Geology topics

Hisashi Nakahara

Publications and source records attributed to Hisashi Nakahara.

4 recordsLinked to original sources

USGS2016

Erratum to Surface‐wave green’s tensors in the near field

Haney and Nakahara (2014) derived expressions for surface‐wave Green’s tensors that included near‐field behavior. Building on the result for a force source, Haney and Nakahara (2014) further derived expressions for a general point moment tensor source using the exact Green’s tensors. However, it has come to our attention that, although the Green’s tensors were correct, the resulting expressions for a general point moment tensor source were missing some terms. In this erratum, we provide updated expressions with these missing terms. The inclusion of the missing terms changes the example given in Haney and Nakahara (2014).

Bulletin of the Seismological Society of America↗

USGS2015

Point spread functions for earthquake source imaging: An interpretation based on seismic interferometry

Recently, various methods have been proposed and applied for earthquake source imaging, and theoretical relationships among the methods have been studied. In this study, we make a follow-up theoretical study to better understand the meanings of earthquake source imaging. For imaging problems, the point spread function (PSF) is used to describe the degree of blurring and degradation in an obtained image of a target object as a response of an imaging system. In this study, we formulate PSFs for earthquake source imaging. By calculating the PSFs, we find that waveform source inversion methods remove the effect of the PSF and are free from artifacts. However, the other source imaging methods are affected by the PSF and suffer from the effect of blurring and degradation due to the restricted distribution of receivers. Consequently, careful treatment of the effect is necessary when using the source imaging methods other than waveform inversions. Moreover, the PSF for source imaging is found to have a link with seismic interferometry with the help of the source-receiver reciprocity of Green’s functions. In particular, the PSF can be related to Green’s function for cases in which receivers are distributed so as to completely surround the sources. Furthermore, the PSF acts as a low-pass filter. Given these considerations, the PSF is quite useful for understanding the physical meaning of earthquake source imaging.

Geophysical Journal International↗

USGS2014

Surface‐wave Green’s tensors in the near field

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

Bulletin of the Seismological Society of America↗

USGS2012

Extension of the spatial autocorrelation (SPAC) method to mixed-component correlations of surface waves

Using ambient seismic noise for imaging subsurface structure dates back to the development of the spatial autocorrelation (SPAC) method in the 1950s. We present a theoretical analysis of the SPAC method for multicomponent recordings of surface waves to determine the complete 3 × 3 matrix of correlations between all pairs of three-component motions, called the correlation matrix. In the case of isotropic incidence, when either Rayleigh or Love waves arrive from all directions with equal power, the only non-zero off-diagonal terms in the matrix are the vertical–radial (ZR) and radial–vertical (RZ) correlations in the presence of Rayleigh waves. Such combinations were not considered in the development of the SPAC method. The method originally addressed the vertical–vertical (ZZ), RR and TT correlations, hence the name spatial autocorrelation. The theoretical expressions we derive for the ZR and RZ correlations offer additional ways to measure Rayleigh wave dispersion within the SPAC framework. Expanding on the results for isotropic incidence, we derive the complete correlation matrix in the case of generally anisotropic incidence. We show that the ZR and RZ correlations have advantageous properties in the presence of an out-of-plane directional wavefield compared to ZZ and RR correlations. We apply the results for mixed-component correlations to a data set from Akutan Volcano, Alaska and find consistent estimates of Rayleigh wave phase velocity from ZR compared to ZZ correlations. This work together with the recently discovered connections between the SPAC method and time-domain correlations of ambient noise provide further insights into the retrieval of surface wave Green’s functions from seismic noise.

Geophysical Journal International↗