Francisco Luzón

Energy Partitions among Elastic Waves for Dynamic Surface Loads in a Semi-Infinite Solid

We examine the energy partitions among elastic waves due to dynamic normal and tangential surface loads in a semi-infinite elastic solid. While the results for a dynamic normal load on the surface of a half-space with Poisson ratio of 1/4 is a well-known result by Miller and Pursey (1955), the corresponding results for a dynamic tangential load are almost unknown. The partitions for the normal and tangential loads were computed independently by Weaver (1985) versus Poisson ratio (0≤ ν ≤1/2), using diffuse-field concepts within the context of ultrasonic measurements. The connection with the surface load point was not explicit, which partially explains why these results did not reach the seismological and engineering literature. The characteristics of the elastic radiation of these two cases are quite different. For a normal load, about 2/3 of the energy leaves the loaded point as Rayleigh surface waves. On the other hand, the tangential load induces a similar amount in the form of body shear waves. It is established that the energies injected into the elastic half-space by concentrated normal and tangential harmonic surface loads are proportional to the imaginary part of the corresponding components of the Green’s tensor when both source and receiver coincide. The relationship between the Green’s function and average correlations of motions within a diffuse field is clearly established.

Multiple Scattering of Elastic Waves by Subsurface Fractures and Cavities

Comprehensive studies in geophysics and seismology have dealt with scattering phenomena in unbounded elastic domains containing fractures or cavities. Other studies have been carried out to investigate scattering by discontinuities located near a free surface. In this last case, the presence of fractures and cavities significantly affects wave motion and, in some cases, large resonant peaks may appear. To study these resonant peaks and describe how they can be affected by the presence of other near-free-surface fractures or cavities we propose the use of the indirect boundary element method to simulate 2D scattering of elastic P and SV waves. The geometries considered are planar and elliptic cracks and cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in both frequency and time domains. In the planar cracks located near the free surface, we validate the method by comparing results with those of a previously published study. We develop several examples of various fractures and cavities to show resonance effects and total scattered displace- ment fields, where one can observe conspicuous peaks in the frequency domain and important wave interactions in the time domain. Finally, we show how our dimen- sionless graphs can be used to deal with materials like clay, sand, or gravel and compare the response with finite-element analysis of elastic beams.

Seismic source parameters for microearthquakes of the Granada basin (southern Spain)

Abstract Ninety-five microearthquakes of the Granada basin (southern Spain) with duration magnitudes ranging from 1.3 to 3.5 (moment magnitude from 0.9 to 2.5) have been spectrally analyzed with digital recordings from ten stations of the Andalusian Seismic Network. The coda-Q quality factor, Qc (assumed to be frequency dependent) was used instead of Qβ for the path correction and the Qα adopted was equal to ( 9 4 ) Qc. The k parameter for site attenuation correction had values in the range of 0.02–0.05. Fourier displacement spectra were calculated for P- and S-waves and analyzed with respect to the source model of Brune (1970, 1971). Spectral parameters were automatically determined by the method of Snoke (1987). The seismic moment ranged from 1017 to 1020 dyne cm, with average M0(P) to M0(S) ratio of 1.02, and the source radii spanned from 0.14 to 0.40 km, with average r(P) to r(S) ratio of 1.3. The seismic energy values ranged from 1 × 103 to 9 × 107 J, with P- to S-energy ratio from 1 to 10 for about 85% of the events, whereas the static stress drop varied from 0.02 to 2.6 bar. The scaling relation between the seismic moment and the stress drop indicates a decrease in stress drop with decreasing seismic moment. Apparent stress is linearly correlated with stress drop and have on average similar values, and this points out to a partial stress drop.

Characterization of the Sedimentary Cover of the Zafarraya Basin, Southern Spain, by Means of Ambient Noise

The sedimentary structure in the Zafarraya basin, located in the south of Spain, is studied by using the horizontal-to-vertical spectral ratio (HVSR) for ambient noise. To improve the reliability of the results, the stability of the HVSR measurement was checked by using a time-dependent analysis of the noise records taking into account only clear peaks. The resonant frequency varies through the basin and does not ever coincide with the maximum of the horizontal power spectrum. Several fits between the frequency of the main peak in the HVSR for microtremors and the depth to the bedrock are obtained for data from 17 sites, where geotechnical information was available. The relation derived using a scheme based on surface waves was considered to be the most reliable one. Thus, a function describing the average velocity versus depth for the sedimentary cover of the basin is also derived under assumptions of lateral homogeneity and smooth vertical variations of velocity due to age and/or confining pressure. The measurement of microtremors at 86 uniformly distributed points provides a map of the sedimentary thickness based on the previously calculated relationships, showing values greater than 200 m at the deeper zones.

On the Horizontal-to-Vertical Spectral Ratio in Sedimentary Basins

The horizontal-to-vertical spectral ratio (HVSR) has been used by many researchers to characterize local conditions in terms of the dynamic response of the soil. One of its variants is that proposed by Nakamura (1989) in which records of microtremors are used. Usually, the analysis is aimed to obtain the predominant period of the site under study. In this work we explore what can be achieved by using this method. We study the response of different configurations under incident waves coming from an explosive source using the indirect boundary element method (IBEM). We investigate two cases: low- and high-velocity contrast, holding constant the physical properties inside the basin and changing only the properties of the bedrock. Then, we compute the seismic response using the horizontal sediment-to-bedrock spectral ratio (SBSR) at various locations on the free surface of the basins, and compare it with the one calculated by the HVSR at the same locations. The comparison shows that, in general, the predominant period computed with the HVSR is not the same as that obtained by the SBSR in all the locations. On the other hand, the HVSR approximation can reasonably well predict the fundamental local frequencies when the impedance contrast between the basin and the bedrock is low. However, HVSR cannot be used in sedimentary basins having a high impedance contrast with respect to the bedrock below.

A Numerical Experiment on the Horizontal to Vertical Spectral Ratio in Flat Sedimentary Basins

Abstract — In this paper we study the seismic response of flat sedimentary basins and carry out numerical experiments to determine the extent to which we could go using the Horizontal to Vertical Spectral Ratio (HVSR) for a given site. The HVSR has been used by many researchers to characterize local conditions in terms of the dynamic response of the soil, and one of its variants, that proposed by NAKAMURA (1989) in which records of microtremors are used, is one of the most applied in recent years. We study the response of different configurations under incident waves coming from an explosive source using the Indirect Boundary Element Method (IBEM), and we investigate two cases: low- and high-velocity contrast. We compute the seismic response using the HVSR technique at various locations in the free surface of the basins, and compare it with the response calculated with the horizontal Sediment to Bedrock Spectral Ratio (SBSR) and with the Horizontal Component (HC) of the transfer function for the displacement at the same locations. The comparison shows that, in general, HVSR cannot provide the predominant period of a site due to the fact that this technique cannot predict accurately the Spectral amplification levels. On the other hand, the HVSR provides an erroneous response in the sedimentary basins which have a low-impedance contrast, with respect to bedrock, and with shape ratios like the one studied here, whereas it can reasonably well predict the fundamental local frequency when there is a high-impedance contrast, except in the center of the basin.

Surface Soil Effects Study Using Short-period Microtremor Observations in Almería City, Southern Spain

Abstract — In Almería city large earthquakes occurred and many buildings were completely destroyed in these historical earthquakes. The actual population of Almería city is about 200,000 people. This population is rapidly increasing and new urbanizing areas are growing to the eastern part of the city where they are located in softer soil conditions. Consequently, the evaluation of surface soil conditions is very important from a standpoint of earthquake disaster mitigation. We have obtained a landform classification map developed by analysing aerial photos, large-scale topographic maps and 80 borehole data. Eleven unit areas, which have different soil conditions, were inferred from this research. Also, S-wave velocity prospecting tests were carried out at several sites within the city. The shear-velocity values of the ground vary from 1689 m/s in hard rock to 298 m/s in soft soil. These results are useful for understanding the uppermost soil characteristics and are used for soil classification. Finally, short-period microtremor observations were densely carried out in the research area and NAKAMURAs method (1989) was applied for determining predominant periods. Microtremors were observed at about 173 sites with mainly 400 m interval in rock sites and 200 m interval in relatively soft soil sites. From the result of these microtremor measurements, the predominant period determined at rock site, in the western part of the city and historic area, is very short, about 0.1 s, and very stable. However at soft soil sites, in the center of the city, near Zapillo Beach and in the newly developed urban area, the predominant period is about 1.0 s and even larger in concordance with the geological conditions. Finally, at medium soil sites, in the eastern part of the city, the predominant period is about 0.4 s and it appears very stable in the whole region. The difference of predominant periods between hard rock and soft soil sites is very clear and it has been observed that the distribution of predominant periods depends heavily on the surface soil conditions.

InSAR volcano and seismic monitoring in Spain. Results for the period 1992–2000 and possible interpretations

Abstract In September 1999, we started a demonstration of the operational use of InSAR technology in the routine volcano monitoring procedures in Spain for the European Space Agency. This project was complemented with national funding to face the seismic activity. The effort focuses on the Canary Islands and the southern part of the Iberian Peninsula (volcanic and seismic cases, respectively) to supplement the traditional geodetic techniques used to date. We present the results obtained and the first interpretation of the obtained displacements. The research in volcanism is mainly focused on Tenerife Island, where a historical analysis with more than 20 images, from 1992 to 2000 has been done. The observed deformations (unknown to date) in the different interferograms are associated to the zones of the most recent activity in the island. In connection with seismic hazards we have studied displacements associated with the December 23, 1993 earthquake (magnitude Mb =5.0) produced between Adra and Berja cities. This earthquake was extensively felt in Spain, producing some damages on the epicentral zone with maximum intensity of VII (MSK). Our results clearly show the need for InSAR techniques to be included systematically as an operational component whenever possible. It would be a powerful and cost-effective way of supplementing the techniques normally used in geodetic monitoring.

A computer code for forward calculation and inversion of the H/V spectral ratio under the diffuse field assumption

During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, over the last decade several schemes for inversion of the full HVSRN curve for near surface surveying have been developed.In this work, a computer code for forward calculation of H/V spectra based on the diffuse field assumption (DFA) is presented and tested. It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Greens function which arises from the ambient noise interferometry theory.The algorithm allows for (1) a natural calculation of the Greens functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wangs orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of body waves.This code has been combined with a variety of inversion methods to make up a powerful tool for passive seismic surveying. H/V spectral ratios of ambient seismic noise are modeled by using full wavefield.The theoretical framework is consistent with ambient noise interferometry.The method provides separate calculations of different wave modes.The software is also suitable for coda waves and any other diffuse-like wavefields.It supports joint inversion of seismic velocity models from H/V and dispersion curves.

Propagation of SH elastic waves in deep sedimentary basins with an oblique velocity gradient

Abstract The propagation of elastic waves in heterogeneous sedimentary basins under incident SH plane waves is computed using the indirect boundary element method (IBEM). We work with sedimentary basins in which the S wave velocity varies with both the horizontal and the vertical directions. We use approximate analytical expressions for the two-dimensional Green’s functions of the medium with an oblique constant-gradient wave velocity. Whereas for the homogeneous half-space, underlying the sedimentary basin, Green’s functions for a homogeneous full space were used. We analyze the response of these basins by means of frequency–space diagrams, frequency–wave-number plots, synthetic seismograms, and snapshots of the displacements. Moreover, a parametric study computing a set of various cases, which have different distributions of physical properties along two dimensions of the space, was carried out. The main differences between the media, using different obliquity angles, are pointed out.