shallow subsurface structure than compressional waves. Low shear-wave velocities and strong lateral velocity variations, however, require a dense data acquisition in the field. The variation of stacking velocities can exceed ± 15% within a profile length of 300 m. The different steps in processing and interpretation of results are described with actual records. The final CMP-stack shows steep-angle fault zones with maximum dislocations of 20 m within a coal seam.     

Compressional- and shear-wave velocities as a function of confining stress in dry sandstones

A laboratory study was carried out to investigate the influence of confining stress on compressional- and shear-wave velocities for a set of rock samples from gas-producing sandstone reservoirs in the Cooper Basin, South Australia. The suite of samples consists of 22 consolidated sublitharenites with helium porosity ranging from 2.6% to 16.6%. We used a pulse-echo technique to measure compressional- and shear-wave velocities on dry samples (cylindrical 4.6 × 2 cm) at room temperature and at elevated confining stress (≤ 60 MPa). Compressional- and shear-wave velocities in samples increase non-linearly with confining stress. A regression equation of the form V = A ? Be^?DP gives a good fit to the measured velocities with improved prediction of velocities at high confining stresses compared with equations suggested by other studies. The predicted microcrack-closure stresses of the samples show values ranging from 70 MPa to 95 MPa and insignificant correlation with porosity, permeability or clay content. There is a positive correlation between change in velocity with core porosity and permeability, but this association is weak and diminishes with increasing confining stress. Experimental results show that pore geometry, grain-contact type, and distribution and location of clay particles may be more significant than total porosity and clay content in describing the stress sensitivity of sandstones at in situ reservoir effective stress. The stress dependence of Cooper Basin sandstones is very large compared with data from other studies. The implication of our study for hydrocarbon exploration is that where the in situ reservoir effective stress is much less than the microcrack-closure stress of the reservoir rocks, the variation of reservoir effective stress could cause significant changes in velocity of the reservoir rocks. The velocity changes induced by effective stress in highly stress-sensitive rocks can be detected at sonic-log and probably surface-seismic frequencies.