Excitation of Earth's Incessant Free Oscillations by
Atmosphere-Ocean-Seafloor Coupling

Junkee Rhie and Barbara Romanowicz

Introduction

The "hum" of the earth is well observed on broadband vertical seismic records on days without large earthquakes (Suda et al., 1998). In other words, fundamental mode Rayleigh waves continuously propagate over the whole globe even if there are no significant earthquakes or volcanic eruptions. Its excitation level is similar to the level due to continuous occurrence of events with $M_w$ 5.75 to 6.00. (Ekström, 2001). Since first observation, two competing models for sources of the hum have been proposed; atmospheric random perturbations (Kobayashi and Nishida, 1998) and processes in ocean (Tanimoto, 2003; Rhie and Romanowicz, 2004).

We are here concerned with developing an array-based method to detect and locate the sources of the hum. The array-based method is designed to measure the propagating direction of Rayleigh waves. By using two different arrays in the globe, we can get locations of the energy sources which generate continuous Rayleigh waves propagating through the solid earth. Our results show that Rayleigh wave originates primarily in the northern Pacific Ocean, during northern hemispheric winter, and in the southern oceans during the summer. The location of the sources shift seasonally and have a correlation with the maxima in significant wave height associated with winter storms. Considering our observation, we infer that atmosphere-ocean-seafloor coupling plays a crucial role in generating the "hum" of the Earth. The energy is transferring from storm to solid earth through infragravity waves.

Method and Observation

As the amplitude of waveform due to the hum is too weak to be detected at any individual recording, amplitude stacking in frequency domain or full great circle anti-dispersion filtering (Ekström, 2001) are used to enhance the signal. Both methods are good to detect the hum but inherently impossible to locate the sources because they are not sensitive to propagating direction of Rayleigh waves at all. To resolve the ambiguity in two competing models, we need to develop the method which is able to locate the sources by taking advantage of propagating properties of Rayleigh waves. An array-based method is a combined method of a traditional beam forming and an anti-dispersion filtering technique. By combining two methods, we can develop an optimal method to detect and measure the propagating direction of the long period (around 240s) surface wave. We used two regional arrays in Northern California (BDSN) and Japan (F-net). More than 10 quiet stations in each array are selected and then an array-based method is applied on vertical velocity seismograms recorded at those stations. Before applying an array-based method, we need to remove waveforms affected by significant earthquakes because we are only interested in non-earthquake sources. We removed all time windows, which can be affected by events of $M_w$ $>$ 5.5. As small events cannot significantly contribute to Rayleigh wave energy above 150s, events with $M_w$ $<$ 5.5 are ignored. An array-based method allows us to estimate the distribution of background energy levels of long period Rayleigh waves as a function of time and back azimuth. As we are interested in the long-term average of energy levels, non-symmetric shape of the array can distort the average levels with respect to back azimuth. To overcome this unwanted effect, we just look at the Fourier spectrum of the stack amplitudes as a function of azimuth. If we compare this spectrum to one from synthetic experiment by assuming uniform distribution of sources, we can find that a synthetic spectrum has a negligible "degree one" component, but our observation has a strong degree one component. It indicates that the sources are not uniformly distributed. Here "degree one" means the Fourier component with period of 360 deg.

Figure 26.1: Amplitude of degree one as a function of time and back-azimuth for quiet days between 2000 and 2002. A "quiet day" contains at least 12 hours uncontaminated by earthquakes. The quiet day with larger amplitude was selected when we have more than 2 quiet days at same Julian day. (a) Back-azimuth corresponding to the maximum in the degree 1 component of stack amplitude for F-net as a function of time. Black circles indicate maxima with amplitude larger than 1.0e-11 (m/s). (b) same as (a) for BDSN. Amplitude criteria for black circles is 3.0e-11 (m/s)
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We considered 3 years of data starting from 2000. One of our final observations is a variation of degree one components of average stacks over one day for different Julian days and arrays. Time variation of maximum amplitudes and maximum directions of degree one components of averaged stacks show significant seasonal variation for each season and two arrays point to different regions for summer and winter (Fig. 26.1a,b). Here summer and winter are defined by 6 months from March through September and other 6 months, respectively. By using two maxima directions of degree one components averaged over each season, we can determine the probable regions where the hum originated during each season in 2000 (see Fig. 26.2a,b). We can get similar results for other years.

Figure 26.2: Comparison of seasonal variations in the distribution of hum-related noise (degree 1 only) and significant wave height in the year 2000. The directions corresponding to mean amplitudes that are larger than 85 percent of the maximum are combined for the two arrays in winter (a) and in summer (b) to obtain the region of predominant sources in each season. Arrows indicate the direction of maxima. Both arrays are pointing to the Northern Pacific Ocean in the winter and to the southern ocean in the summer. Global distribution of significant wave height, in the winter (c) and in the summer (d), averaged from TOPEX/Poseidon images for the months of January and July, 2000, respectively
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Two given regions show strong correlation with maxima of significant wave height for summer and winter (Fig. 26.2c,d) and it infers that energy transfer from ocean to solid earth is happening in these regions. However, there is still a possibility that we failed to locate other source regions because the distribution of arrays are too sparse and we are utilizing only first order information of direction to the sources.

Discussion

Our result implies that the ocean takes an important part in the excitation of the hum. A highly probable scenario of energy transfer from atmosphere to solid earth through oceans is as follows: 1) a significant winter storm generates ocean waves over the mid-latitude oceans; 2) some of the energy leaks out and propagate as free waves into the ocean basins; 3) They interact with the topography of the ocean basin and transfer energy to the solid earth. But the efficiency of generating elastic waves seems to depend on various factors, such as the depth of sea floor, the shape of the continental shelves bounding the ocean basin, and the strength and persistence of storms. For example, the strengths of storms in northern Pacific and northern Atlantic are comparable during northern hemispheric winter, but only northern Pacific seems to generate significant elastic waves, which is in agreement with differences of 20-30dB in pressure noise on the ocean basin between these oceans in the infragravity wave bands (Webb et al., 1999).

References

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

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

Rhie, J., and B. Romanowicz, Excitation of earth's incessant free oscillations by atmosphere-ocean-seafloor coupling, Nature, 431, 552-556. 2004.

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

Tanimoto, J., Jet stream, roaming ocean waves, and ringing earth, EOS Trans. AGU 84(46), Fall Meet. Suppl., Abstract S12F-04, 2003.

Webb, S., X. Zhang, and W. Crawford, Infragravity waves in the deep ocean, J. Geophys. Res., 96, 2723-2736, 1991.

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