Rayleigh-wave Particle Motion Research Articles

Determination of the VS profile at a “noisy” industrial site via active and passive data: The critical role of Love waves and the opportunities of multicomponent group velocity analysis

To define the procedures necessary to unambiguously define the subsurface model, a comprehensive set of active and passive seismic data was collected in an industrial area characterized by an extremely high level of background microtremors. Passive data are recorded to define three observables: the dispersion curve of the vertical component of Rayleigh waves via miniature array analysis of microtremors, the Love-wave dispersion curve via extended spatial autocorrelation, and the horizontal-to-vertical spectral ratio (HVSR). Active data used for the holistic analysis of surface waves are extracted from data recorded through a hybrid acquisition procedure accomplished with only two 3C geophones used to simultaneously define the HVSR at two points. Defined observables are combined according to three different approaches: the joint analysis of Rayleigh waves and HVSR, the joint analysis of Rayleigh and Love waves together with the HVSR, and the joint analysis of multicomponent group velocities together with the HVSR and Rayleigh-wave particle motion (RPM) curves. In agreement with the theory, data indicate that, in general, surface-wave modeling cannot be performed considering modal dispersion curves: dispersion obtained from passive data needs to be modeled considering the effective curve, whereas group velocity obtained from active data can be analyzed using the full velocity spectrum technique. Results indicate that joint inversion of Rayleigh-wave dispersion and HVSR does not necessarily ensure the correctness of the obtained S-wave velocity ([Formula: see text]) profile and that Love waves represent a key observable to fully constrain an unambiguous inversion procedure. However, the joint analysis of multicomponent group velocity spectra (from active multicomponent single-offset data) together with the HVSR and RPM curves is a further efficient way to obtain robust [Formula: see text] profiles through the active and passive data obtained by a single 3C geophone.

Extraction and applications of Rayleigh wave ellipticity in polar regions

AbstractSeismic Rayleigh wave ellipticity measurements are the horizontal-to-vertical ratio of the Rayleigh wave particle motion, and are sensitive to the subsurface structure beneath a seismic station. H/V ratios measured from the ambient vibrations of the Earth are being increasingly used in glaciological applications to determine glacier and ice sheet thickness, seismic velocities and firn properties. Using the newly developed degree-of-polarisation (DOP-E) method which exploits the polarisation properties of seismic noise, we identify and extract Rayleigh waves from seismic stations in Greenland, and relate them to sea ice processes and the geology of the upper crust. Finally, we provide some suggestions for future applications of DOP-E method to gain greater insight into seasonal and long-term variability of sea ice formation and breakup as well as the monitoring of ice sheet thickness, subglacial environment and firn layers in the poles.

The magnifying effect of a thin shallow stiff layer on Love waves as revealed by multi-component analysis of surface waves

In the last decades, surface wave analysis has become a standard tool for an increasingly large number of geotechnical applications that require the determination of the subsurface shear-wave velocity (VS) profile. In the present paper, we investigate the role of a shallow stiff layer on Rayleigh and Love wave propagation. Multi-component synthetic and field data are considered to analyse the vertical (Z) and radial (R) components of Rayleigh waves as well as Love waves (T component). Velocity spectra are analysed according to the Full Velocity Spectrum (FVS) approach together with the Rayleigh-wave Particle Motion (RPM) frequency-offset surface that reveals the actual prograde-retrograde motion of Rayleigh waves. The FVS approach to surface wave analysis reveals particularly powerful in case we intend to reproduce the actual modal energy and when, because of complex mode excitation, the velocity spectra cannot be easily interpreted in terms of modal dispersion curves. The analysis of both synthetic and field data highlights two major facts. On one side, along the T component (Love waves) the presence of a thin shallow stiff layer excites higher modes whose top velocity is controlled by the shear-wave velocity of the deeper layers. On the other side, such a stiff layer does not massively influence the velocity spectra of the Z and R components (Rayleigh waves) and the related RPM: irrespective of the presence of the superficial stiff layer, RPM clearly shows the change from retrograde to prograde due to the VS increase in the deep layers. In case a superficial stiff layer is present (this condition is quite common in urbanized areas such as the one of the field dataset here considered), Love waves can be then an interesting tool for an expeditious estimation of the VS of the deep layers.

On the efficient acquisition and holistic analysis of Rayleigh waves: Technical aspects and two comparative case studies

The present study illustrates a series of technical aspects regarding the holistic acquisition and analysis of Rayleigh waves acquired by a single multi-component geophone.Compared with the common multi-channel and multi-offset active and passive methodologies, this approach requires simple and straightforward acquisition procedures and takes advantage of the joint analysis of the group-velocity spectra of both the vertical and radial components together with the Radial-to-Vertical Spectral Ratio (RVSR), i.e. the ratio between the amplitude spectra of the radial and vertical components.In this way we can fully describe the Rayleigh-wave propagation both in terms of velocities (group-velocity spectra) and relative amplitudes (RVSR) and jointly invert the data by means of a three-objective optimization scheme based on the Pareto optimality.Since the group-velocity spectra of the vertical and radial components are analyzed according to the Full Velocity Spectrum (FVS) approach, data inversion is performed without interpreting the velocity spectra in terms of dispersion curves.The results of the described methodology are assessed by considering two case studies and by comparing the retrieved shear-wave velocity profiles with the ones obtained through the analysis of the dispersion retrieved from standard active and passive multi-channel and multi-offset data also considering the Horizontal-to-Vertical Spectral Ratio (HVSR).Eventually, through a synthetic dataset, the effect of significant lateral variations is discussed with respect to the group-velocity spectra and the RVSR and RPM (Rayleigh-wave Particle Motion) curves.

Joint Inversion of Rayleigh Wave Phase Velocity, Particle Motion, and Teleseismic Body Wave Data for Sedimentary Structures

AbstractMapping seismic structures of sedimentary basins is of great importance to better evaluate energy resources and seismic hazards. In this study, we develop a joint Bayesian Monte Carlo nonlinear inversion method that utilizes the complementary nature of Rayleigh wave phase velocity, Rayleigh wave particle motion, and teleseismic P wave in responding to sedimentary structures. Synthetic tests demonstrate that our joint inversion can retrieve the input sedimentary models better than inversions with surface or body wave data alone. We apply our method to waveform data of two broadband stations inside the Songliao Basin in northeast China to invert for sedimentary structures beneath the two stations. We verify our results by successfully isolating the Moho P‐to‐S conversion from sediment reverberations in surface receiver functions with a wavefield‐downward‐continuation technique. We further demonstrate that we can extend our method to single‐station inversions by excluding the Rayleigh wave phase velocity in the inversion.

Effective Active and Passive Seismics for the Characterization of Urban and Remote Areas: Four Channels for Seven Objective Functions

An efficient system for the joint acquisition and analysis of multi-component active and passive seismic data is presented. It is shown how, in spite of the limited field equipment (the system requires just a 4-channel seismograph, one 3-component and four vertical-component geophones), it is nevertheless possible to define up to seven different (but mutually related and complementary) objects used to constrain a multi-objective joint inversion capable of providing a robust subsurface shear-wave velocity (VS) profile for both geotechnical and seismic-hazard studies. The presented approach relies on acquisition techniques that require simple and straightforward field procedures useful in particular, but not solely, in the characterization of urban and remote areas where, due to logistical problems, standard acquisition procedures cannot be easily applied. Active data recorded by a single 3-component geophone are processed so to define up to five objective functions: the group-velocity spectra of the three components, the radial-to-vertical spectral ratio and the Rayleigh-wave particle motion frequency curve. Passive data are used to compute two further objects: the horizontal-to-vertical spectral ratio and the phase-velocity dispersion curve obtained via miniature array analysis of microtremors. These seven objects are jointly inverted by means of a multi-objective inversion procedure based on the Pareto criterion. Performances are assessed through a comprehensive field dataset acquired in an urban area of NW-Italy. The consistency of the overall procedure is assessed by comparing the results with the analyses accomplished by considering classical multi-channel active and passive data and methodologies (multi-component MASW, multichannel analysis of surface waves and ESAC, extended spatial auto-correlation).

Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint Inversion of Rayleigh-Wave Particle Motion and Vertical- and Radial-Component Velocity Spectra

Rayleigh waves often propagate according to complex mode excitation so that the proper identification and separation of specific modes can be quite difficult or, in some cases, just impossible. Furthermore, the analysis of a single component (i.e., an inversion procedure based on just one objective function) necessarily prevents solving the problems related to the non-uniqueness of the solution. To overcome these issues and define a holistic analysis of Rayleigh waves, we implemented a procedure to acquire data that are useful to define and efficiently invert the three objective functions defined from the three following “objects”: the velocity spectra of the vertical- and radial-components and the Rayleigh-wave particle motion (RPM) frequency-offset data. Two possible implementations are presented. In the first case we consider classical multi-offset (and multi-component) data, while in a second possible approach we exploit the data recorded by a single three-component geophone at a fixed offset from the source. Given the simple field procedures, the method could be particularly useful for the unambiguous geotechnical exploration of large areas, where more complex acquisition procedures, based on the joint acquisition of Rayleigh and Love waves, would not be economically viable. After illustrating the different kinds of data acquisition and the data processing, the results of the proposed methodology are illustrated in a case study. Finally, a series of theoretical and practical aspects are discussed to clarify some issues involved in the overall procedure (data acquisition and processing).

Analysis of Rayleigh‐Wave Particle Motion from Active Seismics

Abstract Back‐azimuth analysis is a classical method used in seismological studies for the determination of the direction (azimuth) of an otherwise‐unknown seismic source. This is accomplished through the analysis of three‐component (3C) data according to a procedure based on the evaluation of Rayleigh‐wave polarity and is typically accomplished by assuming a retrograde motion. The same principles are here considered in the framework of the analyses performed while considering active data collected by a 3C geophone, thus enabling us to easily and unambiguously compute the Rayleigh‐wave particle motion (RPM) frequency curve that describes the motion of Rayleigh waves as a function of the frequency. The analyses performed for three test sites characterized by different stratigraphic conditions show that, contrary to the common assumption, in the considered frequency range (about 2–40 Hz), prograde motion is actually quite common. Although for two of the three presented case studies we consider a single‐offset acquisition, in order to evaluate the variations of the RPM frequency curve as a function of the offset, we also considered two multi‐offset datasets (one synthetic and one from a field acquisition). Results seem to indicate that, although some dependency on the offset necessarily exists, the overall trend is a characteristic of the site. Potential applications of the described approach are discussed in particular with respect to seismic‐hazard studies, as well as in the light of the exploitation of the RPM frequency curve for better constraining the subsurface model. Electronic Supplement: Animations of particle motion.

The domain of existence of prograde Rayleigh-wave particle motion for simple models

The existence of prograde particle motion for fundamental-mode Rayleigh waves is studied systematically in models of increasing complexity by using an exact expression of the ellipticity. This expression, together with the secular equation for the phase velocity, are useful to find the most relevant parameters for prograde particle motion, namely Poisson’s ratio in the layer and the shear-wave velocity contrast between the layer and the half-space. The density contrast between layer and half-space, and up to a certain degree Poisson’s ratio in the half-space, are usually less important. The domain of existence of prograde Rayleigh-particle motion is specified for typical combinations of parameters.

Prograde Rayleigh wave particle motion

SUMMARY Fundamental mode Rayleigh waves generally show retrograde particle motion at the surface of the Earth. If there exists a thick sedimentary layer, however, reversal of the sign of vertical eigenfunction occurs near the surface, resulting in prograde Rayleigh-wave particle motion at the surface. We show that, for structures similar to those found in the Los Angeles basin (with thickness up to 8 km), surface prograde motion may occur within the frequency band 0.05‐ 0.3 Hz. Although it has been suggested that the effect of gravity on waves in unconsolidated surface layer may be important, partitioning of energy between the elatic and gravitational energy shows that the gravitational energy is less than 1 per cent and thus is not important. The phenomenon is caused by elastic effects, mainly caused by extremely slow shallow seismic velocities. Observation of prograde elliptical particle motion may be difficult, however, because particle motion is largely horizontal and high microseismic noise exists in the same frequency band.

Partial derivatives of Rayleigh wave particle motion.

A theory was developed for the partial derivatives of ellipticity of Rayleigh wave particle motion at the free surface. It is based on the variational principle, and the partials are expressed in terms of eigenfunctions and an auxiliary integration of equation of motion. Model calculations for the Gutenberg crustmantle structure show a marked difference in depth dependence between the partials of ellipticity and those of phase velocity. The former decreases more rapidly with depth than the latter, implying a strong influence of near surface structure on the ellipticity. This characteristic is enhanced in higher modes. The new partials may be useful for studying near surface structures with horizontal components of higher mode Rayleigh waves.

Rayleigh wave particle motion and crustal structure

Abstract A feasibility study was made concerning the use of the ellipticity of the Rayleigh wave particle motion for determining earth structures. Variational parameters were computed empirically for both the ellipticity and phase velocity of Rayleigh waves in the period range T = 10-50 seconds. It was found that, in general, the ellipticity and phase velocity are about equally sensitive to structural perturbations, but that near-surface low-velocity sedimentary layers influence the ellipticity much more strongly than they do the phase velocity. Anelasticity has a minor effect on the ellipticity, whereas the presence of interfering waves can have a significant influence. A test of the independence between ellipticity and phase velocity indicated that in our period range ellipticity does contribute independent information, and thus provides an additional constraint toward uniqueness. Using data from LASA, both ellipticity and Rayleigh- and Love-wave phase velocities were measured and the results interpreted in terms of a crustal structure. The ellipticity data proved useful when combined with the phase velocity and some structures that fit the phase velocity data could be rejected on the basis of ellipticity.