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Detection and Location of Potential Sources of Background Low Frequency Surface Wave Energy

Junkee Rhie and Barbara Romanowicz


Earth's background free oscillations were reported recently by Nawa et al. (1998). They observed the excitation of the peaks of fundamental spheroidal modes on superconducting gravimeter data in the frequency range between 0.3 to 5 mHz even during periods of no significant earthquakes. Numerous observations and studies strongly suggest that this phenomenon is real and the coupling of the solid earth with the atmosphere/ocean system is likely involved in source mechanism (Suda, et al., 1998; Tanimoto et al., 1998; Kobayashi and Nishida, 1998; Ekström, 2001). However, the spatial distribution of the sources remains unknown. Previous studies use stacking of power spectral density and correlating multi-orbit surface waves but provide no spatial resolution of the sources. To locate the sources and better understand the source, an array-based method, a modification of the autogram method (Ekström, 2001), can be a useful tool.

Array-based method

There are two basic assumptions of an array-based method: one is that we can approximately map a long-period surface wave field recorded at given station onto any reference point with same back azimuth by introducing some parameters obtained from the spherically symmetric reference earth model (e.g. PREM). We also assume that the surface wave energy propagates as a plane wave if the source is far from the array (Figure 31.1).

We use vertical component recordings at BDSN array. Instrument response is removed and band-pass filter (100-500 sec) is applied. We first map the surface wave field at a given station onto a reference point which is inside the array. The mapping is performed by deconvolving transfer function $T(\omega,\:{\delta}X)$, which represents the propagation effects of surface wave between a given station and reference point. The second step is to break up the deconvolved records into successive time intervals with duration of 500 sec and lagged by 100 sec. The records in each time interval are divided into two subsets, "far" and "near" stations, with respect to the chosen back azimuth. We then stack the records in each subset and each time interval separately. The final step is to compare these two stacked records corresponding to "far" and "near" stations by calculating variance reduction. The above processes are repeated for all possible back azimuths. Final output of the given process is variance reduction as a function of time and back azimuth. Our preliminary results for several known teleseismic events show that the lower threshold of detection can be down to $M_w$ 5.5. And we can get a rough estimate of back azimuth for the source and arrival time of surface wave energy. To locate the sources of the long period surface wave energy, we need other dense arrays, such as arrays in Japan and Germany. Three different estimates of back azimuths and absolute arrival times will better constrain the source location.

Scanning available records from the past 5 years to search for the sources of long period surface wave energy not related to known events is further direction of this work.

Figure 31.1: Map of northern California showing the incidence of a surface wave as a plane wave (solid lines and arrows) on BDSN. Squares: quietest BDSN stations. These were used in example plot, except MOD which was installed in 2001. Triangles: other BDSN stations. The broken line indicates the reference line onto which the waveforms are back (or forward) projected before stacking
\epsfig{file=rhie02_1_fig_01.epsi, width=6cm}\end{center}\end{figure}


The current goal of this work is to estimate the spatial distribution of the sources of background free oscillations. As we mentioned before, our preliminary result shows that the detection limit of this method is at least $M_w$ 5.5 (Figure 31.2). This magnitude is less than the documented level of equivalent magnitudes of excitation of background free oscillation, which are 6.0 or 5.75 based on different approaches (Tanimoto and Um, 1999; Ekström, 2001). It implies that we can detect the long period surface wave energy when only one localized source produces equivalent moment.

Figure 31.2: Examples of analysis for an event of $M_w$ 5.5 in new Ireland region (10/12/1999), depth = 15km, distance = 89.5 deg, backazimuth = 265.5 deg). Top: waveforms at 6 quiet stations, bandpass filtered between 100 and 500 sec.Time starts from origin time of the event. Bottom: detection result: maximum variance reduction (scale shown on the right) corresponds to the arrival of R1. Arrows indicate expected back azimuths and arrival intervals for R1 and R2 corresponding to group velocities between 4.3 and 3.4 km/s. Station YBH exhibits a glitch around 9000 sec. For this smaller magnitude event, and the period range considered, only R1 is clearly detected
\epsfig{file=rhie02_1_fig_02.epsi, width=8cm}\end{center}\end{figure}

However, it is also possible that the previous estimates of equivalent moments are due to numerous localized or broadly distributed sources. In this case, we need a more robust method. We are trying to optimize the method to increase the detection limit by fine tuning optimal duration of interval, optimal stacking scheme and grouping of stations, as well as the choice of traces. Even if we cannot locate the source associated with background free oscillations due to very broad distribution of sources in time and space (Nishida and Kobayashi, 1999), this methodology will still be useful in searching for the silent/slow earthquakes or automatic identification and preliminary location of teleseismic events using a small number of local arrays.


Ekström, G., Time domain analysis of Earth's long-period background seismic radiation, J. Geophys. Res., 106, 26483-26493, 2001.

Kobayashi, N., and K. Nishida, Continuous excitation of planetary free oscillations by atmospheric disturbances, Nature, 395, 357-360, 1998.

Nawa, K., N. Suda, Y. Fukao, T. Sato, Y. Aoyama, and K. Shibuya, Incessant excitation of the Earth's free oscillations, Earth Planets Space, 50, 3-8, 1998.

Nishida, K. and N. Kobayashi, Statistical features of Earth's continuous free oscillations, J. Geophys. Res., 104, 28741-28750, 1999.

Suda, N., K. Nawa, and Y. Fukao, Earth's background free oscillations, Science, 279, 2089-2091, 1998.

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