Dispersion Of Body Waves Research Articles

Preliminary Study on the Duration of High-Frequency Seismic Waves in Northern Taiwan from Deep Regional Earthquakes

The high-frequency seismic waves are usually generated by shallow earthquakes and is observed at a location near the earthquake source. Seismic energy tends to attenuate as it propagates through the Earth’s surface and interior; however, this is not the case at the subduction zone. A regional earthquake that occurred within the subducting slab was observed to have high-frequency energy, although it is from the deep (i.e. > 100 km) and with moderate magnitude (i.e. Mw 5). This phenomenon resulted from the slab effect on focusing the earthquake signal or known as the guided wave. Taiwan has a complicated tectonic feature, where Taipei city, its capital, sits above the oblique subduction of Philippine Sea Plate (PSP), i.e. the southern Ryukyu subduction zone, enhancing its exposure to strong shaking resulting from the deep regional earthquakes. In this study, we use six regional earthquakes at the southern Ryukyu subduction zone recorded by the Formosa Array (FM Array). The FM Array is a dense seismic network with a total of 140 stations located in the northern part of Taiwan, with the distance between stations approximately 5 kilometers. With high-resolution data, we could identify the distribution of the guided wave phenomenon through body wave dispersion of deep regional earthquake signals, where only stations above 10 – 20 km from the plate interface showed dispersion. An Hp/Lp ratio with a 5-second moving window is applied to the dispersed signal. The results indicate that the high-frequency signal has a longer duration at stations that sit 10 to 20 km above the plate interface. This study suggests that the slab effect will produce an anomalous seismic intensity at the subduction region and should be considered in the Ground Motion Prediction Equation (GMPE) so that the damaged to buildings resulting from strong shaking could be reduced.

Body wave dispersion characteristics of regional deep earthquake at Southern Ryukyus subduction zone

The convergent plate boundaries known as the subduction zone is the location where the cold, hydrate, and old oceanic plate subduct under the hot, dry, and young continental plate. The top of the oceanic plate, i.e. the oceanic crust usually is less than 6 km thick carries the hydrate material to the hot continental mantle, which is commonly an indication of the occurrence of the deep earthquake. From the recent studies, the deep regional earthquake body wave signal that occurred at the subduction zone was found dispersed and or shown as a waveguide. Thus, by examining these signals, we could further estimate the body wave characteristics at the subduction zone. A narrow bandpass signal and the maximum of Hilbert transform envelope are being used to estimate the delay time of the dominant frequency energy at the Southern Ryukyus subduction zone. It was found that the Southern Ryukyus has a larger delay with the dominant frequency at 2 Hz, thus, the signal travel within the oceanic crust where it acts as a low-velocity layer compared to the surrounding continental and oceanic mantle, inversely it is known as a high-quality material (preserve the high-frequency energy).

Determination of the damping ratio by multi-channel spectral analysis of seismic downhole data

Soil dynamic parameters such as shear wave velocity and damping ratio are of major interest in earthquake engineering. While the shear wave velocity, directly linked to the shear modulus, can be determined by a number of laboratory and in-situ tests with satisfying accuracy the damping ratio is much more difficult to obtain. Especially the results of in-situ experiments show often large variations. This is in general due to the troublesome determination of precise signal amplitudes whether in time or frequency domain related with these techniques.The paper presented comes back to a relationship between attenuation and velocity dispersion of body waves which replaces the measurement of the amplitude characteristics of seismic signals by a frequency dependent velocity function. The implementation of this method has previously shown to be difficult because of the very small levels of dispersion observed in seismic data. Our approach aims to overcome the problem by applying a multi-channel spectral analysis which is widely used in surface wave testing to calculate a velocity dispersion. Multi-channel measurements have shown to be more tolerant to erroneous phase characteristics of single seismic traces than the more common two station measurements.The velocity dispersion curve is extracted from a phase velocity–frequency spectrum and the damping ratio is calculated by fitting a theoretical dispersion curve to the extracted curve. The method is demonstrated on correlated data of a seismic downhole test performed using a S-wave vibrator source. The obtained results show a reasonable agreement with damping ratios found in the literature for similar soils.

Cross-borehole tomography with correlation delay times

We evaluated a comprehensive numerical experiment of finite-frequency tomography with ray-based (“banana-doughnut”) kernels that tested all aspects of this method, starting from the generation of seismograms in a 3D model, the window selection, and the crosscorrelation with seismograms predicted for a background model, to the final regularized inversion. In particular, we tested if the quasilinearity of crosscorrelation delays allowed us to forego multiple (linearized) iterations in the case of strong reverberations characterizing multiple scattering and the gain in resolution that can be obtained by observing body-wave dispersion. Contrary to onset times, traveltimes observed by crosscorrelation allowed us to exploit energy arriving later in the time window centered in the P-wave or any other indentifiable ray arrival, either scattered from, or diffracted around, lateral heterogeneities. We tested using seismograms calculated by the spectral element method in a cross-borehole experiment conducted in a 3D checkerboard cube. The use of multiple frequency bands allowed us to estimate body-wave dispersion caused by diffraction effects. The large velocity contrast (10%) and the regularity of the checkerboard pattern caused severe reverberations that arrived late in the crosscorrelation windows. Nevertheless, the model resulting from the inversion with a data fit with reduced [Formula: see text] resulted in an excellent correspondence with the input model and allowed for a complete validation of the linearizations that lay at the basis of the theory. The use of multiple frequencies led to a significant increase in resolution. Moreover, we evaluated a case in which the sign of the anomalies in the checkerboard was systematically reversed in the ray-theoretical solution, a clear demonstration of the reality of the “doughnut-hole” effect. The experiment validated finite-frequency theory and disqualified ray-theoretical inversions of crosscorrelation delay times.

ModelHVSR—A Matlab ® tool to model horizontal-to-vertical spectral ratio of ambient noise

ModelHVSR is a user-friendly collection of Matlab ® routines performing a number of tasks related to analysis of microtremor data. Its distinguishing features include: • Computation of amplification spectra for horizontally stratified soil models, for vertically incident P- and S-waves. Q-values may be frequency dependent. For constant- Q models dispersion of body-waves is taken into account; • Computation of theoretical horizontal-to-vertical spectral ratios (HVSR) for body-waves, using estimates of both horizontal and vertical amplification of soil; • Computation of average observed HVSR using standard procedures or Landweber-filtered spectra; • Computation of linear amplification factors (DAF) of the peak-ground acceleration for any soil model and target earthquake; • Inversion of the observed HVSR spectra by Monte Carlo perturbation of initial model parameters, to obtain the best-fitting family of models; • Computation of confidence regions for all inverted model parameters (including DAF). The program may be used during microzonation or similar studies, when one needs to either verify the existing geotechnical models by comparing theoretical HVSR to the observed one, or invert the observed ambient noise measurements to obtain the most-likely geotechnical models of the soil. It is also useful to conduct sensitivity analyses and to explore possible biases between model parameters.

Mantle structure under Gibraltar constrained by dispersion of body waves

We study the Africa‐Iberia plate boundary in the vicinity of Gibraltar. Numerous models have been proposed for that region throughout the last decades, proposing mechanisms that range widely from continental delamination, convective removal, to subduction of oceanic lithosphere. To better constrain upper‐mantle structure under the region, we study waveforms of P‐waves that traverse the Alboran Sea region between Spain and Morocco. These show dispersive behavior, which, together with early arrival times, confirms the presence of an anomalous upper mantle structure under the Alboran Sea. The dispersion is consistent with that expected from subducted lithosphere. Waveforms of body waves therefore provide a way to better constrain the elusive mantle structure and dynamics of the Alboran Sea region.

Enhanced continua and discrete lattices for modelling granular assemblies

This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means of homogenizing the micro-structural interactions between discrete particles. By analysis of the body wave dispersion curves, the enhanced continuum models are compared to corresponding discrete lattice models. Accordingly, it can be examined up to which deformation level the continuum models are able to accurately describe the discrete particle behaviour. Further, the boundary conditions for the enhanced continuum models are formulated, and their stability is considered. It is demonstrated how to use the body wave dispersion relations for the assessment of stability.

New Evidence of Azimuthal Variations at Campi Flegrei: Attenuation and Predominant Frequency

—In this paper we have determined apparent Q from body-wave dispersion and a spectral ratio method for the Campi Flegrei area. A contour map of azimuthal variations of apparent Q (ranging from Q = 4 to Q = 40) reveals that the lower Q (higher attenuation) corresponds to an area that includes the Solfatara Crater (with active fumaroles), near the site of maximum uplift produced during the bradyseismic crisis of 1984, and just over the site evidencing the presence of a magmatic body. A strong azimuthal variation of the predominant frequency of the first pulse of the P wave has been found and is interpreted in terms of a vertical travel time in a surficial resonant layer (∼ 1 km thick) over a halfspace. The attenuation maps, the interpretation of the resonant frequencies, and the additional information provided by the P-wave velocity suggest the presence of a circular structure in the area. Not only does the distribution of the thickness of the resonant layer (obtained through the estimation of the contribution of different harmonics) show the circular structure, but it also agrees with the presence of a thin layer of lighter sediments, determined by means of a microgravimetric study, and with the total magnetic map, previously obtained for this area. The results of the azimuthal variation provide new evidence of the structure that can be used to improve the knowledge of the area.

Measurement of body-wave dispersion and estimation of related attenuation from broadband stations

Abstract Attenuative parameters of the Earth's mantle are obtained for the frequency range 0.5–2 Hz by means of an iterative nonlinear fit to observed body-wave dispersion. Dispersion curves are obtained by directly measuring the arrival time of some selected frequency components of P- and S-wave pulses. The frequency components are obtained by narrow band-pass filtering the signal, and the arrival time is determined as the expectation value of the first pulse, which can be interpreted as the arrival time of the center of gravity of its energy contents. Before any interpretation, arrival time must be corrected by the group delay of filter and instrumental response. The apparent Q, as a function of frequency, is retrieved from broadband records of the Network of Autonomously Recording Stations array corresponding to earthquakes which occurred in the Japan-Kurile Islands region, and interpreted in terms of the continuous relaxation model (CRM) and the power law model (PLM). For the CRM the following parameters are obtained, corresponding to average values of the mantle: for P waves, τ 2 = 0.064s andQ m = 587 ; for S waves, τ 2 = 0.281andQ m = 399 . In both cases, τ 1 has been given an arbitrary value of 1.0E + 05. Using these parameters, the values of Q P = 608andQ S = 464 are obtained for a period of 1 s. For the PLM, the values of Q 0 = 611andγ = 0.07 are obtained for P waves, and Q 0 = 714andγ = 0.6 for S waves, with the same numerical values for Q at 1 s. The predicted values at 1 s agree with average published data for the mantle, except the value Q S = 714 predicted by the PLM, which is 50% higher. Thus, the measurement of body-wave dispersion proves to be an independent method and a powerful complement to classical well-established methods for the study of attenuation based on amplitude analysis.

On the measurement of body wave dispersion

A method is devised to measure body wave dispersion in terms of the arrival time of a narrow band‐pass filtered signal. The arrival time is defined as the expectation of the arrival time of the wave front minus half the duration of the first pulse. Body wave dispersion is related to an absorption band, and its transfer function is found. By interpreting the absorption band as a filter and identifying the dispersion as the (frequency dependent) group delay of the filter the measured dispersion is interpreted as due to a cascade of filters composed of the following elements: intrinsic attenuation, source time function, and finiteness of the fault.

Body-wave dispersion: Measurement and interpretation

Generalizing previous studies on short-period data, it is shown that body-wave dispersion can be measured from broad-band records of earthquakes of moderate magnitude. The method is based on the direct measurement of the arrival time of the frequency components of a seismic wave, and the arrival time is defined by its expectation value. The frequency components of the signal are obtained through a narrow band-pass filtering process. Previous to any interpretation, a correction of the arrival time for instrument response and group delay of the filter is needed. In the first step, body-wave dispersion is related to an absorption band to account for intrinsic attenuation, and thereafter we generalize this interpretation by considering a cascade of filters to account for medium parameters (attenuation and a layered crust) and source parameters (source time function and finiteness of fault). An inversion scheme to obtain the filter parameters can be devised by following, in a formal way, the same procedure as for the case of surface wave dispersion.

Frequency-dependence of velocity and attenuation of elastic waves in granite under uniaxial compression

Velocity as well as attenuation factorQ−1 ofP-wave in a dry granitic rock sample under uniaxial compressions were measured in the range of frequency between 100 kHz and 710 kHz by using the pulse transmission technique. Above the stress of 0.5 σf, where σf is the fracture stress, theP-wave velocity decreases with increasing axial stress, whereasQ−1 increases. Particularly, the change ofQ−1 is greater for high frequency than for low frequency. At a given stress level, the higher the frequency, the higher theP-wave velocity and the largerQ−1. This result means that the velocity decrease with increasing stress is smaller for higher frequency. Because of this frequency-dependence of velocity decrease, theP-wave in the rock under dilatant state shows dispersion. The body wave dispersion is more remarkable at higher stress, and is not found in a homogeneous material with no cracks. Thus the disperison is attributed to the generation of cracks. When the frequency-dependence ofQ−1 is approximated asfn in the present frequency range, the exponentn takes a value from 0.63 to 0.77.

Attenuative body wave dispersion at La Cerdanya, eastern Pyrenees

Coda- Q for P- and S-waves has been measured from digitally recorded events occurring in the La Cerdanya region of the eastern Pyrenees. Interpreted in terms of a power law, Q( f) = Q 0 f η , Q-coda for P-waves is characterized by Q 0 = 14 and η = 1.07, and S-waves by Q 0 = 14 and η = 1.13. Using a generalization of a model due to Dainty (1981), we obtain a Q model for S-waves in which intrinsic- Q is 23, the frequency dependence (ζ) of intrinsic- Q is 1.17, and the turbidity factor is 0.051. Interpreted in terms of a continuous relaxation model, where Q m is minimum Q, and τ 1 and τ 2 are high- and low-frequency cutoffs, respectively, the values of the parameters are Q m = 5 and τ 1 = 0.37 when τ 2 is assumed to be 10 000. Body wave dispersion, as computed from the differences in arrival times of the wave filtered at 3, 6, 12 and 24 Hz relative to that at 6 Hz has been measured and found to range from 0.067 at 3 Hz to −0.075 at 24 Hz. This dispersion constrains τ 2 to be 43.

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.

Frequency dependence of elasticity of rock—test of seismic velocity dispersion

LINEAR theories of attenuation of acoustic or seismic waves in media, such as rocks, which are characterised by constant or nearly constant Q factors (fractional energy loss per cycle equals 2π/Q) imply velocity dispersion and, therefore, frequency dependence of elasticity. The effect is small, corresponding to a change of order 1 % over the period range of seismological interest (1 s to 1 h), and is consequently difficult to observe. However, it leads to an internal inconsistency in the development of earth models by inversion of free oscillation data and to discrepancies between these models and body wave data1–3. It is a matter of considerable geophysical interest to resolve the problem. Validity of the linearity assumption has been questioned4 but we are now observing elliptical hysteresis loops in basalt and granite samples subjected to sinusoidal strains of order 10−6 and this is strong evidence that attenuation does become a linear phenomenon at low strain amplitudes. But whether or not perfect linearity applies, a direct demonstration of body wave dispersion is the most satisfying indication that earth model studies need revision.

An Elasticity Theorem for Heterogeneous Media, with an Example of Body Wave Dispersion in the Earth

Summary An explicit surface integral expression is derived, for the divergence (div u) of elastic displacement in an inhomogeneous anisotropic medium. In isotropic media, simple ray theory methods permit approximate evaluation of the integral; and (to the same order) an approximate relation is found between div u and the irrotational component of u. The resulting formula for P-wave displacement is expected to find application in the study of seismic sources: it is used here to evaluate the frequencydependent interference properties of P-waves, near the shadow boundary of the Earth's core.

Synthetic seismograms ofP-waves propagating in solid wedges with free boundaries

A numerical method for the synthesis of seismograms for body wave propagation in solid wedges is presented. The method is based on the superposition of multiple reflections arising from the entrance of a plane primary wave. Therefore the method is restricted to those domains in time-space where no diffracted waves from the wedge axis occur. In spite of this restriction, the dispersion of body waves in wedges can well be studied by this method.

SYNTHETIC SEISMOGRAMS OF P WAVES PROPAGATING IN SOLID WEDGES WITH FREE BOUNDARIES

A numerical method for the synthesis of seismograms for body wave propagation in solid wedges is presented. The method is based on the superposition of multiple reflections arising from the entrance of a plane primary wave. Therefore the method is restricted to that part of the time domain where no diffracted waves from the wedge axis occur. In spite of this restriction, dispersion of body waves in wedges can well be studied by this method. Seismograms have been synthesized which show the dispersion of a primary p‐signal propagating in a solid 10‐degree and a 5‐degree wedge with free boundaries. For wedge angles less than 10 degrees the signal front (to be distinguished from the wavefront) suddenly decreases its velocity from that in the infinite medium to about that of the plate wave as the signal approaches the wedge axis. Simultaneously in this transition zone a decrease of the dominant period of the interference signal occurs. These observations are concordant with previous model studies. Particle motion diagrams disclose elliptical polarization of the interference signal in the neighborhood of the wedge axis; the polarization changes its sense from prograde to retrograde on passing through the transition zone.