Kyosuke Okamoto

Numerical studies on stress field monitoring using Coda-Q

Summary In this study, we attempt to obtain state parameters of a subsurface medium from stochastic parameter Q. We employ a 2-D finite different method (FDM) and a 2-D boundary integral equation method (BIEM). Using them, we simulate scattering of a 2-D model to see if we can obtain two major state parameters, i.e., the magnitude of the differential stress and the orientation of the principal stress loaded in the underground from the variation of coda-Q. FDM is useful for the description of the change in the macro-scale anisotropic parameters induced by the stress field in the model. On the other hand, BIEM is useful for the description of the change in the micro-scale parameters such as the orientation of each crack in the model. We revealed that the coda-Q has the relationship with the loaded stress. The result of FDM indicates that the magnitude of the stress could be estimated from the variation of the coda-Q. Since the coda-Q shows the behavior depending on the orientation of the loaded stress, it also turned out that the stress orientation could be estimated as well. This tendency is derived from the occurrence of the velocity anisotropy in the elastic wave propagation due to the stress loading. The results from BIEM indicate that that behavior of the coda-Q variation has a different tendency from that from FDM. Although the orientation of each crack, which reflects the stress history of the medium, is aligned to specific direction and influences the behavior of the coda-Q, the tendency in the variation of coda-Q value is perceived similar to that in FDM. In conclusion, our results show the possibility that the loaded stress could be estimated if we obtain the change of the coda-Q varying with the loaded stresses. It means that non-stochastic physical-state properties could be obtained from stochastic-parameter and will lead to more clear deterministic model essential for engineering application of wave theories.

Estimation of stress change in ductile part of the crust inferred from seismic scattering

In the past, stress field in the subsurface has been measured by various techniques. For example, borehole-breakout, stress release method, hydraulic fracturing, strain gauge buried in the ground are used to measure the stress field after costly drilling the subsurface. Beside the techniques requiring direct access to the subsurface, the stress field is also measured indirectly. Electro Distance Meter, Global Positioning System, etc. are used to measure a surface deformation in time. From the surface deformation, stress change in the subsurface is estimated. However the estimated stress change in the subsurface is largely affected by inhomogeneities located near the surface, landslide, slope failure, etc. Thus, stress field in the subsurface can be obtained directly and indirectly although some problems described above are still remaining. Here we focus on seismic scattering wave, particularly coda-Q value, to measure a stress field change in the subsurface. Coda-Q, which is derived from the attenuation of coda envelope, is perceived to be an indicator of the inhomogeneity in the subsurface. In this study, we hypothesize that coda-Q indicates stress change in a deep subsurface since coda-Q is obtained from seismic waves traveling over a wide range of the crust including ductile part of the crust. Numerically it has been revealed that coda-Q indicates the magnitude of the stress change in the deep subsurface, while the surface strain distribution is largely affected by inhomogeneities located near the surface. In this study we confirm that coda-Q indicates stress change in the deep subsurface using real field data that was acquired at the time of the Iwate-Miyagi Nairiku earthquake in 2008. The stress change estimated from coda-Q corresponds with that in the ductile part calculated by a fault model, which is acquired by a seismic wave analysis, whereas the estimated stress change dose not correspond with that from GPS measurement. It means that coda-Q could indicate stress change in the deep subsurface more accurate than GPS measurement.

Temporal Variation in Subsurface Stress Estimated from Seismic Scattering

We focus on seismically scattered waves that bring the information of the earth crust where the seismic waves travel through to estimate stress field in the subsurface. Since seismic scattering is strongly related to the crustal inhomogeneities such as faults, cracks, etc., which are also created by the stress in the crust, we could be able to estimate stress field in the deep subsurface using the seismic scattering. We employ coda-Q (Qc) as a parameter to detect the variation of stress field. Qc is a parameter reflecting the inhomogeneities. Here we hypothesize that Qc could be used to estimate regional-scale stress accumulation in the crust without local and shallow disturbances since Qc is estimated from the scattered seismic waves travelling over a wide range of the crust. We first obtain a relationship between Qc and the stress change using numerical simulations. We calculate the static stress changes associated with the Iwate-Miyagi Nairiku earthquake in 2008 (Mw 6.9) in the subsurface using earthquake dislocation model and the surface deformation for comparison. As the result, it is found that the stress change inferred from Qc shows the similarity of stress change in the deep subsurface calculated by the earthquake dislocation model.

Relationship Between Attenuation of Coda Wave and Crustal Stress

Stress field deep under the ground, like seismogenic depth, is important to know seismic activity, state of oil reservoir, etc. However we can only know stress field near the earth surface using the current equipment and technique. In this study we focus on seismic scattering waves having information of the earth crust where the seismic waves travel through. From the scattering waves, we try to estimate the stress field deep under the ground. At first we employ a 2-D finite different method to reveal a relationship between the seismic scattering and the crustal stress field, i.e., magnitude and direction of the stress. As the result, it is revealed that coda-Q, which is derived from attenuation ratio of a seismic wave, has a proportional relationship with magnitude of the stress and changes periodically against direction of the magnitude. Next it is examined if the relationship can be seen in real field data using seismograms obtained by Hi-net. And it is revealed that coda-Q has the relationship with change in strain obtained by GPS observation and theoretical dislocation calculated from fault movement; both are proxy of the crustal stress field. We conclude that change in crustal stress field can be estimated from monitoring of coda-Q.

Utilization of Waveform for Estimating Stress Change in Time

Coda-Q is a stochastic parameter reflecting the heterogeneities of medium that seismic waves travel through. We investigate a relationship between crustal stress field and the coda-Q. In this study we employ a 2-D Finite Different Method to calculate seismic wave propagation through the lower and upper crust. We confirmed that the coda-Q would vary with the stress loaded to an elastic medium using the numerical simulation. The coda-Q roughly shows a proportional relationship with magnitude of the stress. We also confirmed that the upper crust, where consists of a crack-rich medium, affects the coda-Q dominantly. Next, a relationship between coda-Q obtained from actual seismic records and crustal strain obtained from GPS data is examined, and they mark high correlation coefficient. Also we revealed that coda-Q changes according with the stress change before and after a large earthquake from the observation around Tohoku area in Japan.

Numerical Study on a Relationship between Scattering Seismic Wave and Crustal Stress Filed, and its Possibility of Application to Field Data

Coda-Q is a stochastic parameter reflecting the heterogeneities of medium that seismic waves travel through. We investigate a relationship between crustal stress field and the coda-Q. In this study we employ a 2-D Finite Different Method to calculate seismic wave propagation through the lower and upper crust. We confirmed that the coda-Q would vary with the stress loaded to an elastic medium using the numerical simulation. The coda-Q roughly shows a proportional relationship with magnitude of the stress. We also confirmed that the upper crust, where consists of a crack-rich medium, affects the coda-Q dominantly. Next, a relationship between coda-Q obtained from actual seismic records and crustal strain obtained from GPS data is examined, and they mark high correlation coefficient. The filed example also supports that coda-Q has a correlation with crustal stress.

Numerical Studies on Relationship between Coda-Q and Stress Field, and Prospects for Application to Real Data

Coda-Q is a stochastic parameter which reflects heterogeneity under the ground. In the past, it is said that the coda-Q has a certain relationship with the occurrence of earthquakes or with the change in a stress field. From the perspective that the coda-Q has quantitative relationship with the stress field, this study attempts to reveal that relationship using the numerical calculations. A 2-D Finite Difference Method (FDM) and a 2-D Boundary Integral Equation Method (BIEM) are employed to consider the effects of the loaded stress in the crust for two kinds of possible causes. One would be the occurrence of anisotropy in the velocity field, and the other the distribution of crack orientations. The former could be dealt with in FDM, while the other with BIEM. The results suggested that the variation in the coda-Q has the relationship with the magnitude of the confining pressure and the angle of principal stress. It is also suggested that both the magnitude of the variation in the coda-Q against the confining pressure and against the angle of principal stress shows higher values when the velocity anisotropy is considered. These results imply the possibility to obtain the change in the stress parameters, i.e., both the magnitude and the orientation, using the variation in the coda-Q. Our further work will be conducted to apply the present methodology and to confirm the stability of coda-Q estimation to real data.

Relationship between Coda-Q and Loaded Stress

A coda-wave is formed by superposed signals caused by scatterers such as cracks and medium inhomogeneities in the underground materials. For an inhomogeneous medium, it is natural to deal with stochastic methodologies to interpret seismic data. In the past, it is revealed that coda-Q, which is derived from the coda-wave has relationship with frequency of earthquakes1). If the frequency of earthquakes is reflected the change of loaded stress, there is the relationship between the loaded stress and coda-Q. Our purpose is to reveal that relationship. We employ 2-D finite difference method to simulate scatter waves which is generated by cracks. When the stress is loaded to a simulation model, anisotropy of velocity is occurred along direction of the stress, and formation of the scatter waves is changed. Then value of coda-Q is changed. In this study, we find that coda-Q increases constantly according to the increasing stress and behavior of coda-Q has a tendency according to direction of the stress respectively (i.e. stress is loaded vertically or horizontally). In conclusion, we are able to estimate relative magnitude and the direction of the stress. It might lead a new method in underground monitoring.