We have re-checked the conventional SPatial Auto Correlation (SPAC) method for microtremor array measurement, especially on the necessity of the average over azimuth of the complex coherence function, based on the theory of the newly appeared research field Seismic Interferometry, on the formulas of Green's function tensor for surface waves without the far field approximation and also on the result of our field observation. Then, the followings are revealed. First, the theory of the conventional SPAC method and that of the retrieval of the elastodynamic Green's function are almost completely consistent with an exemption that is in-necessity of the average over azimuth for the cases with the wave length longer than or comparable with the station intervals and the dominance of surface waves. Next, the dependency of the power of microtremor on azimuth can be so moderate in urban areas and their environs that the average over azimuth can be skipped. This in-necessity, however, ought to be considered together with acceptable errors for the estimated phase velocity. Moreover, the following new aspects are suggested: the possibility of two or three dimensional underground velocity structure using SPAC method without average over azimuth, the way to estimate the phase velocity separately for two mode cases, a potential new informant about the velocity structure independent from the dispersion relation.

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 The seismic interferometry simulates the pseudo seismic response by cross-correlating observed records at different receivers simultaneously, which corresponds to the seismic response observed at one receiver due to the source at another receiver location. This is one of the data processing techniques that makes it possible to use background wavefield as signal which have been thought as undesirable noise. The most important feature of the seismic interferometry is to simulate the pseudo shot records as many as the number of receivers. Then, one can visualize the subsurface structures by processing the simulated shot gathers by following the conventional processes. In this paper, we introduce results of our field tests for practical use of the seismic interferometry. We applied the relation between the reflection responses and the transmission responses. First, we carried out the demonstration of the seismic interferometry to obtain subsurface image from underground vibration. In order to make theoretical condition, we use moving sources in tunnels through the mountain, hitting type sources and a running truck, and observe the ground vibration by receivers on the slopes of the mountain. Then, we image the subsurface structures by applying the seismic interferometry to the passive observation records. The well-agreeable results with geological features show strong possibility of this method for the subsurface visualization by recording the wavefield in the ground. Second, we tried to apply the seismic interferometry to the subsurface imaging under the restrictions on an arrangement of sources. We used few explosive sources sparsely distributed on the surface, and we adopted the observed record as the transmission responses to apply the method. It is the useful result for the practical use of the seismic interferometry that we obtained the subsurface image from such sparse sources. The results of our experiments in this paper show that the seismic interferometry will play an important role in many fields in subsurface exploration.

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 In this study, we applied the seismic interferometry to inverse VSP data, and image subsurface structures. By applying the relation between transmission responses and reflection responses to the seismic records due to a source in the ground with receivers on the surface, we can simulate pseudo shot records as many as the number of receivers, and then we can image the subsurface structures from the simulated shot records. We deal with the theoretically difficult data for simulating the pseudo shot records by the seismic interferometry because only one source is located above the boundary in the ground. At first, we examined the simulating the shot records and the imaging the structure under such a tough condition by numerical simulation. On using one source in the ground, the simulated pseudo shot records look different from the true reflection responses. However, by migrating the simulated data with true velocity model, the modeled boundary could be imaged clearly from the effect of the stacking signal and/or noise. Next, we applied this technique to the data of the wavefield due to an explosive source used for excavating a shaft, and we imaged two-dimensional subsurface structures around the shaft. The obtained image after CMP stacking and time migration is sufficient to estimate the boundary between the sedimentary layer and the basement. It agrees with the result of a conventional surface reflection method. Our results show that a reasonable subsurface overview was obtained even from one explosive source in ground by means of the seismic interferometry technique.

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 The seismic interferometry reconstructs pseudo shot records from seismic data observed simultaneously at two different receivers by cross-correlation. The reconstructed record is equivalent to the seismic shot record observed at one of the receiver location. This methodology is being investigated recently by many researchers as a technique that can turn noise into signal. By using this technique, subsurface structure can be imaged by recording noise such as running vibration of vehicles and trains and microearthquake etc., without surface artificial sources adopted to a conventional seismic reflection survey.
 In order to examine the applicability of this technique, the field data acquisitions and data processing were carried out. As a result, we obtained as follows.
 1) The field experiment in a mountain with blastings in creek: In the case of the sources located at mountain streams around the receiver array, the quality of the reflection wave was better than in the case of the partial arrangement.
 2) The field experiment on the road slope with a few S-wave sources in surface: By using all the eight S-wave sources on the receiver array, shot record was reproducible from pseudo shot records.
 3) The field experiment near the bridge pier of a highway elevated bridge: The S-wave and its after phase was obtained by pseudo shot records. This indicates strong possibility of this method for subsurface visualization by using surface line vibration source and the line receiver array parallel to source array data set.
 4) The field experiment near sea coast: The quality of pseudo shot records improved by removing the large coherent noise.
 5) The field experiment in aftershock area after the 2007 Noto Hanto earthquake: Seismic reflection structure was imaged by applying seismic interferometry to aftershock record.
 From the above experimental studies, the seismic reflection survey by using a few artificial sources or running vehicle vibration is achieved by application of seismic interferometry. Moreover, it is also effective to use natural phenomena such as sea wave or natural earthquakes as a vibration source of seismic interferometry.

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 We review theory of the seismic interferometry, and show some results by numerical simulations. The cross-correlation of two recordings of a wavefield at different receivers yields the Green's function between these receivers. By using this processing technique, we can use background noise as a signal which have been thought as undesirable noise in conventional seismic explorations, and can investigate the subsurface with controlled sources and a ingenious deployment of receivers adapted to an environment of a target field. Equations for synthesizing Green's function are derived from the reciprocity theorem and the principle of time reversal invariance. In this paper, we show the derivation of the equations, and basic equations for the seismic interferometry in an acoustic wavefield and in an elastic wavefield. The numerical simulations show examples of the synthesis of Green's functions by the seismic interferometry. The concept of stationary phase is important for retrieving seismic signals, and it is useful for planning the location of sources and receivers in a field. Because the seismic interferometry can simulate the simulated shot gather as many as the number of receivers used in an observation, we can image or analyze the subsurface from the simulated pseudo data. We show a numerical example of the subsurface imaging from a random wavefield in the ground. In near future, the seismic interferometry will be effectively used with ingenuity depending on an environment and a target.

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 We can find many polygonal gravity anomalies in the gravity map series(1:200,000) published by Geological Survey of Japan,AIST.To analyze these gravity anomalies, the authors reviewed the computing equations of vertical gradient of gravity caused by the model bodies with a polygonal shaped horizontal cross ection(vertical solid polygonal cylinder, polygonal cone, polygonal parabola, polygonal ellipsoid, polygonal error function haped bodies). Some Characteristics are described in the maps drawn by these computing equations.

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 This study provides coupled simulations of elastic wave propagation and failure phenomena using a MPS (Moving Particle Semi-implicit) method which is one of particle methods. It is simpler to model objects for analysis in MPS method because a mesh or lattice structure is not needed in the particle methods. Additionally, the absence of the mesh or lattice structure simplifies large deformation and failure phenomena in numerical analyses. For confirming the validation of MPS code developed in this study, numerical simulation is first conducted with respect to elastic wave propagation by comparing with FDM (Finite Difference Method). The result shows good agreement with that of FDM with respect to the reproducibility of P and S waves in the displacement velocity field. It is also examined that the numerical stability is dominated by velocity of media, grid spacing and time interval. Also, reflected waves excited at a physical boundary are reproduced in MPS as precisely as in FDM.
 Next, we focus our attention on the Hopkinson's effect as a failure phenomenon induced by the elastic wave propagation. We apply the MPS method to the simulation with a specimen that is modeled as a two-dimensional long bar. Stress wave is generated in the specimen by applying the pressure on one edge. Compressive wave propagation in the interior of the specimen induced by incident external pressure is observed clearly, and the dynamic spalling of the bar was reproduced numerically. Then, the broken piece of the bar falls away from the main body. Consequently, these results show that MPS method could simultaneously reproduce not only wave propagation but failure phenomena. We think that this method has potential to be a common standard for dealing with both wave propagation and failure at the same time.

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