Sensing of faults by waveform data of intermediate-depth earthquakes

T. Murakoshi⁽¹⁾, H. Takenaka⁽¹⁾ , and D. Suetsugu⁽²⁾

¹ Faculty of Science, Kyushu University, Fukuoka 812-8581, JAPAN (murakosi@geo.kyushu-u.ac.jp),
² IISEE, Building Research Institute, Tatehara 1, Tsukuba 305-0032, JAPAN.

ABSTRACT

We developed a method for imaging subsurface faults using waveform data of nearby intermediate-depth earhtquakes. The target of our method is not an entire velocity structure, but location and size of a subsurface fault. The imaging algorithm is based on the steepest descent method which is also used in the waveform inversion of reflection data. This approach need not iteration, but only one forward and reverse-time computations of the wavefield are required.

The idea of the method was originally proposed by Takenaka et al.(1996). In the present paper we propose two special techniques, the multi-event stacking and multi-master stacking, to obtain clearer images of subsurface faults.

We examined the feasibility of our approach using the synthetic data and several trial models in the two dimensional SH cases. In the numerical experiments, we could recover the image of the subsurface fault for all trial models we used, which indicates our method has a potential for sensing real subsurface faults, and it encourages further studies of the method.

KEY WORDS: imaging algorithm, subsurface faults, multi-event stacking, multi-master stacking

INTRODUCTION

In studies of disaster prevention, detection of subsurface faults is an essential problem because there exist a lot of subsurface faults that are still unclear by geological investigations or studies of air photographs. For this reason, a new method for detecting subsurface faults using teleseismic-wave records is proposed by Takanaka et al.(1996). The target of this method is not an entire velocity structure, but location and size of a subsurface fault. The imaging algorithm of this method is based on the steepest descent method, which is also used in the waveform inversion of reflection data. Since this approach needs not iteration, only one forward iteration and reverse-time computations of the wavefield are performed. Murakoshi et al.(1996) performed some numerical experiments on imaging subsurface faults, using SH synthetic data, and demonstrated the possibility of a new method based on wavefield.

In this paper we propose two techniques : the multi-event stacking and multi-master stacking, to obtain clearer image of subsurface faults. Then we demonstrate the feasibility of our approach by numerical experiments using the synthetic SH data with different noise ratios, pulse durations and incident angles.

IMAGING METHOD

The method consists of the following steps:
(1) pre-processing of observed records,
(2) selection of trial models (initial model structures),
(3) estimation of incident wave from the bottom of the studied region,
(4) forward calculation of wavefield of the trial models,
(5) calculation of the steepest descent direction of the model parameters to be applied to the trial model,
(6) image analysis and identification of faults.

Details of each step is described in Takenaka et. al.(1996) and Murakoshi et al.(1996). Here we introduce two new techniques, the multi-event stacking and the multi-master stacking. Multi-event stacking is to stack the images derived from the data of different earthquakes, while the multi-master stacking is a technique using the data of only one earthquake, which stacks the calculated images by using different ``master receiver'' employed by removing the initial pahse from the observed records, estimation of incident wavefield and synchronizing the observed and theoretical data.

NUMERICAL EXPERIMENTS

We employ a simple model in Fig.1 as the true structure, the same structure as used in Fig.1 of Murakoshi et al.(1996). This structure includes horizontal layers and vertical fault with a vertical offset of 500 m and total size of 1.5 km. There are 28 receivers with an interval of 500 m from x = -7 km to x = 7 km on the free surface.

The incident wave is a plane SH wave, which source time function is bell-shaped with a pulse duration of 0.5 or 0.8 sec. The incident angle is ±5^o, ±10^o, ±15^o, ±20^o or ±30^o.

Our finite-difference modeling is second order in accuracy of time and space (Boore, 1972). In the finite-difference run, we use a square grid of 50 m and a time increment of 0.01 sec, which satisfies the stability condition and assures negligibly small grid dispersion within the frequency range we employed. Absorbing boundary conditions are imposed on the sides and the bottom of the finite-difference grid as described by Reynolds (1978), and the top of the grid was assumed as a free surface.

To test our imaging method, we produces two synthetic data used as observed records: noise-free data and the data containing the random noise. The signal-to-noise ratio is defined by the relation N/S = ( 1.4 ×noise_rms ) / ( data_max ) (Kong et al., 1985), where data_max and noise_rms are the maximum amplitude of pre-processed records and the root mean square of the random noise, respectively. We assume N/S = 0.1, 0.2 or 0.5.

We apply the imaging procedure to the synthetic data which are used as ``observed" data.

For real data processing, trial models should be constructed by using all available geological and geophysical information. We employ five different trial models that are horizontally layered structures without fault, shown in Fig.2, where the values of velocity and density of each layer are the same as those of the true model. Although each trial model is rather simple, it gives better understanding of our imaging technique.

After selection of a trial model, a forward calculation is performed for each model. Using the estimated incident wave from the observed data (Murakoshi et al., 1996), the seismic response of the trial model can be calculated by using the finite-difference method.

We next obtain residuals for each trial models, 1 - 5. The image of the rigidity adjustment distribution(the steepest descent direction) for each trial model is calculated using these residuals.

We show a result of the multi-event stacking (Fig.3). Fig.3b is the image obtained by the multi-event stacking of the noise-free data (i.e. N/S = 0.0) of the events for the incident angle ±5^o, ±10^o, ±15^o, ±20^o and ±30^o and t = 0.5 sec using the trial model 3. To show the effect of the multi-event stacking, the single-event imaging for trial model 3, N/S = 0.0, t = 0.5 sec and incident angle +15^o is also shown in Fig.3a. The black and white colors indicate positive and negative adjustment, respectively. Since the target of our imaging is the fault, only the image in the area -7 < x < 7 (km), 0.6 < z < 3.5 (km) is shown (The area 0 < z < 0.6 (km) is also shown with gray color for easy comparison with Fig.1).

In Fig.3, the interfaces of the layered structure of the trial and true models are characterized by black and white color. The multi-event stacking technique more emphasizes these interfaces and reduces ghost patterns, compared with the image by single event. The offset due to the fault is clearer in multi-event stacking. This indicates that we can estimate the location and size of fault by this method.

We then apply a simple image analysis to the image in Fig.3 to detect the offset due to the fault more clearly. We perform a spatial differentiation in the horizontal direction. Since most subsurface structures are approximately horizontally layered ones except for the offset due to the faults. The horizontal differentiation can eliminate the horizontal patterns of the image and emphasize the offset.

Fig.4 is the horizontal derivative of the rigidity adjustment vector in Fig.3. The differentiation has been approximated by the central difference. The black and white colors indicate positive and negative derivatives, respectively. A strong contrast pair of black and white spots corresponds to the fault, because the signal of the fault is characterized by positive vertical bands in the rigidity adjustment vector. Comparing the true and trial models, we can identify two pairs of the black and white spots around the upper and lower parts of the fault offset, which are useful to determine a depth extent of the fault.

Let us examine about the multi-event stacking with different source durations. Fig.5b shows the image obtained by the multi-event stacking of the noise-free data (i.e. N/S = 0.0) of the events for the incident angle ±15^o and t = 0.5 and 0.8 sec using the trial model 3. To identify the effect of the multi-event stacking, the single-event imaging for trial model 3, N/S = 0.0, t = 0.5 sec and incident angle -15^o is also shown in Fig.5a. In Fig.5, the interfaces of the layered structure of the trial and true models are characterized by black and white color. It is also apparent from Fig.5 that use of the multi-event stacking technique is effective in detecting the location and size of a subsurface fault.

We now show a result of the multi-master stacking. Fig.6b is the image obtained by the multi-master stacking for the ``master receivers'' x_mas = -7.0, -3.5, 3.5 and 7.0km using the trial model 3, from the synthetic data of N/S = 0.2, t = 0.5 sec and incident angle of 15^o. To show the effect of the multi-master stacking, the image by the single-master imaging for the data of N/S = 0.0 using x_mas = -7.0km is also shown in Fig.6a. The black and white colors indicate positive and negative adjustment, respectively. Fig.6 shows the multi-master stacking technique is useful to detect the location and the size of a subsurface fault.

DISCUSSION

We shall discuss intermediate-depth earthquakes, of which incident seismic wave correspond to our imaging technique. Fig.7 shows relationships of the source depth and the epicentral distance to incident angle of the direct S wave in the basement(V_s = 3.0km), which is based on the iasp91 model (Kennett et al., 1991). In our method we assumed a plane incident wave. When the epicentral distace is smaller than the source depth, we can generally apply a plane wave assumption to the incident wave. This indicates that our imaging technique is applicable to eathquakes of which sources distribute at the left side of the thick line in Fig.7. If the incident angle is larger than 30^o, our imaging method produces the vague image of interfaces and ghost patterns, and thus it is difficult to detect the location and the size of a subsurface fault.

Fig.8 shows the relationship between the seismic moment M₀ and the moment magnitude M_w versus the source duration. Relationships between the seismic moment and the source duration in the deep and shallow earthquakes are defined by the following equations, respectively (Kikuchi and Ishida, 1993) .

Let us take an example of earthquakes, which are applicable to our imaging technique. Fig.9 shows the seismicity of earthquakes M < 4.0 and deeper than 60 km in Japanese Island region during the period from 1965 to 1995, determined by Japan Meteorological Agency. For real data processing in Japanese Island region, we can use a great number of earthquakes in Fig.9, when magunitude is smaller than 6 and the distance between receiver and hypocenter is shorter than 700 km.

The multi-event stacking technique works to improve the detectability of subsurface faults. Althogh we used only four master receivers for x_mas = -7.0, -3.5, 3.5 and 7.0km for the the multi-master stacking, we could obtain clear image of subsurface faults. We can then expect the multiple effect of both the multi-event and multi-master stacking techniques at a time. Moreover, the practical problem of processing the real data is how to construct the initial model of underground velocity structure. In order to overcome this problem, it is necessary to calculate wavefield for a lot of more complex trial models, which are similar to real structures, and to store the data to interpret the result of image analysis. In addition to this insepection, it is important to consider the effect of the interval of receivers and the scale of the detectable faults.

CONCLUSION

The objective of the study is to improve the imaging technique for sensing the subsurface fault and to investigate the applicability of the technique. The multi-event stacking and multi-master stacking techniques introduced in this paper are useful to detect the location and the size of subsurface faults.

ACKNOLEDGEMENT

We are grateful to O. Nishizawa and an anonymous referee for helpful comments.

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