Shinichi Matsushima

Differences Between Site Characteristics Obtained From Microtremors, S-waves, P-waves, and Codas

We examine differences of empirical site characteristics among S waves, P waves, coda, and microtremors using records at 20 sites in and around the Sendai basin, Japan, and interpret the differences theoretically. At soft soil sites the horizontal-to-vertical spectral ratios (HVRs) for early P coda become different from HVRs for a P wave with increasing time and eventually converge on HVRs for microtremors. The HVRs for an S coda become similar to HVRs for microtremors with increasing time in the frequency range lower than 3 Hz at soft soil sites. By contrast, at a rock site and two hard soil sites, HVRs for S coda agree well with HVRs for an S wave. The soil-to-rock spectral ratios for horizontal (HHRs) and vertical (VVRs) components for early S coda are larger than those for an S wave at soft soil sites. When we use the deep sedimentary structures above the bedrock before Tertiary age, theoretical HVR for the fundamental mode of Rayleigh waves is consistent with observed HVR for microtremors and theoretical HVR for an obliquely incident SV wave is consistent with observed HVR for an S wave. Theoretical S -wave site amplification factor explains well observed HHR for S wave but does not coincide with HVR for microtremors. In general the frequencies of maximum peaks of HVRs for microtremors do not coincide with those of HVRs and HHRs for S wave. However, if we select HVRs with peak frequencies lower than 1 Hz and peak amplitudes larger than three, the peak frequencies of HVRs for microtremors roughly coincide with those of HVRs and HHRs for S wave. Even under these constraints, their amplitudes do not coincide with each other. Concerning coda, we conclude that the Rayleigh wave contamination in coda is significant in the frequency range lower than 3 Hz at soft soil sites.

Estimation of S-Wave Velocity Structures in and around the Sendai Basin, Japan, Using Array Records of Microtremors

We conducted array measurements of microtremors at six sites in and around the Sendai basin to estimate deep S -wave velocity structures above the seismological bedrock (pre-Tertiary bedrock). After estimating phase velocities of microtremors in the frequency range from about 0.5 to 3 Hz, we succeeded to estimate the deep structures above the pre-Tertiary bedrock at four soil sites (KATA, OKIN, ARAH, and MYG15) and only the upper part just beneath the Pliocene layer at the other soil site (TRMA) using a Rayleigh-wave inversion technique. At TRMA and a rock site TAMA, we roughly estimate the deep S -wave velocity structures using empirical site amplification factors derived from strong-motion records. The deepest bedrock depth is 1 km, and the shallowest depth is 200 m among these six sites. The difference of the bedrock depth between the eastern side and the western side of an active thrust fault, the Nagamachi-Rifu line, is only 120 m. The difference of the bedrock depth between two sites in the east of the basin reaches about 500 m, although any geological boundaries or buried faults have not been mapped. Since the deep S -wave velocity structure of the Sendai basin had been basically unknown, we delineate it for the first time in this article using array measurement of microtremors.

The Optimal Use of Horizontal-to-Vertical Spectral Ratios of Earthquake Motions for Velocity Inversions Based on Diffuse-Field Theory for Plane Waves

The coda of earthquake motions and microtremors are sometimes referred to as diffuse-wave fields. They are generated by the multiple scattering due to the complexity of the Earth. It is accepted that the average cross correlation between the diffuse-field motions at pairs of receivers, in the frequency domain, is proportional to the imaginary part of the Green’s function between these locations. The average autocorrelation of a single receiver is also proportional to the imaginary part of the Green’s function when both the source and receiver are the same. In this study we explored the application of diffuse-field concepts to analyze earthquake records at a site when its site effect can be described using a 1D model. We derived a corollary of Claerbout’s result for a 1D layered medium. We found that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave. We considered a set of incoming plane waves (of P , SV , and SH types) with varying azimuths and incidence angles. After summing up a few hundred synthetics with inclined incidences we obtained horizontal-to-vertical (H/V) spectral ratios that match the ratios estimated from the simple theory of diffuse field. By using observed records in Japan, we found that the earthquake H/V ratios are quite stable and converge rapidly regardless of what part of the waveform is used, except the P -wave part. We also found that their spectral characteristics can be reproduced well by the velocity structures estimated in previous studies. However, theory and observation were not in perfect agreement, which in turn means that the inversion of a 1D structure could be accomplished by adopting the proposed theory for earthquake H/V spectral ratios.

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.

Applicability of Theoretical Horizontal-to-Vertical Ratio of Microtremors Based on the Diffuse Field Concept to Previously Observed Data

Abstract Horizontal-to-vertical spectral ratios of microtremors (MHVRs) have been interpreted as representing either the Rayleigh-wave ellipticity or the amplitude ratio of the sum of Rayleigh and Love waves in a horizontally layered structure. However, based on the recently established diffuse field concept, the theoretical form of MHVR has been proposed to be the square root of the ratio between the imaginary part of the horizontal Green’s function on the surface and that of the vertical one. The theory assumes that the energy of a wavefield inside the earth will be equipartitioned among the various states in 3D space. In the case of microtremors, this may occur for randomly applied point-force loadings on the surface after sufficient lapse time to allow multiple scattering. Recent works on diffuse fields suggest that equipartition may arise in several ways, but understanding the emergence of equipartition in realistic settings requires further scrutiny. In the meantime, the resulting formula is quite simple, and its meaning has theoretical support from deterministic exact solutions. As references, we use observed microtremor data from several sites that were reported previously and validate the diffuse field method (DFM) as an alternative method to explain observed MHVR. We use only sites with reliable velocity structures to compare different methods quantitatively. As a result, we found that the DFM solutions with the corresponding 1D layered structures well explain the observed MHVRs for most of the sites. Thus, we believe that MHVR can be used to invert a 1D velocity structure by using DFM as a theoretical tool.

Validation of a New Velocity Structure Inversion Method Based on Horizontal‐to‐Vertical (H/V) Spectral Ratios of Earthquake Motions in the Tohoku Area, Japan

The earthquake motion generated by the multiple scattering due to the complexity of the underneath soil structure can be referred to as a diffuse wave field. Under the assumption of the well‐diffused wave field it is accepted that the average autocorrelation of a single receiver is proportional to the imaginary part of the Green’s function when both source and receiver are located at the same point. In this study we focus on sites where the site effect can be described using a 1D model. Previous studies show that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave with unit amplitude. It is then possible to carry out an inversion of the 1D velocity structure using the relationship between the horizontal‐to‐vertical (H/V) spectral ratio and the ratio of horizontal and vertical transfer functions. We verify that the average H/V spectral ratio computed with a sufficiently large number of earthquake data depends only on the underneath geological structure and not on the set of data used to compute it. We then carry out inversions of the velocity structures for 10 sites of the K‐NET and KiK‐net networks in the Tohoku area, Japan, following the proposed theory for earthquake H/V spectral ratios. We verify that there is a good match between the observed H/V spectral ratios and the theoretical ones corresponding to the proposed velocity structures for the 10 target sites studied in the present work. Online Material: Figures showing variations of H/V spectral ratios and results of the inversions and tables of inversion parameters.

The cause of heavy damage concentration in downtown Mashiki inferred from observed data and field survey of the 2016 Kumamoto earthquake

To understand the cause of heavy structural damage during the mainshock (on April 16, 2016) of the 2016 Kumamoto earthquake sequence, we carried out a field survey from April 29 through May 1, 2016, in Mashiki where heavy damage concentration was observed. The heavy damage concentration in downtown Mashiki could be understood based on the observed strong motions with the Japan Meteorological Agency instrumental seismic intensity of VII and information collected by the field investigation. First, the fundamental features of the structural damage in downtown Mashiki were summarized. Then, a distribution map of peak frequencies was derived from horizontal-to-vertical spectral ratios of microtremors. We could not see any systematic correlation between the peak frequencies and spatial distribution of damage ratios. We also analyzed observed strong motion data at two sites to obtain fling-step-like motions in the displacement time histories through the double integration of unfiltered accelerograms. It turned out that at both strong motion observation sites in Mashiki, only the east–west (EW) components had very strong velocity pulses westward before the emergence of the fling-step-like motion eastward, which would be the primary cause of heavy structural damage in downtown Mashiki, not site effects nor the fling-step-like motion itself.

Soil Amplification and Nonlinearity Studies at K-Net Sites in Miyagi Prefecture, Tohoku, Japan Based on H/V Spectral Ratios for Earthquake Ground Motions

We have proposed an optimal way to use horizontal-to-vertical (H/V) spectral ratios for underground structure exploration, which is based on diffuse field concepts (Kawase et al. (2011) The optimal use of horizontal-to-vertical spectral ratios of earthquake motions for velocity inversions based on diffuse-field theory for plane waves. Bull Seismological Soc Am 101(5): 2011–2014). This approach is applicable to earthquake and microtremor ground motions. We show here analysis on the observed data around K-NET station in Japan where very large peak ground acceleration was observed. We compare H/V spectral ratios of the strong motions during the Off the Pacific Coast of Tohoku Earthquake of March 11, 2011, with those averaged over several weak motions to see soil nonlinearity effects on the H/V spectral ratios. After we determine detailed velocity structures based on the H/V spectral ratios of the seismic motions, we estimate deconvolved bedrock motions during main shock considering nonlinearity and then simulate strong motions around the K-NET station.