Inversion Of Dispersion Curves Research Articles

Small-strain stiffness and damping ratio of Pisa clay from surface wave tests

Small-strain stiffness and damping ratio are important parameters for modelling the dynamic behaviour of soils. In particular, the experimental evaluation of the damping ratio is problematic, especially for hard-to-sample soils. Surface wave tests have proven to be a reliable tool for the in-situ determination of soil stiffness at very small strains. Recently, the simultaneous determination of stiffness and damping ratio has been developed. The technique is based on the measurement and inversion of dispersion and attenuation curves of Rayleigh waves. In this paper a novel transfer function procedure is presented. The application to data collected at the Leaning Tower of Pisa testing site, where many results from previous in-situ and laboratory test are available for comparison, is reported.

Small-strain stiffness and damping ratio of Pisa clay from surface wave tests

Small-strain stiffness and damping ratio are important parameters for modelling the dynamic behaviour of soils. In particular, the experimental evaluation of the damping ratio is problematic, especially for hard-to-sample soils. Surface wave tests have proven to be a reliable tool for the in-situ determination of soil stiffness at very small strains. Recently, the simultaneous determination of stiffness and damping ratio has been developed. The technique is based on the measurement and inversion of dispersion and attenuation curves of Rayleigh waves. In this paper a novel transfer function procedure is presented. The application to data collected at the Leaning Tower of Pisa testing site, where many results from previous in-situ and laboratory test are available for comparison, is reported.

Inversion of shallow-seismic wavefields: II. Inferring subsurface properties from wavefield transforms

The problem of inferring subsurface properties from shallow-seismic data is solved by a two-stage scheme that fits the full wavefield by its synthetic counterpart. In a first stage (described in a companion paper) I derive Fourier—Bessel expansion coefficients for the recorded data through a wavefield transformation. The present paper describes the joint inversion of these coefficients together with P-wave arrival times to infer subsurface properties. In this way we exploit the full signal-content including the dispersion of higher-modes, leaky-modes, their true amplitudes, and, at least partly, body waves. Owing to the multi-mode character of shallow-seismic field-data conventional techniques of dispersion analysis are not applicable. Since an initial model appropriate for inversion of full seismograms is rarely available in shallow seismics, the direct inversion of waveforms is not feasible. The wavefield transformation removes a remarkable amount of non-linearity from the data. In consequence the proposed method is robust even in the absence of a priori information. In distinction to the inversion of dispersion curves, it does not require the identification of normal-modes prior to inversion. The method performs well when applied to the multi-mode wavefields present in most shallow-seismic data sets. Compared to waveform fitting, it can be more efficient by about a factor of ten, because we need not evaluate the Bessel-expansion and therefore need less calculations of the forward problem. Subsurface properties are derived for the two sets of field-data that were already presented in the first paper. One of them includes a pronounced low-velocity channel. For both we observe a remarkably good resolution of S-velocity down to the bedrock, which is found in 6 and 16 m depth, respectively. In both cases it would not be possible to infer the depth of bedrock from P-wave data alone. Synthetic seismograms calculated from the final model match the recorded waveforms surprisingly well, although no waveform fitting was applied. A subsequent waveform inversion becomes feasible with initial models taken from the results of this method. Finally it is shown by example, that conventional techniques of dispersion-curve fitting are likely to give misleading results when applied to our field-data.

Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure

SUMMARY Simulated annealing was used to invert fundamental and higher-mode Rayleigh wave dispersion curves simultaneously for an S-wave velocity profile. The inversion was applied to near-surface seismic data (with a maximum depth of investigation of around 10 m) obtained over a thick lacustrine clay sequence. The geology was described either in terms of discrete layers or by a superposition of Chebyshev polynomials in the inversion and the contrasting results compared. Simulated annealing allows for considerable flexibility in model definition and parametrization and seeks a global rather than a local minimum in a misfit function. It has the added advantage in that it can be used to determine uncertainties in inversion parameters, thereby highlighting features in an inverted profile that should be interpreted with caution. Results show that simulated annealing works well for the inversion of multimodal near-surface Rayleigh wave dispersion curves relative to the same inversion that employs only the fundamental mode.

Simultaneous measurement and inversion of surface wave dispersion and attenuation curves

Surface wave tests are non-invasive seismic techniques that have traditionally been used to determine the shear wave velocity (i.e. shear modulus) profile of soil deposits and pavement systems. Recently, Rix et al. [J. Geotech. Geoenviron. Engng 126 (2000) 472] developed a procedure to obtain near-surface values of material damping ratio from measurements of the spatial attenuation of Rayleigh waves. To date, however, the shear wave velocity and shear damping ratio profiles have been determined separately. This practice neglects the coupling between surface wave phase velocity and attenuation that arises from material dispersion in dissipative media. This paper presents a procedure to measure and invert surface wave dispersion and attenuation data simultaneously and, thus, account for the close coupling between the two quantities. The methodology also introduces consistency between phase velocity and attenuation measurements by using the same experimental configuration for both. The new approach has been applied at a site in Memphis, TN and the results obtained are compared with independent measurements.

Shallow Velocity Structure at the Shagan River Test Site in Kazakhstan

— During 1997 and 1998, twelve chemical explosions were detonated in boreholes at the former Soviet nuclear test site near the Shagan River (STS) in Kazakhstan. The depths of these explosions ranged from 2.5 to 550 m, while the explosive yield varied from 2 to 25 tons. The purpose of these explosions was for closure of the unused boreholes at STS, and each explosion was recorded at local distances by a network of seismometers operated by Los Alamos National Laboratory and the Institute of Geophysics for the National Nuclear Center (NNC). Short-period, fundamental-mode Rayleigh waves (Rg) were generated by these explosions and recorded at the local stations, resultingly the waves exhibited normal dispersion between 0.2 and 3 seconds. Dispersion curves were generated for each propagation path using the Multiple Filter Analysis and Phase Match Filtering techniques. Tomographic maps of Rg group velocity were constructed and show a zone of relatively high velocities for the southwestern (SW) region of the test site and slow propagation for the northeastern (NE) region. For 0.5 sec Rg, the regions are separated by the 2.1 km/sec contour, as propagation in the SW is greater than 2.1 km/sec and less in the NE region. At 1.0 sec period, the 2.3 km/sec contour separates the two regions. Finally, for 1.5 and 2.0 sec, the separation between the two regions is less distinct as velocities in the NE section begin to approach the SW except for a low velocity region (<2.1 km/sec) near the center of the test site. Local geologic structure may explain the different regions as the SW region is composed predominantly of crystalline intrusive rocks, while the NE region consists of alluvium, tuff deposits, and Paleozoic sedimentary rocks. Low velocities are also observed along the Shagan River as it passes through the SW region of the test site for shorter period Rg (0.5–1.0 sec). Iterative, least-squares inversions of the Rg group velocity dispersion curves show shear-wave velocities for the southwestern section that are on average 0.4 km/sec higher than the NE region. At depths greater than 1.5 km the statistical difference between the models is no longer significant. The observed group velocities and different velocity structures correlate with P-wave complexity and with spatial patterns of magnitude residuals observed from nuclear explosions at STS, and may help to evaluate the mechanisms behind those observations.

Crustal structure of south-central Mexico estimated from the inversion of surface-wave dispersion curves using genetic and simulated annealing algorithms

A partir de catorce sismos de subducción, agrupados en dos trayectorias (una perpendicular y otra paralela a la línea de costa), se calculó un apilado sobre las curvas de dispersión de velocidad de grupo. Estas curvas promedio fueron invertidas usando, por separado, los métodos de algoritmos genéticos y recristalización simulada. Los resultados muestran fuertes diferencias entre ambos modelos corticales, sobre todo, en los parámetros de la capa más somera y en la localización del Moho. Estas diferencias pueden ser explicadas debido a que la primera trayectoria atraviesa el terreno tectonoestratigráfico "Guerrero" y la segunda el "Oaxaca". La inversión con algoritmos genéticos (GA) probó ser considerablemente más rápida que aquélla con recristalización simulada (SA). Por otro lado SA requiere una pequeña cantidad de memoria y alcanza un desajuste menor que G.A.

Objective regionalization of Rayleigh wave dispersion data by clustering algorithms: an application to the Mediterranean basin

The main target of the present study is an objective and automated regionalization of Rayleigh wave dispersion data for the Mediterranean basin, without a priori seismotectonic constraints, and to determine the corresponding regional shear-velocity structures. The database used is formed by almost 200 Rayleigh wavetrains corresponding to 42 regional events, with surface-wave magnitude greater than 4.5, recorded at the MedNet very-broad-band stations in the Mediterranean area. Path-averaged group velocities for the Rayleigh wave fundamental mode are derived for each available epicentre-station trajectory crossing the Mediterranean basin. After this, a principal component analysis and a clustering process are applied to local group velocities, obtained for 13 different periods from 10 to 70s, in order to classify the Mediterranean basin into several homogeneous regions. The stochastic inversion of the averaged group velocity dispersion curve obtained for each region provides the respective shear-velocity structures, down to a depth of 150–160km. The characteristics of these areas and their possible correlation with the main seismotectonic features of the Mediterranean region are discussed. The regional models reveal significant lateral changes in the elastic structure, with the main differences concerning particularly the upper 35–40km. Within this depth range, low shear velocities, varying from 2.8 to 3.9kms−1, characterize the Eastern Mediterranean, whereas higher velocities, ranging from 3.0 to 4.2kms−1, are deduced for the Western Mediterranean. These results suggest a thicker crust in the eastern part, but with a greater thickness of sedimentary layers. However, for depths of between 80 and 110km, lower shear velocities are obtained in the Western part, while higher shear velocities are derived for the Eastern Mediterranean Sea, in the Aegean Sea, Greece, the south of Italy, Sicily and Tunisia. This velocity pattern suggests an averaged thicker lithosphere under the latter areas, as the top of the asthenosphere is detected at a mean depth of 75km for the remaining regions. This thicker lithosphere can be related to processes associated with the convergence of the Eurasian and African plates and subduction under the Calabrian and Hellenic Arcs.

Study on Mechanism and Inversion of Zigzag Dispersion Curves in Rayleigh Wave Exploration

AbstractThe propagation mechanism of zigzag dispersion curves in the Rayleigh wave exploration is theoretically analyzed. The propagation characteristics and interrelation of the guided waves are studied. It is suggested that the zigzag structure of Rayleigh wave is the result of the many modes generated by the low‐velocity layers or fractures in multilayered media. The inverse problems of the formation structure with the dispersion curves of the Rayleigh wave by the damping method of least squares and the genetic algorithm are analyzed. It is found that the damping method of least squares is not suitable to the inverse study of zigzag dispersion problem of Rayleigh wave while the genetic algorithm is a good method for this problem and can be used successfully.

Upper Crustal Velocity Structure in Slovenia from Rayleigh Wave Dispersion

The inversion of surface-wave dispersion curves can provide information on the average elastic properties of the upper crustal layers that are usually poorly sampled by body waves. The broad band digital records of earthquakes which recently occurred in Slovenia and neighbouring regions are used to extract the group velocity of the fundamental mode of Rayleigh waves, using frequency-time analysis (FTAN). The obtained dispersion curves permit a good resolution for the velocity and the thickness of the upper crust. The thickness of the uppermost sedimentary layer varies between 4 and 6 km and its shear-wave velocity is less than 3 km/s. The lower sedimentary layer is 7 to 9 km thick and its shear-wave velocity ranges from about 3.05 km/s in eastern Slovenia, to about 3.25 km/s in western Slovenia. The shear-wave velocity in the crystalline layer is around 3.5–3.7 km/s in the eastern part, while in the western part it reaches a rather high value of about 3.85 km/s.

Inferring the Orientation-distribution Function from Observed Seismic Anisotropy: General Considerations and an Inversion of Surface-wave Dispersion Curves

Inferring the Orientation-distribution Function from Observed Seismic Anisotropy: General Considerations and an Inversion of Surface-wave Dispersion Curves

Application of genetic algorithms to constrain shallow elastic parameters using in situ ground inclination measurements

Among the class of global optimization techniques, which includes Monte Carlo and simulated annealing methods, the Genetic Algorithms constitute a new class of methods to solve highly non-linear optimization problems. The issue has generated considerable interest in the field of artificial intelligence, and recently, in some multi-parameter optimization geophysical problems. In this study, we explore the applicability of genetic algorithms to the inversion of high resolution ground inclination measurements produced by known loads placed at known distances. Our objective is to find a model for dynamic properties of the subsoil such as shear and compressional wave velocities and depth distributions of the uppermost strata, which are related to elastic moduli. Three parameters are needed for describing elastic isotropic horizontally homogeneous media: mass density ρ and Lame constants λ and μ or mass density and P-wave and S-wave velocities. In general, the choice of parameters is not always a simple matter. In fact, although theoretically equivalent, if they are not adequately chosen, the numerical algorithms in the inversion can be inefficient. Ground inclination surveys were performed at the virgin Texcoco Lake, near Mexico City, and at the European Synchrotron radiation facility (ESRF) of Grenoble, France. From both sets of data we study the feasibility of applying genetic algorithms to rapidly and effectively explore the model space to find an optimal model for the shallow structure under study. Forward solution of vertical and radial displacements in a layered medium, under static loads, is calculated by means of the stiffness matrix approach (Kausel, E. & Roesett, J. M. Stiffness matrices for layered soil. Bulletin of the Seismological Society of America, 1981, 71(6), 1743–1761.) Comparisons with results from common established techniques such as seismic wave refraction profiles, cone resistance values and inversion of surface wave dispersion curves were used for validation purposes. Our procedure represents a fast and accurate alternative method to infer the shallow elastic parameters in surficial soils.

Surface-wave propagation across the Mexican Volcanic Belt and the origin of the long-period seismic-wave amplification in the Valley of Mexico

A network of nine broad-band seismographs was operated from March to May 1994 to study the propagation of seismic waves across the Mexican Volcanic Belt (MVB) in the region of the Valley of Mexico. Analysis of the data from the network reveals an amplification of seismic waves in a wide period band al the stations situated in the southern part of the MVB. The group velocities of the fundamental mode of the Rayleigh wave in the period range 2–13 s are found to be lower in the southern part of the MVB than in its northern part and in the region south of the MVB. The inversion of dispersion curves shows that the difference in group velocities is due to the presence of a superficial low-velocity layer (with an average S-wave velocity of 1.7 km s-1 and an average thickness of 2 km) beneath the southern part of the MVB. This low-velocity zone is associated with the region of active volcanism. Numerical simulations show that this superficial low-velocity layer causes a regional amplification of 8–10 s period signals, which is of the same order as the amplification measured from the data. This layer also increases the signal duration significantly because of the dispersion of the surface waves. These results confirm the hypothesis of Singh et al. (1995), who suggested that the regional amplification observed in the Valley of Mexico is due to the anomalously low shear-wave velocity of the shallow volcanic rocks in the southern MVB

Beamforming on seismic interface waves with an array of geophones on the shallow sea floor

The problem of locating very low frequency sound sources in shallow water is made difficult by the interaction of propagating acoustic waves with the sea floor. It is known that low frequency sound waves enter the bottom and are converted to a variety of compressional and shear wave types, including seismic interface waves. One of the latter is the Scholte wave, which travels in an elliptical orbit along the sediment-water interface. Scholte waves, although dispersive, often have speeds very much slower than the speed of sound in water. Slow wave speeds and the attendant short wavelengths suggest that low frequency beamforming and source localization with sea floor geophones can be accomplished with relatively small arrays when compared with hydrophone arrays in the water column. To test the feasibility of this approach, experiments were carried out in the shallow water of the Malta Channel of the Straits of Sicily where the Scholte wave speed was some 10 to 20 times slower that the speed of sound in water. A linear array of ten vertically gimballed geophones was deployed and measurements were made on propagating seismic wave fields generated by explosive shots. The spatial coherence of the dispersive Scholle waves across the 40-m array was found to be above 0.9 for all shots, while the spatial coherence of the noise fell to 0.5 over a distance of 18 m along the array, indicating good prospects for array beamforming and noise rejection. Frequency dependent group velocities were obtained from the dataset and used to obtain phase velocities needed to implement an algorithm for dispersive beamforming. Since the phase velocities were quite low (130-200 m/s), narrow beams were formed at very low frequencies with this small array; half-power widths of 22° at 7 Hz and 16° at 11 Hz were obtained. The resulting directivities, beam patterns, and sidelobe characteristics are in excellent agreement with array theory, which suggests that coherent processing is a viable technique on which to base new applications for seismic arrays on the sea floor. Supporting material on the geophysics of Scholte waves is also presented, as are calculations of the wave field at the site, made possible by inversion of the velocity dispersion curves.

Deep structure of the Iberian Peninsula determined by Rayleigh wave velocity inversion

SUMMARY A rigorous study of velocity dispersion of surface waves generated by teleseismic events propagating across the Iberian Peninsula and traversing main geological units, has been carried out from a set of selected analogue data, as digital records have only become available recently. Dispersed seismic signals have been obtained over a period of 16 years, between 1967 and 1982, at the five Iberian stations having long-period instruments. In our study, we have considered many earthquakes thus obtaining a fairly good path coverage of most of the peninsula for two-station Rayleigh wave velocity measurements. In all cases, the approach azimuths of the wavefronts were carefully checked. Several digital filtering techniques have been employed to remove the effects of multipathing and modal contamination, and to isolate the fundamental mode from Rayleigh wavetrains. Thus, we have obtained good estimates for both phase and group velocities. A time-variable filter has reduced the influence of noise and removed higher mode interference. Multiple filtering is then used to compute group velocity. Frequency-domain Wiener deconvolution is used to compute the interstation phase velocity. The determined average Rayleigh wave velocities reveal differences in the propagation conditions of the seismic energy across the peninsula. A mapping of velocities for various periods of reference, together with a mapping of errors in velocity, are the basis for obtaining the Rayleigh wave velocity distribution in the peninsula. Theoretical 2-D layered earth models are obtained by joint inversion of phase and group velocity dispersion curves using the stochastic inverse operator. In our inversion scheme, we use velocities corrected for anelastic effects. Finally, a 3-D mapping of S velocity is performed. This study shows important regional features of the deep structure of Iberia; we see small lateral inhomogeneities and also two low-velocity layers: one with shear velocities usually ranging from 4.23 to 4.31 km s-1 directly under the Moho, and another, the asthenosphere, with a negative velocity gradient for depths between 81 and 181 km, terminated at the bottom by a sharp discontinuity.

Seismic anisotropy of the Pacific Ocean inferred from long-period surface waves dispersion

The dispersion of surface (Rayleigh and Love) waves in the period range 40–300 s along a large number of paths, allows the estimation of both the azimuthal anisotropy and the shear-wave polarization anisotropy. The regional dispersion is determined, taking into account simultaneously its dependence with age and an azimuthal factor. The Pacific Ocean has been divided into 5 regions for Rayleigh waves and into 3 regions for Love waves. This partition discriminates the regions of extreme age which show a fast variation of dispersion with age, from the regions of intermediate age where the variation is weak. A variation of ∼ 2% of Rayleigh-wave group velocity with the azimuth of the path, measured with respect to the direction of spreading is displayed, up to very long-period. On the contrary, the azimuthal anisotropy for Love waves is difficult to resolve. For Rayleigh waves, the present-day direction of plate motion seems to agree best with the direction of maximum velocity. On the other hand, the isotropic inversion of the regional dispersion curves indicates, except for young regions, a discrepancy between Rayleigh-wave and Love-wave models. With this hypothesis, SH-velocities are higher than SV-velocities for the regions older than 23 Ma, down to a depth of 300 km, which is indicative of the presence of polarization anisotropy. The latter, very weak for the young part of the ocean, increases with age and reaches 7%, for the oldest region.