Mode Rayleigh Waves Research Articles

Shallow shear-wave velocity profiles and site response characteristics from microtremor array measurements in Metro Manila, the Philippines

This paper presents the outcome of reconnaissance surveys in metropolitan Manila (Metro Manilla), the Philippines, with the aim of mapping shallow shear-wave velocity structures. Metro Manila is a seismically active and densely populated region that is in need of detailed investigation of the subsurface structures, to assess local site effects in seismic hazard estimation. We conducted microtremor array observations and used the spatial autocorrelation method to estimate the shear-wave profiles at 32 sites in major geological settings in Metro Manila. We applied a hybrid genetic simulated annealing algorithm to invert phase velocity data from the spatial autocorrelation method to generate shear-wave velocity models near the global best-fit solution. The comparison between the inferred shear-wave velocity profiles and PS logging showed good agreement in terms of the fundamental mode of Rayleigh waves and site responses. Then, we utilised the inferred shear-wave velocity profiles to compute the site amplifications with reference to the motion in engineering bedrock. Subsequently, the site amplifications have been grouped, based on NEHRP site classes. The amplification factor has also been compared with the average shear-wave velocity of the upper 30 m at each site, to produce a power-law regression equation that can be used as a starting basis for further site-effects evaluation in the metropolis.

Ground structure imaging by inversions of Rayleigh wave ellipticity: sensitivity analysis and application to European strong-motion sites

The knowledge of the local soil structure is important for the assessment of seismic hazards. A widespread, but time-consuming technique to retrieve the parameters of the local underground is the drilling of boreholes. Another way to obtain the shear wave velocity profile at a given location is the inversion of surface wave dispersion curves. To ensure a good resolution for both superficial and deeper layers, the used dispersion curves need to cover a wide frequency range. This wide frequency range can be obtained using several arrays of seismic sensors or a single array comprising a large number of sensors. Consequently, these measurements are time-consuming. A simpler alternative is provided by the use of the ellipticity of Rayleigh waves. The frequency dependence of the ellipticity is tightly linked to the shear wave velocity profile. Furthermore, it can be measured using a single seismic sensor. As soil structures obtained by scaling of a given model exhibit the same ellipticity curve, any inversion of the ellipticity curve alone will be ambiguous. Therefore, additional measurements which fix the absolute value of the shear wave velocity profile at some points have to be included in the inversion process. Small-scale spatial autocorrelation measurements or MASW measurements can provide the needed data. Using a theoretical soil structure, we show which parts of the ellipticity curve have to be included in the inversion process to get a reliable result and which parts can be omitted. Furthermore, the use of autocorrelation or high-frequency dispersion curves will be highlighted. The resulting guidelines for inversions including ellipticity data are then applied to real data measurements collected at 14 different sites during the European NERIES project. It is found that the results are in good agreement with dispersion curve measurements. Furthermore, the method can help in identifying the mode of Rayleigh waves in dispersion curve measurements.

On the characteristics of high-frequency Rayleigh waves in stratified half-space

SUMMARY The Rayleigh wave is dispersive in a stratified half-space. The modes of Rayleigh waves in a stratified half-space are usually defined by the order of the dispersion curves, such as fundamental mode, first higher mode, etc. However, the propagation characteristics of the same mode can be essentially different (e.g. surface wave and trapped wave) at different frequencies, and there is no rule to explain which parts of dispersion curves correspond to the surface wave or trapped wave. Actually, when the frequency is high, by decomposition of dispersion equation, three basic modes (R mode, R-period mode and S-period mode) of Rayleigh waves can be defined, and the mode can be further named by the phase velocities such as R1 mode, R1∼2 mode, etc. By the new definition, the dispersion curves can be divided into several velocity zones, and the modes can then be determined. In this paper, with generalized R/T coefficient method, the eigendisplacements of the three basic modes at high frequencies are studied. The study shows the physical advantage of the new definition of modes: Rayleigh waves of the same mode share the similar characteristics, and the main eigendisplacement characteristics of one mode remain the same when the medium is changed. With the definition of modes, the study makes it possible to know the basic eigendisplacement characteristics of high-frequency Rayleigh waves at different parts of the dispersion curves immediately. Especially, it presents a rule to explain which parts of dispersion curves correspond to the surface wave or trapped wave. Besides, based on the new definition, the modes in the vicinity of the osculation points are analysed. The ‘coupled modes’ that show the characteristics of two different modes simultaneously are found. It is found that the two neighbouring dispersion curves can exchange their corresponding modes of Rayleigh waves sometimes: one mode changes into another one gradually via coupled modes on each dispersion curve. The mode conversion can happen not only between surface wave mode and trapped wave mode, but also between two different trapped wave modes. However, when there is only one mode in the vicinity of the osculation points, there will be no mode conversion.

A parametric study of effective phase velocity of surface waves in layered media

In layered soils, there are multiple modes in the surface-wave field. The vibrations of these modes interfere constructively or destructively with each other. The phase velocity (i.e. the effective phase velocity) of the superposed particle vibration is different from those of the modes. Because of limitations in the current data acquisition methods in geotechnical engineering tests, the modes are not easily separated and the experimental dispersion data are often corresponding to the effective phase velocity. In the present work, the relationship between the effective phase velocity and the phase velocities of the natural modes (i.e. the modes of planar Rayleigh waves under the natural state) is established by using the thin layer stiffness matrix method. Effects of higher modes and the mode incompatibility on the effective phase velocity are analyzed for three typical layered media. The results show that influenced by both the higher modes and the mode incompatibility, the effective phase velocity depends not only on the frequency but also on the offset. Effects of changes in soil properties such as the density, Poisson’s ratio and the damping ratio, on the effective phase velocity are investigated. The analyses indicate that changes in the density and the material damping ratio have negligible influences on the effective phase velocity and dispersion of modes, whereas change in Poisson’s ratio shows relatively obvious influences in the case that a stiffer layer is trapped into two soft layers. The results are helpful for reducing the non-uniqueness in the back analysis of the experimental dispersion data.

Interaction of laser generated ultrasonic waves with wedge-shaped samples

Wedge-shaped samples can be used as a model of acoustic interactions with samples ranging from ocean wedges, to angled defects such as rolling contact fatigue, to thickness measurements of samples with non-parallel faces. We present work on laser generated ultrasonic waves on metal samples; one can measure the dominant Rayleigh-wave mode, but longitudinal and shear waves are also generated. We present calculations, models, and measurements giving the dependence of the arrival times and amplitudes of these modes on the wedge apex angle and the separation of generation and detection points, and hence give a measure of the wedge characteristics.

Green’s functions for a volume source in an elastic half-space

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green's function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green's function obtained following the first approach. The Green's function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.

Application of MASW Method for Evaluating Dynamic Properties of Lu-Liao-His Earth Dam

In the paper the shear wave velocity and Poisson’s ratio profile are studied using the MASW test. Slant stacking was adopted in experimental dispersion curve constructing. Theoretical dispersion curve can be constructed by thin layer stiffness matrix method. A real-parameter genetic algorithm is required to minimize the error between the theoretical and experimental dispersion curves. Test results show that spectrum using slant stacking shows the fundamental mode of Rayleigh wave in the frequency range from 15 Hz to 50Hz. To reduce the error of experimental and theoretical dispersion curve using real-parameter genetic algorithm is feasible. The results also show that the strata of Lu-Liao-His Earth Dam can be modeled as 3 soil layers with an underlying half space.

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.

Constraints on the long-period moment-dip tradeoff for the Tohoku earthquake

Since the work of Kanamori and Given (1981), it has been recognized that shallow, pure dip-slip earthquakes excite long-period surface waves such that it is difficult to independently constrain the moment (M_0) and the dip (δ) of the source mechanism, with only the product M_0 sin(2δ) being well constrained. Because of this, it is often assumed that the primary discrepancies between the moments of shallow, thrust earthquakes are due to this moment-dip tradeoff. In this work, we quantify how severe this moment-dip tradeoff is depending on the depth of the earthquake, the station distribution, the closeness of the mechanism to pure dip-slip, and the quality of the data. We find that both long-period Rayleigh and Love wave modes have moment-dip resolving power even for shallow events, especially when stations are close to certain azimuths with respect to mechanism strike and when source depth is well determined. We apply these results to USGS W phase inversions of the recent M9.0 Tohoku, Japan earthquake and estimate the likely uncertainties in dip and moment associated with the moment- dip tradeoff. After discussing some of the important sources of moment and dip error, we suggest two methods for potentially improving this uncertainty.

새로운 표면탄성파를 이용한 변형률 센서 개발

A SAW strain sensor based on Shear Horizontal wave with an 92 ㎒ central frequency was developed. It consists of SAW sensor, PCB substrate and bonding material (Loctite 401). External force applied to PCB substrate bonded to a piezoelectric substrate induces strain at the substrate surface, which causes changes in the elastic constant and density of the substrate and hence the propagation velocity of the SAW. The change in the velocity of the SAW result in a frequency shift of the sensor and by measuring a frequency shift, we can extract the strain induced by the external force. The 41° YX LiNbO₃ was used because it has a Leaky shear horizontal(SH) wave propagation mode and a high electromechanical coupling coefficient (K²=17.2%). And to compare with Rayleigh wave mode, 128° YX LiNbO₃ was used. And to make a stable and low insert loss, Split IDT structure was used. The obtained sensitivity and linearity of the SAW strain sensor in the case of Split IDT were measured to be 17.2 ㎑ / % and 0.99, respectively.

Velocity structure under the Trans-Mexican Volcanic Belt: preliminary results using correlation of noise

SUMMARY Prediction of ground motion in central Mexico is of great consequence not only for Mexico City but also for several other cities in the region. However, the geometry and velocity distribution of the geological structures in central Mexico is unknown. In this paper, the velocity structure in central Mexico is investigated using seismic noise records from three different arrays, one permanent and two temporary. Distances between stations span 3–300 km. Seismic noise is analysed using time domain cross-correlation to estimate the Green's function between stations. Only the fundamental mode of Rayleigh waves is recovered in the cross-correlation of vertical component records, between 5 and 10 s period. At smaller periods, we obtain no correlation, even between closely spaced stations. This suggests that the heterogeneity of the Trans-Mexican Volcanic Belt (TMVB) hampers the propagation of Rayleigh waves smaller than 9 km. We observe a large velocity contrast between the Guerrero terrain and the TMVB. This velocity contrast, measured here for the first time at this scale, explains the appearance of regional amplification in central Mexico and the origin of the diffracted waves behind the long duration of ground motion observed in Mexico City. In the large scale, average Rayleigh wave group velocity at 5 s period is about 2.5 km s−1 in the TMVB and larger than 3.6 km s−1 outside it. Significant lateral heterogeneity is evident. In the stations of the dense Meso-American Subduction Experiment array we analysed, we observe in addition a significant increase in velocity from north to south in the central portion of the TMVB. Our results are part of ongoing studies with the final objective of building a model of TMVB that may be used to simulate ground motion in central Mexico from subduction zone earthquakes.

Upper mantle structure of marginal seas and subduction zones in northeastern Eurasia from Rayleigh wave tomography

The upper mantle structure of marginal seas (the Seas of Japan and Okhotsk) and subduction zones in northeastern Eurasia is investigated, using the three-stage multimode surface wave tomography incorporating finite-frequency effects. Broadband waveform data from 305 events with magnitude greater than 5.5 from 1990 to 2005 recorded at 25 stations of the IRIS network in northeastern Eurasia and Japan and at 8 stations of the broadband seismic network in Far-Eastern Russia from 2005 to 2008 are employed in our analysis. The dispersion curves of the fundamental mode and first two higher modes of Rayleigh waves are simultaneously inverted for the shear-wave velocity structure of the region. The off-great circle propagation due to strong heterogeneities in the region is also taken into account in the construction of intermediary phase velocity models for each mode as a function of frequency. The obtained 3D S-wave velocity model is well resolved down to 200km depth. Checkerboard tests show the average horizontal resolution of 5° in the study region. The subducting Pacific plate is clearly imaged as a high velocity anomaly up to 6%. The mantle wedge above the Pacific plate is associated with low velocity anomalies. The absolute minimum S-wave velocity in the mantle wedge is 4km/s in the Sea of Okhotsk in the depth range from 80 to 160km, probably indicating the presence of partial melt. The anomalous spot with conspicuous low velocity in the southern end of the Sea of Okhotsk may indicate the existence of hot upwelling flow in the mantle. A high velocity anomaly subparallel to the present subduction zone is found in the northwestern Sea of Okhotsk in the depth range from 100 to 200km. The position of this anomaly correlates well with the high velocity anomaly found in the P-wave tomography of Gorbatov et al. (2000), which may be interpreted as a relict of the Okhotsk plate subducted in the past. We also attempted a mapping of azimuthal anisotropy in this region. The fast phase velocity directions near the Pacific plate are observed subparallel to the Kuril and Japan Trenches at all the periods, indicating a strong effect of the subducting Pacific plate on the mantle flow, while the anisotropy appears to be weak in tectonically inactive marginal seas.

New formulas derived from seismic interferometry to simulate phase velocity estimates from correlation methods using microtremor

I have developed two theoretical formulas on the basis of the power partition ratios among different modes of Rayleigh waves that are newly derived theoretically from seismic interferometry (SI). These formulas, one for the spatial autocorrelation method (SPAC) and another for the centerless circular array method (CCA), are used to simulate the estimates of the dispersion curves that can be obtained from the correlation methods using microtremor in situations when the higher normal modes are present along with the fundamental mode. The formulas can provide a way to overcome the problem caused by the assumption of the dominance of the fundamental mode, which is not always true. In addition, I have conducted a numerical validation check using the synthetic microtremor waveform data that were produced by the finite-difference method. I have found that the CCA can be an alternative to the SPAC to estimate the dispersion curves. The formula for the CCA can well simulate the dispersion curves estimated by the SPAC and CCA methods, and are better than the formula based on the above-mentioned assumption. Moreover, using the data mentioned above, I have discovered that the dual-mode inversion, which considers the presence of the fundamental and first higher modes on the basis of the formula for the CCA, performs better than the conventional single-mode inversion, which rests on the above-mentioned assumption. These positive results partially support the theoretical consequence of SI, i.e., the power partition ratio, and, further, SI itself on which the theoretically derived formulas fully rely.

Seismic surface wave method for near surface soil exploration.

There are many applications that require the information of near surface soil properties. The related areas include agricultural land management, levee/dam evaluation, landmines/UXO/tunnel detection, battle field condition assessment, and site foundation characterization, to name a few. To obtain soil properties in a non-invasive manner, a multi-channel analysis of surface wave (MASW) method based on laser-Doppler vibrometer was developed recently and reported in 157th ASA Meeting, Portland, OR. This talk will present the latest development. In particular, two methods of determination of the dispersive curve, i.e., the phase slope method and the two dimensional FFT transformation method, will be discussed. The emphasis will be given to demonstrate the capabilities of the two methods in identifying the fundamental mode and high modes of Rayleigh waves. An inversion algorithm using the measured dispersive curve can back calculate the soil profile, i.e., the shear wave velocity as a function of depth. Several case studies of the MASW method will be addressed.

High resolution Rayleigh wave group velocity tomography in North China from ambient seismic noise

Abstract This study presents the results of the Rayleigh wave group velocity tomography in North-China performed using ambient seismic noise observed at 190 broadband and 10 very broadband stations of the North-China Seismic Array. All available vertical component time-series for the 14 months span between January, 2007 and February, 2008 are cross-correlated to obtain empirical Rayleigh wave Green functions that are subsequently processed, with the multiple filter method, to isolate the group velocity dispersion curves of the fundamental mode of Rayleigh wave. Tomographic maps, with a grid spacing of 0.25o×0.25o, are computed at the periods of 4.5s, 12s, 20s, 28s. The maps at short periods reveal an evident lateral heterogeneity in the curst of North-China, quite well in agreement with known geological and tectonic features. The North China Basin is imaged as a broad low velocity area, while the Taihangshan and Yanshan uplifts and Ordos block are imaged as high velocity zones, and the Quaternary intermountain basins show up as small low-velocity anomalies. The group velocity contours at 4.5s, 12s and 20s are consistent with the Bouguer gravity anomalies measured in the area of the Taihangshan fault, that cuts through the lower crust at least. Most of the historical strong earthquakes (M≥6.0) are located where the tomographic maps show zones with moderate velocity gradient.

Estimation of S-wave Velocity Profile by Inversion of Coda H/V Spectrum

微動H/Vスペクトルを説明するために提案された「表面波H/Vスペクトル理論」を用いて，地表1点の地震記録によるコーダ波H/Vスペクトルの逆解析からS波速度構造を推定することを試み，新たな速度構造推定手法としての可能性を検討した．基盤強震観測網（KiK-net）成田観測点，及び都路観測点の地震観測データを用いて手法の適用性を検討し，当該観測点におけるPS検層，鉛直アレイ地震観測（地盤同定解析）等による速度構造結果の比較から，地震基盤までのS波速度構造を概ね精度良く推定できることが示された．コーダ波H/VスペクトルのフィッティングによりS波速度構造を精度良く推定するには，レイリー波の基本モードのみならず高次モードの影響やラブ波の影響，さらにはレイリー波とラブ波の水平振幅比の影響を考慮することが必要不可欠である．

Research on the Cross of the Dispersion Curves of Rayleigh Waves and Multi‐Modes Coupling Phenomenon

AbstractRayleigh wave, which used to be seen as the interferential wave, can be used in the inversion for the structure near the surface. It is also very meaningful in geophysical exploration, oil exploration and so on. There will be some dispersion curves that seem to cross each other in multi‐layered medium containing a low velocity layer. However, there is no systematic research about the phenomenon. In fact, it can be seen that some seemingly crossing dispersion curves are actually not crossing. Changing the thickness and the S‐wave velocity of the low velocity layer, we found that the more evident the low velocity is (i.e. the low velocity layer is thicker or has a lower S‐wave velocity), the harder the dispersion curves to cross. Fan et al. found that there are four basic modes of Rayleigh wave dispersion curves, so there are two different modes in the area that dispersion curves seem to cross. In this paper, the ‘cross' phenomenon in the area that has both R mode and S2 mode is analyzed. First, with vertical eigendisplacement curves, it can be found that the energy of vibration of R mode wave is mainly near the surface of the medium and decreases quickly with depth and forms a surface wave; while the energy of vibration of S2 mode waves is mainly in the second layer and forms a guide wave. Eigendisplacement curves show that some Rayleigh waves near the ‘cross point' have both the characters of R mode and S2 mode, so they are a kind of coupled mode. From the research with a given model, we found that in the area near the ‘cross point', if the two dispersion curves do not cross, transformation between R mode and S2 mode via coupled mode happens to the mode on each curve, we call the phenomenon ‘coupling phenomenon' of Rayleigh wave mode in this paper. If the two dispersion curves are crossing, the mode corresponding to the same dispersion curve is almost the same, though there is some coupled mode very close to the cross point, we say the modes do not couple. The content of this paper can be used as a reference in the inversion for the structure with low velocity layer.

Rayleigh-wave mode separation by high-resolution linear Radon transform

Multichannel analysis of surface waves (MASW) method is an effective tool for obtaining vertical shear wave profiles from a single non-invasive measurement. One key step of the MASW method is generation of a dispersion image and extraction of a reliable dispersion curve from raw multichannel shot records. Because different Rayleigh-wave modes normally interfere with each other in the time and space domain, it is necessary to perform mode separation and reconstruction to increase the accuracy of phase velocities determined from a dispersion image. In this paper, we demonstrate the effectiveness of high-resolution linear Radon transform (LRT) as a means of separating and reconstructing multimode, dispersive Rayleigh-wave energy. We first introduce high-resolution LRT methods and Rayleigh-wave mode separation using high-resolution LRT. Next, we use synthetic data and a real-world example to demonstrate the effectiveness of Rayleigh-wave mode separation using high-resolution LRT. Our synthetic and real-world results demonstrate that (1) high-resolution LRT successfully separates and reconstructs multimode dispersive Rayleigh-wave energy with high resolution allowing the multimode energy to be more accurately determined. The horizontal resolution of the Rayleigh-wave method can be increased by extraction of dispersion curves from a pair of traces in the mode-separated shot gather and (2) multimode separation and reconstruction expand the usable frequency range of higher mode dispersive energy, which increases the depth of investigation and provides a means for accurately determining cut-off frequencies.

Dipping-interface Mapping Using Mode-separated Rayleigh Waves

Multichannel analysis of surface waves (MASW) method is a non-invasive geophysical technique that uses the dispersive characteristic of Rayleigh waves to estimate a vertical shear (S)-wave velocity profile. A pseudo-2D S-wave velocity section is constructed by aligning 1D S-wave velocity profiles at the midpoint of each receiver spread that are contoured using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. Based on the assumption that a dipping-layer model can be regarded as stepped flat layers, high-resolution linear Radon transform (LRT) has been proposed to image Rayleigh-wave dispersive energy and separate modes of Rayleigh waves from a multichannel record. With the mode-separation technique, therefore, a dispersion curve that possesses satisfactory accuracy can be calculated using a pair of consecutive traces within a mode-separated shot gather. In this study, using synthetic models containing a dipping layer with a slope of 5, 10, 15, 20, or 30 degrees and a real-world example, we assess the ability of using high-resolution LRT to image and separate fundamental-mode Rayleigh waves from raw surface-wave data and accuracy of dispersion curves generated by a pair of consecutive traces within a mode-separated shot gather. Results of synthetic and real-world examples demonstrate that a dipping interface with a slope smaller than 15 degrees can be successfully mapped by separated fundamental waves using high-resolution LRT.

Approximation to Cutoffs of Higher Modes of Rayleigh Waves for a Layered Earth Model

A cutoff defines the long-period termination of a Rayleigh-wave higher mode and, therefore is a key characteristic of higher mode energy relationship to several material properties of the subsurface. Cutoffs have been used to estimate the shear-wave velocity of an underlying half space of a layered earth model. In this study, we describe a method that replaces the multilayer earth model with a single surface layer overlying the half-space model, accomplished by harmonic averaging of velocities and arithmetic averaging of densities. Using numerical comparisons with theoretical models validates the single-layer approximation. Accuracy of this single-layer approximation is best defined by values of the calculated error in the frequency and phase velocity estimate at a cutoff. Our proposed method is intuitively explained using ray theory. Numerical results indicate that a cutoffs frequency is controlled by the averaged elastic properties within the passing depth of Rayleigh waves and the shear-wave velocity of the underlying half space.