Seismic Wave Anisotropy Research Articles

A matrix-fracture-fluid decoupled PP reflection coefficient approximation for seismic inversion in tilted transversely isotropic media

Fracture-induced azimuthal anisotropy of seismic waves has useful applications in the characterization of hydrocarbon reservoirs as well as the overburden. Existing theories face problems estimating the fracture-weakness parameters, identifying the saturating fluid, and constraining the depth model building. To overcome these problems, we have adopted an azimuthal amplitude variation with angle/offset inversion for the estimation of these parameters and identification of the fluid. First, we define more intuitive fracture and fluid indicators based on rock physics, identifying the fluid by decoupling the fracture weakness parameters. Then, we derive a “rock matrix-fracture-fluid” decoupled PP-wave reflection coefficient approximation of a weakly tilted transversely isotropic medium by using a perturbation matrix and scattering theory. Compared with the conventional fracture weakness-based approximation, our method incorporates the fracture density and the fluid indicator. The inversion test finds that our approximation is effective.

A physical model study of shale seismic responses and anisotropic inversion

The seismic responses of the shale properties are critical for shale gas reservoir evaluation and production. It has been widely reported that the clay minerals have substantial influences on the seismic wave anisotropy and brittleness. Hence, knowing the seismic responses of the clay-rich shales and estimation of shale elastic properties are significant for the shale gas industry. A physical model containing two groups of shale blocks as the target formations is constructed in laboratory. The group S contains six shale blocks with different clay contents, and the group N contains six shale blocks with different porosity. The acquired 2D seismic data is used to analyze the seismic responses of two corresponding seismic lines. An anisotropic three-term inversion method is applied to one of the seismic inline to estimate the elastic properties the target shale blocks. The inversed attributes can be used to reveal the effects of shale clay contents. This study shows the substantial significance of using a physical model to observe the seismic responses of shale properties. The inversion results indicate that the anisotropic three-term inversion method could provide accurate results of elastic properties as well as the P- wave anisotropy parameter for shale formations.

Joint inversion of logging-while-drilling multipole acoustic data to determine formation shear-wave transverse isotropy

Seismic-wave anisotropy has long been an important topic in the exploration and development of unconventional reservoirs, especially in shales, which are commonly characterized as transversely isotropic ([TI] or vertical TI [VTI]) media. At present, the shear-wave (S-wave) TI properties have mainly been determined from monopole Stoneley- or dipole flexural-wave measurements in wireline acoustic logging, but the feasibility of those obtained from logging-while-drilling (LWD) acoustic data needs to be established. We have developed a joint inversion method for simultaneously determining formation S-wave transverse isotropy and vertical velocity from LWD multipole acoustic data. Our theoretical analysis shows that the presence of anisotropy strongly influences LWD Stoneley- and quadrupole-wave dispersion characteristics. Although the monopole Stoneley and quadrupole waves are sensitive to the formation S-wave TI parameters, they suffer from the typical nonuniqueness problem when using the individual-wave data to invert parameters alone. Thus, the respective dispersion data can be jointly used to estimate the formation S-wave TI properties. By the joint inversion, the nonuniqueness problem in the parameter inversion can also be effectively alleviated. The feasibility of the method has been verified by the processing results of theoretical synthetic data and field LWD acoustic-wave data. Therefore, the result offers an effective method for evaluating VTI formation anisotropy from acoustic LWD data.

Azimuth-, angle- and frequency-dependent seismic velocities of cracked rocks due to squirt flow

Abstract. Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing noninvasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries, appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid–solid deformation at the pore scale based on coupled Lamé–Navier and Navier–Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. Furthermore, the overall anisotropy of a medium mainly increases due to squirt flow, but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface.

On the anisotropy of seismic waves in the Carpathian region

The anisotropy of seismic waves in the continental regions still belongs to the category of controversial issues, since its estimates in different areas show a different sign of the anisotropy coefficient. In contrast to studies of oceanic regions, where SH velocities always prevail over SV velocities, in the continental regions the relations between the velocities are very different. The explanation for this, first of all, is the difference in structure. The structure of the crust and upper mantle under the oceans is much more homogeneous in comparison with the structure of the continental regions. There are several approaches to the estimation of anisotropy. The most traditional method is to use the maximum amount of data separately for Love and Rayleigh waves to study the lateral distributions of SH- and SV-wave velocity, despite the fact that the density of the coverage by paths, and, consequently, the regions of best resolution can be of different shapes and sizes. It was decided to use this method as the first approximation in creating an anisotropic portrait of the Carpathian region. The Carpathian region was chosen as the object of study, since it contains interesting contrasting features: (1) the Pannonian Basin, which is characterized by a thin crust, a thinned lithosphere, and anomalously high values of the heat flux; (2) the Tornquist-Teisseyre zone, which is parallel to the strike of the Eastern Carpathians, and represents the contact zone of the Precambrian lithosphere of the EEP and the relatively young lithosphere of Western Europe. (3) The third feature is the Vrancea zone, one of the most active seismic zones in Europe. It is located in the junction of young tectonic structures: the Southern and Eastern Carpathians, the Transylvanian Depression and the Pre-Carpathian Depression. The results of the study confirm that the Tornquist-Teisseyre Zone divides the structures of the ancient East European Platform and orogenic zones of Western Europe: the upper mantle throughout EEP is characterized by high velocities, whereas velocities throughout WE are markedly lower. Low velocity anomalies prevail under Pannonian Basin which is characterized by anomalously high heat flow values. The distribution of the anisotropy coefficient demonstrates an extended layer of low values of the anisotropy coefficient at depths of 150-200 km. Above this layer, velocity distributions reveal the block structure of the lithosphere. The earthquake sources in the Vrancea zone fall into the transition zone from the highvelocity mantle under the EEP to the low-velocity mantle under the WE. Earthquakes do not occur below the revealed asthenospheric layer.

Fracture connectivity can reduce the velocity anisotropy of seismic waves

Abstract The degree of connectivity of fracture networks is a key parameter that controls the hydraulic properties of fractured rock formations. The current understanding is that this parameter does not alter the effective elastic properties of the probed medium and, hence, cannot be inferred from seismic data. However, this reasoning is based on static elasticity, which neglects dynamic effects related to wave-induced fluid pressure diffusion (FPD). Using a numerical upscaling procedure based on the theory of quasi-static poroelasticity, we provide the first evidence to suggest that fracture connectivity can reduce significantly velocity anisotropy in the seismic frequency band. Analyses of fluid pressure fields in response to the propagation of seismic waves demonstrate that this reduction of velocity anisotropy is not due to changes of the geometrical characteristics of the probed fracture networks, but rather related to variations of the stiffening effect of the fracture fluid in response to FPD. These results suggest that accounting for FPD effects may not only allow for improving estimations of geometrical and mechanical properties of fracture networks, but may also provide information with regard to the effective hydraulic properties.

Пружна симетрія і параметри азимутальної анізотропії сейсмічних хвиль осадової товщі за даними методу вертикального сейсмічного профілювання

Пружна симетрія і параметри азимутальної анізотропії сейсмічних хвиль осадової товщі за даними методу вертикального сейсмічного профілювання

Processing microseismic monitoring data, considering seismic anisotropy of rocks

Using the model information and in situ data on hydrofracturing in an oil and gas reservoir of the Bakken Formation (USA), potential of locating hypocenters of microseismic events concurrently with determining parameters of velocity anisotropy of seismic waves in rock mass is analyzed. It is shown that inclusion of anisotropy in the analysis improves accuracy of spatial location of microseismic event hypocenters and increases validity of estimation of the fracturing direction.

Imaging Archaean-age whole mineral systems

Structural fabrics that cause seismic wave anisotropy within the lithospheric mantle of the Slave craton of northwest Canada are interpreted as fluid conduits that form a macroscopic-scale stockworks of metasomatised peridotite dykes within depleted harzburgitic mantle. These metasomatised peridotite conduits probably are composed of rocks such as pyroxenite or wehrlite and must occupy 10% of the mantle in order to explain this distinct anisotropy where it is present. Reduced mantle shear-wave speeds associated with these stockworks may prove diagnostic of their presence deep in the sub-continental lithospheric mantle. The former (and present?) fluid conduits have been hypothesized as source regions for diamonds and kimberlite magmas, and may also be metal-enriched regions. In order to form a whole mineral system, such stockworks of metasomatised mantle conduits must communicate with crustal conduits leading to near-surface mineral deposits. Seismic evidence for these conduits at all levels has been observed beneath a few major mining camps.

Stability field of the hcp‐structure for Fe, Fe‐Ni, and Fe‐Ni‐Si alloys up to 3 Mbar

The phase relations of Fe, Fe90Ni10 and Fe87.9Ni4.4Si7.7 were investigated up to 273(6) GPa and 4490(560) K, 250(19) GPa and 2730(110) K and 304(3) GPa and 2780(210) K, respectively, and the hexagonal close‐packed structure was found to be stable in all of these compounds under the pressure and temperature conditions studied. We did not observe other phases such as a body‐centered cubic structure. The axial ratio (c/a) of Fe87.9Ni4.4Si7.7 at 300 GPa showed an almost constant value of 1.593–1.596 against temperature. The weak temperature dependency of the axial ratio of hcp‐Fe‐Ni‐Si alloy indicates that the c‐axis is still harder than the a‐axis at high temperature condition. Therefore the alignment of hcp‐Fe–Ni–Si alloy with the c‐axis parallel to the Earth's rotation axis could account for the observation of the seismic wave anisotropy of the inner core.

Constructing a Craton

Geophysics![Figure][1] CREDIT: USGS The cores of continents, or cratons, make up the stable lithosphere. Their formation probably occurred billions of years ago, though the mechanisms responsible remain unclear. One way to seek further insight is to look below the present-day continents for clues, such as where the lithosphere ends and the asthenosphere begins. Miller and Eaton used receiver function seismic analysis to study a transect across the width of Canada, revealing the lithosphere-asthenosphere boundary in addition to tilted discontinuities in the mid-lithosphere. These discontinuities may be the scars of an ancient collision of several smaller microcontinents that ultimately fused together to form the North American craton. In a related study, Yuan and Romanowicz modeled the anisotropy of seismic waves across nearly the entire North American continent and observed not only a continuous lithosphere-asthenosphere boundary, but another shallower, laterally variable boundary within the middle of the lithosphere. Based on its thickness and a correlation with geochemical evidence, this new boundary may separate the older part of the craton from a relatively younger layer. Although the two studies present a contrasting view of the evolution of the lithosphere beneath North America, they suggest that accretion processes, and not hot mantle plumes, were primarily responsible for its formation. Geophys. Res. Lett. 10.1029/2010GL044366 (2010); Nature 466 , 1063 (2010). [1]: pending:yes

Brittle deformation and damage-induced seismic wave anisotropy in rocks

SUMMARY We study the relations between rock fracturing, non-linear deformation and damage- and stress-induced anisotropy of seismic waves by comparing theoretical predictions of a damage rheology model to results of laboratory experiments with granite samples. The employed damage model provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework of cracked media incorporating degradation and recovery of the effective elastic properties, along with gradual accumulation of irreversible deformation beyond the elastic regime. The model assumes isotropic distribution of local microcracks expressed in terms of a scalar damage variable, but the non-linear elastic response caused by the opening, closure and evolution of the internal cracks is predicted to lead to seismic wave anisotropy. We develop relations between the seismic wave anisotropy, internal rock damage and stress field, and test the viscoelastic damage rheology against sets of laboratory experiments with cylindrical granite samples. The observed data include measurements of stress and strain in three loading cycles culminating in a final macroscopic failure, together with measured wave velocities along and perpendicular to the axis of the cylinder. Using a single set of parameters, the model fits well the overall evolution of the axial and transversal stress–strain relations, as well as the anisotropic elastic wave velocities, during all cycles from the onset of fracturing in the first cycle until the macroscopic failure in the final cycle.

Subsurface structure, physical properties, fault-zone characteristics and stress state in scientific drill holes of Taiwan Chelungpu Fault Drilling Project

Continuous cores and a suit of geophysical measurements were collected in two scientific drill holes to understand physical mechanisms involved in the large displacements during the 1999 Chi-Chi earthquake. Physical properties obtained from wire-line logs including P- and S-wave sonic velocity, gamma ray, electrical resistivity, density and temperature, are primarily dependent on parameters such as lithology, depth and fault zones. The average dip of bedding, identified from both cores and FMI (or FMS) logs, is about 30° towards SE. Nevertheless, local azimuthal variations and increasing or decreasing bedding dips appear across fault zones. A prominent increase of structural dip to 60°–80° below 1856 m could be due to deformation associated with propagation of the Sanyi fault. A total of 12 fault zones identified in hole-A are located in the Plio-Pleistocene Cholan Formation, Pliocene Chinshui Shale and Miocene Kueichulin Formation. The shallowest fault zone occurs at 1111 m depth (FZ1111). It is a 1 m gouge zone including 12 cm of thick indurate black material. We interpreted this zone as the slip zone during Chi-Chi earthquake. FZ1111 is characterized by: 1) bedding-parallel thrust fault with 30-degree dip; 2) the lowest resistivity; 3) low density, V p and V s, 4) high V p/ V s ratio and Poisson's ratio; 5) low energy and velocity anisotropy, and low permeability within the homogeneous 1 m gouge zone; 6) increasing gas (CO 2 and CH 4) emissions, and 7) appearance of smectite within the primary slip zone. In situ stresses at the drill site were inferred from leak-off tests, borehole breakouts and drilling-induced tensile fractures from borehole FMS/FMI logs, and shear seismic wave anisotropy from DSI logs. The dominant fast shear-wave polarization direction is in good agreement with regional maximum horizontal stress axis, particularly within the strongly anisotropic Kueichulin Formation. A conjugate set of secondary directions are parallel to microcrack orientations. A drastic change of orientation of fast shear-wave polarization across the Sanyi thrust fault at the depth of 1712 m reflects the change of stratigraphy, physical properties and structural geometry.

An attempt to estimate isotropic and anisotropic lateral structure of the Earth by spectral inversion incorporating mixed coupling

We present a way to calculate free oscillation spectra for an aspherical earth model, which is constructed by adding isotropic and anisotropic velocity perturbations to the seismic velocity parameters of a reference earth model, and examine the effect of the velocity perturbations on the free oscillation spectrum. Lateral variations of the velocity perturbations are parametrized as an expansion in generalized spherical harmonics. We assume weak hexagonal anisotropy for the seismic wave anisotropy in the upper mantle, where the hexagonal symmetry axes are horizontally distributed. The synthetic spectra show that the velocity perturbations cause not only strong self-coupling among singlets of a multiplet but also mixed coupling between toroidal and spheroidal multiplets. Both the couplings give rise to an amplitude anomaly on the vertical component spectrum. In this study, we identify the amplitude anomaly resulting from the mixed coupling as quasi-toroidal mode. Excitation of the quasi-toroidal mode by a vertical strike-slip fault is largest on nodal lines of the Rayleigh wave, decreases with increasing azimuth angle and becomes smallest on loop lines. This azimuthal dependence of the spectral amplitude is quite similar to the Love wave radiation pattern. In addition, the amplitude spectrum of the quasi-toroidal mode is more sensitive to the anisotropic velocity perturbation than to the isotropic velocity perturbation. This means that the mode spectrum allowing for the mixed-coupling effect may provide constraints on the anisotropic lateral structure as well as the isotropic lateral structure. An inversion method, called mixed-coupling spectral inversion, is devised to retrieve the isotropic and anisotropic velocity perturbations from the free oscillation spectra incorporating the quasi-toroidal mode. We confirm that the spectral inversion method correctly recovers the isotropic and anisotropic lateral structure. Moreover introducing the mixed-coupling effect in the spectral inversion makes it possible to estimate the odd-order lateral structure, which cannot be determined by the conventional spectral inversion, which takes no account of the mixed coupling. Higher order structure is biased by the mixed coupling when the conventional spectral inversion is applied to the amplitude spectra incorporating the mixed coupling.

Iron‐Nickel alloy in the Earth's core

The phase relations of an Fe10wt%Ni alloy were investigated in a diamond anvil cell up to 86 GPa and 2382 K. Adding nickel into iron stabilizes the fcc phase to higher pressures and lower temperatures compared to pure iron, and a region of two‐phase coexistence between fcc and hcp phases is observed. Iron with up to 10 wt% nickel is likely to be in the hcp structure under inner core conditions. The axial ratio (c/a) of hcp‐Fe10wt%Ni has a weak pressure dependence, but it increases substantially with increasing temperature. The extrapolated c/a ratio at ∼5700 K and ∼86 GPa is approximately 1.64, lower than a theoretically predicted value of nearly 1.7 for hcp‐Fe at 5700 K and inner‐core pressure. A lower c/a ratio should have an effect on the longitudinal anisotropy of the hcp phase, and hence, may influence the interpretation of the seismic wave anisotropy of the inner core.

Correlation between seismic anisotropy and major geological structures in SW Iberia: A case study on continental lithosphere deformation

In this paper we postulate a correlation between the lithospheric structure and seismic anisotropy inferred from geophysical data and the major structures and tectonic history (past tectonothermal features) of the outcropping basement rocks in SW Iberia. Oblique plate convergence, orogenesis, and terrane accretion have been documented for pre‐Mesozoic times in this area. However, the deviations and areal variations observed between the azimuthal anisotropy of seismic waves and the structural trends of the accessible crust indicate that the tectonic model of orogen‐parallel lithospheric deformation does not appear to succeed in relating Hercynian surface geology and the structural geology of the subcontinental lithospheric mantle. The model of polyorogenic lithosphere deformation proposed accounts for this divergence and is supported from additional perspectives including the manifestation of thermal effects induced in the crust by lithospheric mantle shear zones, the incidence of crust‐mantle coupling and/or decoupling, and the scales of subcrustal heterogeneity.

The lattice Boltzmann phononic lattice solid

I present a Boltzmann lattice gas-like approach for modeling compressional waves in an inhomogeneous medium as a first step toward developing a method to simulate seismic waves in complex solids. The method is based on modeling particles in a discrete lattice with wavelike characteristics of partial reflection and transmission when passing between links with different properties as well as phononlike interactions (i.e., collisions), with particle speed dependent on link properties. In the macroscopic limit, this approach theoretically yields compressional waves in an inhomogeneous acoustic medium. Numerical experiments verify the method and demonstrate its convergence properties. The lattice Boltzmann phononic lattice solid could be used to study how seismic wave anisotropy and attenuation are related to microfractures, the complex geometry of rock matrices, and their couplings to pore fluids. However, additional particles related to the two transverse phonons must be incorporated to correctly simulate wave phenomena in solids.

Self‐similar distribution and properties of macroscopic fractures at depth in crystalline rock in the Cajon Pass Scientific Drill Hole

This study was conducted in order to characterize the frequency, orientation, and aperture of macroscopic fractures in the crust and their effect on physical properties over an appreciable depth interval (1829–3450 m). The following are our major findings: (1) Over the range of apparent apertures measured with confidence, the frequency of fractures with a given aperture decreases as aperture increases. With applied corrections for sampling bias, the observed distribution of fracture aperture has a power law form providing evidence of the self‐similar nature of fractures in the crystalline crust. Fractal analysis of the fracture aperture data yields a fractal dimension of 1.4 over the range of reliable aperture measurements in this study from 15 to 100 mm. (2) Fracture frequency does not systematically decrease with depth in the study interval. (3) No significant correlation was found between fracture occurrence and lithology, and both fracture spacing and aperture are uncorrelated with fracture orientation or depth. (4) The majority of fractures encountered in the well strike NNW‐SSE and dip steeply to the west. One set of steeply dipping fractures appears to be related to the NW striking San Andreas fault and appears to be related to steeply dipping, NW striking shear fractures observed in nearby outcrops that are characterized by laumontitic alteration. (5) The fractures bear no obvious relation to the current northeast direction of maximum horizontal compression but do correlate with anomalies in physical properties measurements of compressional and shear velocity, porosity, and resistivity. (6) Macroscopic fractures strike in a direction nearly orthogonal to the fast propagation direction of seismic wave anisotropy determined from vertical seismic profiling experiments in the well. These fractures appear to be unrelated to the observed seismic anisotropy. (7) Hydraulically conductive fractures and major faults indicate that fluid‐conducting fractures are a subset of the overall statistically significant population and not related to the San Andreas fault or to the orientation of SHmax in an obvious way.

Recent advances in rock physics

The need to extract more information about the subsurface from geophysical and petrophysical measurements has led to a great interest in the study of the effect of rock and fluid properties on geophysical and petrophysical measurements. Rock physics research in the last few years has been concerned with studying the effect of lithology, fluids, pore geometry, and fractures on velocity; the mechanisms of attenuation of seismic waves; the effect of anisotropy; and the electrical and dielectric properties of rocks. Understanding the interrelationships between rock properties and their expression in geophysical and petrophysical data is necessary to integrate geophysical, petrophysical, and engineering data for the enhanced exploration and characterization of petroleum reservoirs. The use of amplitude offsets, S‐wave seismic data, and full‐waveform sonic data will help in the discrimination of lithology. The effect of in situ temperatures and pressures must be taken into account, especially in fractured and unconsolidated reservoirs. Fluids have a strong effect on seismic velocities, through their compressibility, density, and chemical effects on grain and clay surfaces. S‐wave measurements should help in bright spot analysis for gas reservoirs, but theoretical considerations still show that a deep, consolidated reservoir will not have any appreciable impedance contrast due to gas. The attenuation of seismic waves has received a great deal of attention recently. The idea that Q is independent of frequency has been challenged by experimental and theoretical findings of large peaks in attenuation in the low kHz and hundreds of kHz regions. The attenuation is thought to be due to fluid‐flow mechanisms and theories suggest that there may be large attenuation due to small amounts of gas in the pore space even at seismic frequencies. Models of the effect of pores, cracks, and fractures on seismic velocity have also been studied. The thin‐crack velocity models appear to be better suited for representing fractures than pores. The anisotropy of seismic waves, especially the splitting of polarized S‐waves, may be diagnostic of sets of oriented fractures in the crust. The electrical properties of rocks are strongly dependent upon the frequency of the energy and logging is presently being done at various frequencies. The effects of frequency, fluid salinity, clays, and pore‐grain geometry on electrical properties have been studied. Models of porous media have been used extensively to study the electrical and elastic properties of rocks. There has been great interest in extracting geometrical parameters about the rock and pore space directly from microscopic observation. Other models have focused on modeling several different properties to find relationships between rock properties.

Studies of mantle structure of U.S.S.R. territory on long-range seismic profiles

Long-range seismic sounding carried out during the last few years on the territory of the U.S.S.R. has shown a basic inhomogeneity of the uppermost mantle, as well as evidence of regularities in the distribution of its seismic parameters. The following data were used: times and apparent velocities of P- and S-waves for investigation of mantle velocities, converted waves for seismic discontinuity model studies and wave attenuation for Q-factor estimation. Strong regularities were distinguished in the distribution of average seismic velocities for the uppermost mantle, in their dependence on the age and type of geostructure and on their position relative to the central part of the continent. Old platforms and the inner part of the continent are marked by velocities under the Mohorovičić discontinuity of more than 8.2–8.3 km s −1, young platforms and outer parts of the continent by 8.0–8.2 km s −1, and orogenic and rift zones by 7.8–8.0 km s −1. The difference becomes more pronounced at a depth of about 100–200 km: for the old platform mantle velocities of 8.5–8.6 km s −1 are typical; beneath the orogenic and rift areas, inversion zones with velocities less than 7.8 km s −1 are observed. The converted waves show fine inhomogeneities of the crust and uppermost mantle, the presence of many discontinuities with positive and negative changes of velocity, and anisotropy of seismic waves in some of the layers. Wave attenuation allowed the determination of the Q-factor in the mantle. It varied from one region to another but a close relation between Q and P-wave velocity is the main cause of its variation.