Inversion Of Phase Velocities Research Articles

Crust and upper mantle shear velocity structure beneath the Tibetan plateau and surrounding regions from interevent surface wave phase velocity inversion

Average a priori shear velocity models are constructed for the Tien Shan, Tarim basin, Pamir‐Hindu Kush, Himalaya and NE India. These models are shown to account for most of the lateral velocity heterogeneity at wavelengths >1000 km. Interevent fundamental mode Rayleigh and Love wave phase velocities were measured in the period range 32–200 s and were inverted for path‐averaged shear velocity structures. These, in turn, were regionalized to estimate average, isotropic structures beneath the six regions listed above. Low upper mantle velocities are observed beneath the western and eastern Tien Shan. The Tarim basin structure is poorly constrained but exhibits very low upper crustal velocities (probably due to deep sedimentary accumulation), and either very high upper mantle velocities exist (>4.8 km/s) in a layer 70 km thick or the lithosphere is very thick (∼180 km). Low upper mantle velocities are observed beneath the Chang Thang region, the central, and the northeast plateau but not beneath the southern or southeastern plateau. The crustal velocity gradient with depth is zero in the east central plateau consistent with lower crustal basaltic intrusions there but is positive to the west and southeast of this zone. Upper mantle structures show that the Indian lithosphere could have subducted beneath the entire plateau only if either 1 mantle in the depth range 115–185 km has been altered (or removed) to reduce its average velocity or 2 the Indian lithosphere is only ∼85 km thick.

Shear-wave velocity structure in the northern Basin and Range province from the combined analysis of receiver functions and surface waves

AbstractA new method based on the joint inversion of receiver functions and surface-wave phase velocities results in well-determined shear-velocity structures that are consistent with the compressional-wave structure, gravity, heat flow, and elevation data in the northern Basin and Range. This new inversion method takes advantage of average-velocity information present in the surface-wave method and differential velocity information contained in the receiver function method, thus minimizing the nonuniqueness problem that results from the velocity-depth trade-off.An unusually thick (38 km) and relatively faster crust and upper mantle are found in central and eastern Nevada compared to the thin (28 to 34 km) and slower crust and upper mantle of the western Basin and Range. We interpret the regions of thicker and faster crust and upper mantle as zones that have undergone less Cenozoic extension relative to the surrounding regions to the west and north. The thick crust and consequently greater depth to the dense mantle material is consistent with the gravity low pattern in central and eastern Nevada. Simple gravity modeling shows both local and regional isostatic compensation occur within 40 km of the surface, indicating a near-classical Airy type of compensation in the province.We analyze in detail the shear-wave (S-wave) velocity model derived from the receiver functions at station BMN and compressional-wave (P-wave) velocity models derived from the 1986 PASSCAL experiment in northwestern Nevada. The most interesting feature of these models is the presence of negative-velocity gradients in the S-wave model with no corresponding velocity decrease in the P-wave models between depths of 10 and 24 km. This combined velocity model may be explained by high pore fluid pressures at these depths. This model favors a layered fluid porosity model proposed in the literature to explain extensive middle- to lower-crust continental seismic reflections and high electrical conductivity. An upper-mantle, gradational low-velocity zone is present between 32 and 38 km in the S-wave model. This upper-mantle, shear-wave, low-velocity zone is consistent with partial melt, which may be the source material for magmatic underplating in this region.

A proper methodology aimed at surface wave tomography

When applying a methodology for obtaining the 3D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. In order to avoid the application of consecutive inversions and to overcome these drawbacks, we propose alternative mapping methods, for example spatial prediction methods, or else the use of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS). Among the first ones, we try inverse weighted distance interpolation. The POCS algorithm we have used discretises a second order differential equation for the velocity field with boundary conditions. All these imaging techniques aimed at volumetric modelling and the visualisation of data are discussed, and finally we show some results based on ray path velocities obtained previously by inversion of phase and group velocities of Rayleigh waves propagating across the Iberian peninsula.

大阪平野東部における地下構造探査

A survey of the geological subsurface structure was conducted in the east of the Osaka basin in order to predict seismic motions. The reflection survey revealed a detailed P-velocity structure down to the basement rock embedded at a depth of 1.5km to 1.7km. The features appearing commonly in reflection profiles of the Osaka basin are comfirmed in the reflection profiles as well: the sediments are divided into a shallow layer composed of alternate stacks of marine and non-marine deposits and a deep layer composed of only non-marine deposits. The array analyses of microtremors also revealed S-velocity structures down to the basement rock, using the inversion of microtremor phase velocities. Furthermore, a two-dimensional east-west subsurface structure model of the Osaka basin is proposed, combining geological information obtained by present and past surveys.

遺伝的アルゴリズムによる位相速度の逆解析

The applicability of genetic algorithms in an inversion of surface-wave phase velocities to infer an S-wave velocity profile was examined. S-wave velocities and thicknesses are coded to binary strings, and an individual model is generated by connecting all strings for a subsurface structure model. The fitness is defined by squared summation of differences between observed and calculated phase velocities. In addition to three basic genetic processes of selection, crossover, and mutation, the algorithm was improved by the introduction of elite selection rule and dynamic mutation in which the mutation probability varied according to the variety of individuals in a generation. We applied the method to the inversions of synthetic phase velocities and phase velocities from an actual array observation of long-period microtremors. These results indicate that the GA is highly applicable in phase velocity inversion.

Ground roll: A potential tool for constraining shallow shear‐wave structure

The objective of this study is to demonstrate that a laterally varying shallow S‐wave structure, derived from the dispersion of the ground roll, can explain observed lateral variations in the direct S‐wave arrival. The data set consists of multichannel seismic refraction data from a USGS-GSC survey in the state of Maine and the province of Quebec. These data exhibit significant lateral changes in the moveout of the ground‐roll as well as the S‐wave first arrivals. A sequence of surface‐wave processing steps are used to obtain a final laterally varying S‐wave velocity model. These steps include visual examination of the data, stacking, waveform inversion of selected traces, phase velocity adjustment by crosscorrelation, and phase velocity inversion. These models are used to predict the S‐wave first arrivals by using two‐dimensional (2D) ray tracing techniques. Observed and calculated S‐wave arrivals match well over 30 km long data paths, where lateral variations in the S‐wave velocity in the upper 1–2 km are as much as ±8 percent. The modeled correlation between the lateral variations in the ground‐roll and S‐wave arrival demonstrates that a laterally varying structure can be constrained by using surface‐wave data. The application of this technique to data from shorter spreads and shallower depths is discussed.

On the structure of the crust and upper mantle beneath the Afro-Arabian region from surface wave dispersion

The deep structure beneath the Afro-Arabian region was investigated using Rayleigh and Love waves in the period range 20–250 s. Models of crustal and upper mantle structure were inferred by simultaneous inversion of both phase and group velocities. Our choice of model parametrization allowed for a transverse isotropic medium and a variable depth of the Moho. The crustal thicknesses were found to vary from 43 to 45 km on the African plate. The Moho is deeper in the Arabian plate (45–47 km), but in the vicinity of the Red Sea the crust becomes much thinner (30 km). The upper mantle under Arabia is more similar to that of an African mobile zone than to that of a shield. A low velocity zone (LVZ) with an S-wave velocity of 4.14–4.2 km/s was found in the depth range 120–140 km. However, this LVZ is less pronounced than that found in the vicinity of the Red Sea (S-wave velocity 4.08 km/s). In agreement with previous studies, the anisotropy (V SH − V SV) V SV) has been verified for the Afro-Arabian region. We interpret the anisotropies uisng the hypothesis of lattice-preferred orientation of the olivine crystals in the upper mantle. The inference is that a vertical flow exists up to near the surface in the vicinity of the Red Sea rift ( V sv is 8–9% faster than V SH ). Under the African and Arabian sides the flow is essentially vertical below depths of 200 ± 40 km and becomes essentially horizontal above with a V SH from 6% to 14% faster than V SV .

Relationship between phase velocities and polarization in transversely isotropic media

Most techniques used to estimate anisotropy from multiple‐source offset VSP data assume angles measured from particle motion as an incidence angle. However, the difference between P‐wave polarization and the propagation direction for an anisotropic medium can be higher than 8 degrees. This difference provides a nonnegligible error in the estimation of anisotropy parameters from phase velocities. An exact model, proposed to describe P‐ and SV‐phase velocity variations for a transversely isotropic medium (TIM), takes into account the polarization angles. This model is a function of two anisotropy parameters (η and τ), of the vertical P‐ and SV‐wave phase velocities and of the polarization angle γ. However, η and τ can be used to express the polarization angle equation in a much simpler way. To quantify the error in estimated anisotropy parameters due to the assumption that the polarization angle is equal to the incidence angle, I study five TIMs. Each medium has an anisotropy that is representative of those observed in seismic surveying. The anisotropy parameters are recovered by inverting the P‐ and SV‐wave phase velocities for different incidence angles, and these incidence angles are assumed to be equal to the corresponding polarization angles. The mean error in estimated parameters is about 10 percent. This error is about the same as the one that would be obtained for velocities with uncertainties in their measurements. Unfortunately, the inversion of phase velocities measured from a real multiple‐source offset VSP to estimate anisotropy parameters needs, for calculating the misfit function, to add both errors in velocities due to hypothesis for angles and errors in velocity measurements due to uncertainties in data. In this case an exact model eliminates errors due to the assumption for the model and provides a more accurate estimation of anisotropy parameters.

Crustal and upper mantle structures of the brazilian coast

The Rayleigh wave phase and group velocities in the period range of 24–39 sec, obtained from two earthquakes which occurred in northeastern brazil and which were recorded by the Brazilian seismological station RDJ (Rio de Janeiro), have been used to study crustal and upper mantle structures of the Brazilian coastal region. Three crustal and upper mantle models have been tried out to explain crustal and upper mantle structures of the region. The upper crust has not been resolved, due basically to the narrow period range of the phase and group velocities data. The phase velocity inversions have exhibited good resolutions for both lower crust and upper mantle, with shear wave velocities characteristic of these regions. The group velocity data inversions for these models have showed good results only for the lower crust. The shear wave velocities of the lower crust (3.86 and 3.89 km/sec), obtained with phase velocity inversions, are similar to that (β=3.89 km/sec) found byHwang (1985) to the eastern South American region, while group velocity inversions have presented shear velocity (β=3.75 km/sec) similar to that (β=3.78 km/sec) found byLazcano (1972) to the Brazilian shield. It was not possible to define sharply the crust-mantle transition, but an analysis of the phase and group velocity inversions results has indicated that the total thickness of the crust should be between 30 and 39 km. The crustal and upper mantle model, obtained with phase velocity inversion, can be used as a preliminary model for the Brazilian coast.

Processing and Inversion of Long-Period Surface-Wave Data Collected in the Iberian Peninsula

SUMMARY Several filtering techniques have been used to remove the effects of multipathing and modal contamination, and to isolate the fundamental mode from Rayleigh wavetrains. Group velocity data are obtained by means of the multiple-filter technique. A time-variable filter has allowed the influence of noise as well as the interference produced by higher modes to be removed. Multiple filtering is then used again to compute group velocities at each station. the interstation group velocity for the fundamental mode Rayleigh wave is estimated according to the velocities at two stations. Frequency-domain Wiener deconvolution is used to compute the phase velocity between two stations. the well-known three-station method is applied to correct the distances travelled by the waves across the array and therefore to determine interstation phase and group velocities in a more accurate manner. On the other hand, lateral refraction at the Atlantic continental edge of the Peninsula is also studied. Phase velocities are corrected for the anelastic effect. Inversion of the interstation Rayleigh wave phase velocities is then made in accordance with generalized inversion theory to obtain theoretical 2-D layered earth models. In this paper, these methods are applied to Rayleigh waves generated by teleseismic events propagating across the Iberian Peninsula and recorded at WWSSN stations. As a consequence, new and principal features for the Iberian lithosphere-asthenosphere system are obtained. A very interesting feature of the the Iberian lithosphere was found-a low-velocity layer directly under the Moho, between 39 and 64 km depth, with shear velocities ranging from 4.12 to 4.37 km s-1. the Iberian asthenosphere, which lies between 100 and 180km depth, is not an homogeneous layer and shows a negative velocity gradient from top to bottom together with a sudden increase in shear velocity beneath the low-velocity zone.

Inversion of Apparent Attenuation and Phase Velocity to Determine Scattering Parameters

Summary We invert apparent attenuation in order to determine the scattering power spectrum. Examples are given illustrating this general inversion procedure including Wu's (1982) single-scattering theory for acoustic waves, and Lerche & Petroy's (1987) mean-field scattering model of both compressive and shear-waves by fluid-filled fractures. Frequency dependent phase velocity and attenuation factors for both compressive and shear-waves provide improvements in the inverse methods for separating intrinsic and apparent attenuation factors. In the cases where only total attenuation factors (phase velocities) are available, phase velocities (attenuation factors) can be determined by using causality considerations. For a small degree of attenuation per unit wavelength travelled approximate solutions provide relatively simple expressions connecting phase velocity and attenuation. If both phase velocity and apparent attenuation factors are measured for compressive and/or shear-waves, then the Kramers-Kronig causality relations provide consistency requirements which must be met. the non-linear nature of these causal requirements is used to explore an inverse method for separating intrinsic and apparent attenuation factors. the non-linear connections of (1) total attenuation to wave phase speeds, and (2) apparent attenuation to intrinsic attenuation, can be used to determine intrinsic properties of the propagation characteristic of the medium.

Estimation of scalar moments from explosion-generated surface waves

AbstractRayleigh waves from underground nuclear explosions are used to estimate scalar moments for 40 Nevada Test Site (NTS) explosions and 18 explosions at the Soviet East Kazakh test site. The Rayleigh wave spectrum is written as a product of functions that depend on the elastic structure of the travel path, the elastic structure of the source region, and the Q structure of the path. We use our results to examine the world-wide variability of each factor and the resulting variability of surface wave amplitudes. The path elastic structure and Q structure are found by inversion of Rayleigh wave phase and group velocities and spectral amplitudes. The Green's function derived from this structure is used to estimate the moments of explosions observed along the same path.This procedure produces more consistent amplitude estimates than conventional magnitude measurements. Network scatter in log moment is typically 0.1. In contrast with time domain amplitudes, the elastic structure of the travel path causes little variability in spectral amplitudes. When the mantle Q is constrained to a value of approximately 100 at depths greater than 120 km, the inversion for Q and moment produces moments that remain constant with distance. Based on the best models available, surface waves from NTS explosions should be larger than surface waves from East Kazakh explosions with the same moment. Estimated scalar moments for the largest East Kazakh explosions since 1976 are smaller than the estimated moments for the largest NTS explosions for the same time period. This contrasts dramatically with mb values for the same events which show the opposite behavior.

Shear velocity logging in slow formations using the Stoneley wave

We apply an iterative, linearized inversion method to Stoneley waves recorded on acoustic logs in a borehole. Our objective is to assess inversion of Stoneley wave phase and group velocity as a practical technique for shear velocity logging in slow formations. Indirect techniques for shear logging are of particular importance in this case because there is no shear head wave arrival. Acoustic logs from a long‐spaced sonic tool provided high‐quality, low‐noise data in the 1 to 10 kHz band for this experiment. A shear velocity profile estimated by inversion of a 60 ft (18 ⋅ 3 m) section of full‐wave acoustic data correlates well with the P‐wave log for the section. The inferred shear velocity ranges from 60 to 90 percent of the sound velocity of the fluid. Formal error estimates on the shear velocity are everywhere less than 5 percent. Moreover, application of the same inversion method to synthetic waveforms corroborates these error estimates. Finally, a synthetic acoustic waveform computed from inversion results is an excellent match to the observed waveform. On the basis of these results, we conclude that Stoneley‐wave inversion constitutes a practical, indirect, shear‐logging technique for slow formations. Success of the shear‐logging method depends upon availability of high‐quality, low‐noise waveform data in the 1 to 4 kHz band. Given good prior estimates of compressional velocity and density of the borehole fluid, only rough estimates of borehole radius and formation density and compressional velocity are required. The existing inversion procedure also yields estimates of formation Q inferred from spectral amplitudes of Stoneley waves. This extension of the method is promising, since amplitudes of Stoneley waves in a slow formation are highly sensitive to formation Q. Attenuation caused by formation Q dominates over attenuation caused by fluid viscosity if the viscosity is less than about [Formula: see text]. However, Stoneley‐wave amplitudes are also sensitive to gradients in shear velocity in the direction of propagation. In some cases, correction for the effects of shear‐velocity gradients is required to obtain the formation Q from Stoneley‐wave attenuation.

Shear‐velocity structure from regionalized surface‐wave dispersion in the basin and range

Lateral variations of shear velocity structure in the western United States are studied using observations of Rayleigh‐ and Love‐wave phase velocity dispersion. We measured Rayleigh‐wave dispersion in the 6‐60 sec period range on over 80 paths using both single‐and two‐station methods. Love‐wave dispersion was also measured on about 50 paths. A pure‐path regionalization method employing a block‐province grid is used to determine lateral variations of dispersion in the Basin and Range and adjacent geologic regions. Structural inversions of the regionalized Rayleigh‐wave dispersion curves indicate significant lateral variations in the crust and upper mantle structure of the Basin and Range and transition areas. A pronounced low‐velocity zone in the upper mantle is found under the Eureka heat flow province in the central Basin and Range. The lithospheric thickness in this province is 45 km in contrast to the Great Basin model of Priestley and Brune (1978; ∼65 km). Regionalization of Love‐wave data, together with the Rayleigh‐wave results, suggest the existence of polarization anisotropy in many areas of the Basin and Range. If verified, anisotropy must be accounted for in phase velocity inversions for the structure of the Basin and Range.

The utility of regional Chinese seismograms for source and path studies in central Asia

Broadband seismograms from the National Seismic Network of the People's Republic of China (PRC) have recently become available through a data exchange programme between NOAA and the State Seismological Bureau of the PRC. In this study, regional surface waves recorded at the Urumchi station located about 700 km north of the Tibetan Plateau in the Sinkiang Province are used to study East Kazakh explosions and wave propagation in central Asia. The data consist of broadband (flat to displacement between 0.1 and 10 Hz), photographic records from an SK Kirnos galvanometric system. Simultaneous inversion of Rayleigh wave phase and group velocities for the path from East Kazakh through the Dzhungarian Basin yields a crustal model dominated by the presence of very low velocities and a strong positive velocity gradient above 15 km depth. Velocities below 15 km depth are not significantly different from other continental structures underlain by Palaeozoic or Precambrian basement. Seismic moments were estimated for seven East Kazakh explosions using models of explosion sources with associated tectonic strain release. The largest explosion studied occurred on 1980 September 14 and had an mb of 6.2 and a seismic moment of 2.7 × 1023 dyn cm. The observed amplitude spectra of Rayleigh waves are richer in high frequencies than spectra calculated from our models. This could be caused by a path effect involving seismic wave focusing by the Dzhungarian Basin, although source medium effects cannot be ruled out.

Inversion of phase velocity of long-period microtremors to the S-wave-velocity structure down to the basement in urbanized areas.

Engineering seismology now requires a convenient and easy survey method for S-wave-velocity structures which enables exploration down to the basement even in urbanized areas. We have attempted an application of long-period (0.5Hz to 3.0Hz) microtremors to answer this demand. The method consists of three steps: (1) microtremors are observed using an array of seismometers; (2) their phase velocities are determined by the frequency-wavenumber-spectral analysis of array data; and (3) the S-wave-velocity structure is determined from the obtained phase velocities by the generalized inversion method. As an exploration method, this procedure has several advantages: (1) microtremors can be observed at any time and location; (2) observation is much easier than with other exploration methods; (3) it causes no environmental problems; and (4) geological conditions down to a depth of more than 100m can be inverted, as far as microtremors of required frequency range are observed. The method was applied at two sites located in and near urban areas, and the whole S-velocity structure above the basement was determined. This method proves to be a useful and practical tool for determining S-wave-velocity structures especially in urbanized areas.

Shear velocity structure in the Eastern United States from the inversion of surface-wave group and phase velocities

Abstract : Single-station group velocities at periods between 4 and 70 seconds and single-station phase velocities at periods between 10 and 50 seconds are obtained for a broad region of the eastern United States for both Rayleigh and Love waves. These data were obtained by the single-station method using earthquakes with known fault-plane solutions in the central United States. The group velocity data are combined with earlier acquired attenuation data to yield Q values for Rayleigh and Love waves in the eastern United States. Inversions of the dispersion curves for shear-velocity models of the crust and upper mantle indicate that all of the data can be explained satisfactorily by a single model which is isotropic in its elastic properties. This model includes a surface layer of low-velocity sediments, and is characterized by upper crustal shear- wave velocities which increase from 3.4 to 3.7 km/sec with increasing depth, by lower crustal shear-wave velocities between 4.0 and 3.8 km/sec, and by an upper- most mantle shear-wave velocity of about 4.8 km/sec. The fundamental-mode data of this study do not require a low-velocity zone in either the crust or upper mantle. Higher-mode velocities and wave forms, although having potentially greater resolving power than the fundamental-mode data, were too inconsistent to contribute to the elucidation of detailed features of the crust-upper mantle model.

Simultaneous inversion of surface-wave phase velocity and attenuation: Rayleigh and Love waves over continental and oceanic paths

A formalism for the simultaneous inversion of surface-wave phase velocity and attenuation, previously developed for Love waves, is extended in this paper to Rayleigh waves. The simultaneous inversion technique permits the specification of the intrinsic dispersion-attenuation relation that arises from linearity and causality, and takes full account of the dependence of surface-wave phase velocity and Q −1 on the real and imaginary parts of an anelastic earth structure. The formalism, including resolution analysis and extremal inversion, is applied to combined Love- and Rayleigh-wave data sets for a tectonically active and a stable continental path and to Rayleigh-wave data for a stable oceanic path. The depth to the low Q zone is 60 ± 20 km for the central Pacific, 80 ± 20 km for western North America, and 130 ± 30 km for east-central North America. Q −1 within the low- Q , low-velocity zone, however, is greater beneath western North America than beneath the central Pacific; the low- Q zone beneath east-central North America need not be a low-velocity zone at frequencies above 1 Hz. The surface-wave data cannot distinguish among several possible intrinsic dispersion-attenuation relations for the upper mantle.

The significance of isotropic inversion of anisotropic surface-wave dispersion

Summary. The limitations of isotropic modelling in the inversion of anisotropic surface-wave phase velocities are examined. Inversion of synthetic dispersion data for some model ocean-basin structures is used to demonstrate that isotropic inversions can give inaccurate and misleading estimates of upper-mantle properties when anisotropy is present.

Simultaneous inversion of surface wave phase velocity and attenuation: Love waves in western North America

A formalism is developed for simultaneous inversion of surface wave phase velocity and attenuation to determine shear wave velocity and Q−1 in the earth. A simultaneous inversion takes full account of the dependence of surface wave velocity and attenuation on both the elastic and the dissipative part of an earth structure and permits inclusion of the physical relationship between anelasticity and intrinsic dispersion that arises from linearity. The procedure is mathematically more complete than the approach of correcting phase velocity data for the intrinsic dispersion due to anelasticity and inverting the corrected velocity data alone, and it gives different results. The proposed formalism, including resolution analysis, weighted least squares inversion, and extremal inversion, is applied to Love waves in western North America. Various intrinsic dispersion‐attenuation relations are tested, including Q independent of frequency, Q varying as a power of frequency, and Q specified by a sum of relaxation mechanisms. The results of the inversions confirm the coincidence of the low‐velocity and low Q zones beneath western North America for frequencies in the surface wave band. Compared with previous inversion of Q−1 data alone, the simultaneous inversion results in improved depth resolution of Qs−1 and the elimination of an apparent incompatibility of low‐attenuation data at 20‐ to 25‐s periods. The Love wave data do not discriminate among the various dispersion‐attenuation relations, though a constant Q leads to the removal of the requirement for a low‐velocity zone at frequencies above 1 Hz. The predicted intrinsic dispersion within the low‐velocity zone varies from 1% to 10% between 0.01 and 1 Hz for the various models; broadband measurements of body wave dispersion offer the greatest promise for choosing among the models.