Fig. 3 Schematic illustration of hydraulic fracturing experiments. (1) A borehole is drilled. (2) Several measurements are done to check that there is no fracture on the bore wall where hydraulic fracturing experiments will be done. (3) Hydraulic experiments are done. (a) The region for the experiment is sealed by two packers. (b) Inject water to pressurise the region between packers. (c) Hydraulic fracture occurs. Then flow rate of the injected water is controlled to measure the shut in and shut out pressures of the fracture. (d) Deflate and pull up the packers.

Since these experiments are conducted at a single point around the fault, it is difficult to obtain a spatial variation of absolute stress. We only have local pin-point stresses. If we drilled at many sites around the fault we might be able to obtain the stress distribution. But, in reality, it is not possible because of the expensive drilling costs. Since what we need for the reconstruction of earthquake dynamic rupture is the distribution of absolute stress around the fault, a method is required to extrapolate the stress distribution from pin-point stresses.

To overcome this situation, earthquake focal mechanisms play an important role. Earthquake focal mechanisms are considered as strain changes at the focal area of each earthquake. Each focal mechanism does not indicate directly the stress field but an assembly of them does include the information on the stress field that caused the earthquake. If we assume that the stress is uniform inside the target area and that each earthquake slip occurs along the maximum stress direction, we are able to estimate the stress field from a group of focal mechanisms by using the variation in focal mechanism solutions in the dataset [Angelier (1979); Gephart and Forsyth (1984)]. The fault plane does not always direct to 45° to the maximum principal direction but is distributed around this direction depending on the frictional property of the fault. By processing many focal mechanism data statistically, we can estimate the stresses [Hardebeck and Hauksson (2001); Fukuyama et al. (2003a); Kubo and Fukuyama (2004)].

It should be noted that these estimated values are not sufficient to describe the total stress field; three principal stress directions and the stress ratio (R) are estimated by the stress tensor inversion. R is defined by (01 — o"2)/(o~i — 03), where o1, o2 and o3 are maximum, intermediate and minimum principal stresses, respectively and compression is taken positive. An important advantage of this method is that when earthquake focal mechanisms are estimated in a region, we are able to estimate the stress field from the focal mechanisms. In order to calibrate the stress field esit-mated by the focal mechanisms, one or two in-situ stress measurements are required.

During the 2000 western Tottori earthquake, about 75 focal mechanisms were estimated [Fukuyama et al. (2003a)] by the moment tensor inversion of broadband seismograms at regional distances [Fukuyama et al. (1998); Fukuyama et al. (2001); Kubo et al. (2002)] (Fig. 4a). The source region was divided into two: coseismic (#1-#4 in Fig. 2c) and post seismic slip (#5-#13) regions. By examining the focal mechanisms in Fig. 4(a), the predominant directions of the P-axes of the focal mechanisms appears different between coseismic and postseismic regions.

Figure 4(b) and (c) shows the results of the stress tensor inversion. Taking into account the 95% confidence region, the principal stress directions are well constrained by the data. Although the focal mechanisms are slightly differnet between northern postseismic region and southern coseis-mic region, stress field is considered to be similar [Fukuyama et al. (2003a)]. R value is estimated at 0.6, which is consistent with the fact that all the focal mechanisms are of strike slip type.

An alternative method is to measure the distribution of aseismic slips near the fault. The current stress field is considered to be the tectonically applied stress contaminated by the stress caused by aseismic slips. Since the materials around the fault are considered to be elastic, we can estimate the distribution of stress change around the fault due to the aseismic slip

Mw 6

IVIw U

Mw 5

Mw 3

Mw 6

IVIw U

Mw 5

Mw 3

133.2oE 133.4oE

(a) Estimated Moment Tensors (Mw>3.5)

Fig. 4 Results of the stress tensor inversion using aftershock moment tensors. (a) Distribution of estimated moment tensor solutions whose moment magnitudes are greater than 3.5. The lower hemisphere projection is employed. (b) The result of the stress tensor inversion. Optimum solution for the principal stress directions are shown as solid big symbols. 95% confidence regions are shown for each stress direction. (c) Distribution of stress ratio R for the solutions within the 95% confidence region. The R value for the optimum solution was 0.60. Plot in (b) is in lower hemisphere projection [Modified from Fukuyama et al. (2003a)].

133.2oE 133.4oE

(a) Estimated Moment Tensors (Mw>3.5)

(b) Inversion Result with 95% Confidence Region

(c) Frequency of R

(c) Frequency of R

Fig. 4 Results of the stress tensor inversion using aftershock moment tensors. (a) Distribution of estimated moment tensor solutions whose moment magnitudes are greater than 3.5. The lower hemisphere projection is employed. (b) The result of the stress tensor inversion. Optimum solution for the principal stress directions are shown as solid big symbols. 95% confidence regions are shown for each stress direction. (c) Distribution of stress ratio R for the solutions within the 95% confidence region. The R value for the optimum solution was 0.60. Plot in (b) is in lower hemisphere projection [Modified from Fukuyama et al. (2003a)].

on the fault. Once we know the information on the tectonic stress applied to this region, the current stress field can be estimated by adding the stress change due to the aseismic slips on the fault. This aseismic slip distribution can be obtained by the analysis of strain distribution on the surface obtained by GPS (global positioning system) data [Hirahara et al. (2003)]. To calibrate the stress distribution estimated above, again, in-situ stress measurements around the fault become important.

This idea was applied to the estimation of the fault strength [Yamashita et al. (2004)], which could be equivalent to the shear stress value just before the earthquake. The in-situ stress measurements near the fault can only be done after the occurrence of earthquakes and the continuous monitoring of stress is not now possible. The distribution of coseismic slip, however, can be obtained by the waveform inversion analysis of mainshock seismograms, and the coseismic stress change around the fault can be estimated. By subtracting the stress change estimated from the coseismic slip from the post seismic stress measured by the in-situ stress measurements, the pre-shock stress can be estimated, which should be balanced by the strength of the fault.

Was this article helpful?

## Post a comment