Detection of Long Period Surface Wave Energy

Junkee Rhie and Barbara Romanowicz

Introduction

Since the 1960s, array seismology has been developed mainly due to the need for detection of nuclear tests. Now there are many seismic arrays of various sizes in the world which are used for detecting nuclear tests, but also very weak but important seismic phases for refining fine-scale structure of the deep earth.

In this study, we are interested in weak low-frequency surface waves. Low-frequency surface waves are usually the dominant phases in waveforms generated from earthquake. They have been widely used for determining global earth structure and for the retrieval of earthquake source parameters. In addition, they can be used for detecting the existence of special types of seismic sources, such as slow/silent earthquakes(Beroza and Jordan, 1990), back ground free oscillations (Ekström, 2001) and other unknown sources. Usually, the low-frequency surface waves generated from these kinds of sources are too weak to be detected by a single station.

The main goal of this study is to detect weak energy from some low-frequency seismic sources and locate them. To do that, we need to design an optimal array method and guarantee this method to work. Hereafter we call this optimal method an array-based method.

An Array-Based Method

Most array methods are based on beam forming method (Rost and Thomas, 2002). Beam forming method can enhance the amplitudes of the same phases with an identical horizontal slowness u. For body waves, each phase has a constant slowness, but surface waves are dispersive, that is, slowness is a function of frequency. Our array-based method is also based on beam forming, but it does not use constant slowness, it uses the dispersive property of surface wave. The following equation describes the propagation of surface waves over a distance $x$ from the source, in the frequency domain.

\begin{displaymath}D({\omega},{\theta},x)=S({\omega},{\theta})
\exp\left(\frac{{...
...ht)
\exp\left(\frac{{-{\omega}x}}{{2U(\omega)Q(\omega)}}\right)\end{displaymath}

where $D$ is waveform in frequency domain at distance $x$ and $\theta$ is an azimuth. $C$, $U$ and $Q$ are phase, group velocity and quality factor respectively. These parameters are obtained from a reference 1D model such as PREM (Dziewonski and Anderson, 1981). Although surface wave propagation is also affected by lateral heterogeneities, ellipticity and rotation of the Earth, PREM is a good approximation when the frequency band that we are interested in is low enough. By using the above equation we can align the surface waves with respect to a reference point within one array. The relative propagation distance is just a function of back azimuth when we assume plane wave propagation. The relation between back azimuth and waveform cannot be represented as a linear equation. Thus a model parameter search method can be used to measure back azimuth. The detailed process is as follows. We assume any back azimuth and imagine an imaginary source at 90 deg. away from the reference point (center of the array). Epicentral distances for all stations are calculated from an imaginary epicenter. We get relative distances between stations and the reference point by subtracting 90 deg. from calculated epicentral distances. The mapped waveform into reference point from each station can be calculated by using the above equation. Next process is to stack mapped waveforms to enhance coherent surface waves and reduce incoherent noise. The stacking can increase the possibility of detection by increasing the S/N ratio. Because neither do we have very dense distribution of stations nor all of them are quiet, stacking may not be able to increase the S/N ratio significantly. But in most cases, it can be helpful. The most common stacking method is a simple mean process, but we used N-th root stacking method. The advantage of this method is that it can severely reduce incoherent noises relative to a simple mean process, but it can distort the waveforms after stacking (Muirhead and Datt, 1976). Now we have one stack from original recordings for a given back azimuth. If a given back azimuth is close to real one, amplitude of surface wave is preserved and incoherent noise is reduced. The final step is to apply moving time window and take averaged amplitude of recording in time window. The definition of averaged amplitude is

\begin{displaymath}S\left(\frac{t_1 + t_2}{2}\right) =
\sqrt{\frac{\int_{t_1}^{t_2}\left(v(t)w(t)\right)^2dt}
{\int_{t_1}^{t_2}w(t)^2dt}}
\end{displaymath}

where $w(t)$ is a taper function. The length and shift of time window will be different with respect to the applications and frequency content. In this study, we use a duration of 500 sec, shift of 100 sec and band pass between 50-200 sec. The above procedure is repeated for all possible back azimuths and then finally we can obtain averaged amplitudes as a function of time and back azimuth. We applied this array based method for three different arrays in the world during the period of January 2000.

Discussion

Our detection method is not completely established. Although we still need more refined detector which can identify signal from noise, the detection of the signal from large events ($M_{w}$ $>$ 6.0) is obvious because they have much larger amplitudes relative to the back ground amplitude level. Figure 24.1 shows maximum averaged amplitudes in back azimuth as a function of time calculated for three different arrays - FNET (Japan), GRSN (Germany) and BDSN (Northern California). Because low-frequency displacement amplitudes are proportional to scalar seismic moment, maximum averaged amplitudes can be tied to $M_{w}$ by introducing a scaling factor. Most signals due to large events can be clearly identified in all three arrays. The background noise levels are different for three arrays, GRSN shows much larger noise level than other two networks. This difference can be explained partly by different internal noise of seismometer in GRSN. GRSN consists of STS-2, but STS-1 is installed on other stations which are used in this study..

Figure 24.1: Maximum averaged amplitude plot for January, 2000. Amplitudes for FNET, BDSN and GRSN are shown from top to bottom. Small circles indicate arrival times and $M_{w}$ for events listed in CMT. An arrival time is corrected by assuming group velocity of 3.8 km/sec
\begin{figure}\begin{center}
\epsfig{file=rhie03_1_1.eps, width=7cm}\end{center}\end{figure}

The final goal of application of array-based method is to detect and locate seismic sources. To check the reliability of the current method, we manually detect signals and compare their arrival time and back azimuth with those calculated from the earthquake catalog (Harvard CMT). There were 13 events with $M_{w}$ larger than 6 in January, 2000. All 13 events are clearly detected for three arrays. Comparison result is written in following table.

Figure 24.2: Table of detection result. Time difference means arrival time difference between observed and calculated ones. BAZ1 is back azimuth calculated form CMT and BAZ2 is measured back azimuth.
\begin{figure}\begin{center}
\epsfig{file=rhie03_1_2.epsi, width=6.5cm}\end{center}\end{figure}

As you can see in the table, all measured back azimuths are within 20 deg. from actual back azimuths and time differences between measured and calculated times are not significant. It indicates that we can locate the source from measured parameters. This result shows an array-based method can measure arrival time and back azimuth precisely enough to locate the source when energy released from the source is quite large. We still need to know the limit of detection and whether there is any detectable signal due to sources that are not standard events. To do that, we will apply this method on whole data of 2000 and look at other frequency bands.

References

Beroza, G. and T.H. Jordan, Searching for slow and silent earthquakes using free oscillations, J. Geophys. Res., 95, 2485-2510, 1990.

Dziewonski, A.M. and D.L. Anderson, Preliminary reference Earth model (PREM), Phys. Earth Planet. Inter., 25, 289-325, 1981

Ekström, G., Time domain analysis of Earth's long-period background seismic radiation, J. Geophys. Res., 106, 26,483-26,493, 2001.

Muirhead, K.J. and R. Datt, The N-th root process applied to seismic array data, Geophys. J. R. Astr. Soc., 47, 197-210, 1976.

Rost, S. and C. Thomas, Array seismology: Methods and applications, Rev. Geophys., 40(3), 1008, doi:10.1029/2000RG000100, 2002.

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