Vibrations from the “Perfect Storm”



[1] Microseismic vibrations during the famous October 1991 “Perfect Storm” were observed at seismic stations across North America. The extreme wave conditions during this storm, in conjunction with the occurrence of Hurricane Grace to the south, are ideal for studying where such vibrations originate and their inland propagation. High-amplitude primary and double-frequency (DF) microseisms were observed at broadband seismic station HRV in eastern Massachusetts. Similar spectral variation observed at seismic station ANMO at Albuquerque, New Mexico, shows transcontinental propagation of vibrations from the Perfect Storm. Cross correlation between wave spectra from widely separated buoy measurements and corresponding DF microseism spectra at HRV give high-correlation coefficients, R2, from the New England coast to Cape Hatteras. Contours of peak R2 scaled by the magnitude of the lag at the peak, together with similarities between wave and microseism spectral variation, imply that the dominant source area of DF microseisms during the Perfect Storm is near the southern Massachusetts coast, not in the open ocean where the highest waves occurred.

1. Introduction

[2] Two concurrent intense storm systems occurred in the northwest Atlantic at the end of October 1991. Strong winds from these storms, dubbed the “Perfect Storm” and Hurricane Grace by the National Weather Service (see http://www. for details), generated high-amplitude waves measured by several buoys along the East Coast. The chronology of their storm tracks (Figure 1) suggests that waves from these storms should have intersected in the open ocean distant from coastlines. The nonlinear interaction of opposing wave components having nearly the same wave number results in a pressure excitation spectrum that propagates away from the sea surface at double the ocean wave frequency and couples into seismic waves at the ocean bottom, causing the gravity wave induced noise called microseisms. The “double-frequency” (DF) microseism peak dominates the seismic noise spectrum in the [0.1, 0.5] Hz band. Analysis of microseism particle motion and phase relationships both on the ocean floor [Barstow et al., 1989] and on land [Haubrich and McCamy, 1969] indicate that microseisms propagate primarily as fundmental mode Rayleigh waves. Because Rayleigh waves propagate at velocities (∼3.5 km/s) much greater than gravity waves (<20 m/s), near-coastal seismometers effectively sense microseisms at the time of their generation, and thus reflect the spectral characteristics of the gravity wave field at that time. The simultaneous occurrence of the Perfect Storm and Hurricane Grace provides an excellent opportunity to study the variation of DF microseism levels and estimate their generation areas at a time of extreme wave activity from multiple sources. Knowledge of the generation areas that provide principal contributions to microseism levels are important for identifying optimal ocean bottom seismic monitoring sites, and are also of concern for land based instruments sensitive to small vibrations such as large aperture laser interferometers.

Figure 1.

Locations of NOAA buoys (solid circles) and inland seismometer site (HRV, solid triangle) in eastern Massachusetts. Bathymetric contours are in meters below sea level. Note the rapid decrease in water depth from 2000 to 300 m near buoy 44011. The storm tracks (green lines) from NOAA satellite observations for both the storm (the Perfect Storm to the north) that became Unnamed Hurricane #8 and Hurricane Grace (to the south) are shown, with the stars at 6 hr intervals. Locations of peak winds are indicated (in orange) for each storm.

[3] The double-frequency microseism mechanism theory is well established (see Kibblewhite and Wu [1991] for a review), with Longuet-Higgins [1950] showing that DF microseism amplitudes are proportional to the product of the amplitudes of the opposing wave components producing them. Although the characteristics of microseisms have been investigated by numerous studies (see Webb [1998] and Orcutt et al. [1993] for reviews), the dominant source areas and propagation characteristics are uncertain because of the lack of multiple, concurrent, colocated gravity wave and seismometer data from sufficiently separated seafloor locations away from coastlines and islands. Crustal Rayleigh waves propagate with little attenuation across oceanic and continental regions [Dorman et al., 1991], and can potentially contribute significantly to microseism levels outside the generation area. Land-based seismometer array studies of microseism propagation from the open ocean give conflicting results, with Haubrich and McCamy [1969] detecting no Rayleigh wave microseism energy arriving from the open ocean while Cessaro [1994] located DF microseism source areas that appear to be generated beneath storms in the deep ocean as well as near the coast. While the dominant wave directional spectra can be estimated from buoy measurements, the opposing wave spectra and the area of wave–wave interaction are generally uncertain. The presence of extreme waves from the Perfect Storm and Hurricane Grace should have provided high amplitude opposing swell components, potentially causing very high amplitude DF microseism generation in the open ocean.

[4] In addition to double-frequency microseisms, “single-frequency” or primary microseisms are generated only in shallow water at gravity wave frequencies, producing a comparatively low amplitude spectral peak in the [0.04, 0.09] Hz band [Haubrich and McCamy, 1969]. Although not well understood, possible mechanisms for coupling ocean wave energy directly to the solid earth include the interaction of the ocean wave pressure signal with the sloping seafloor and/or the breaking of waves at the shoreline [Hasselmann, 1963]. Primary microseism levels depend on the gravity wave wavelength and wave amplitude as well as the length of shoreline impacted. Gravity waves begin to interact with the seafloor when the water depth, h, is less than half the deep water wavelength, L, determined using the Airy linear wave theory approximation as L = gT2/2π, where g is the gravitational acceleration and T is the wave period. L is about 350 and 624 m for 15 and 20 s waves, respectively. Bathymetry along the New England coast (see Figure 1) indicates that water depths less than 200 m extend 200–300 km from the shore, providing a potentially large area for bottom interaction and primary microseism generation from long period swell. Detection of concurrent associated primary and DF microseisms is important because this indicates shallow water, nearshore generation of both signals.

[5] Some DF microseism energy is undoubtedly generated almost continuously throughout the oceans and along coastlines. The goals of this study are to determine (1) whether dominant DF source areas exist and can be localized, and (2) whether wave–wave interactions away from coastlines generate DF microseisms that can be observed on land. The correlation of the microseism spectrum with the gravity-wave spectrum along the East Coast during the Perfect Storm is used to identify dominant microseism source areas by comparing buoy data from several locations with broadband seismometer data from seismic station HRV in eastern Massachusetts (locations in Figure 1) during October 26 to November 3, 1991. Broadband seismometer data were obtained from the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC). Hourly buoy measurements of wave and wind parameters are available from the National Oceanic and Atmospheric Administration (NOAA) National Oceanic Data Center (NODC).

2. Correlating the East Coast Wave Climate During the Perfect Storm With DF Microseism Levels on Land

[6] The wave climate during the Perfect Storm developed as a broad-scale, deepening low moved off the Northeast coast of the United States and Nova Scotia on October 28, 1991, becoming a huge cyclonic storm system initially centered near Sabre Island on October 29 (Figure 1). Along the New England coast, the wave climate associated with this low was initially dominated by local seas generated by winds from the north. Characteristic of local sea development, the wave energy at the onset of the storm at the end of October 28 at buoys 44011, 44008, and 44013 (Figures 2a–2c) was initially highest at shorter periods (higher frequencies), with the energy in the wave spectrum at longer periods (lower frequencies) progressively increasing as winds persisted through October 29. Intensification of the steady northerly winds on October 30, 1200 UT to about 25 m/s, in conjunction with long period swell arriving from the direction of the approaching center of the Perfect Storm from the east, resulted in significant wave height (the height of the highest 1/3 of the waves, Hs) of nearly 13 m at buoy 44011.

Figure 2.

Gravity wave spectral variation from October 28 to November 3, 1991, along the East Coast. Spectral values outside the ranges shown are set equal to their respective bound. Temporal tickmarks are at 12 hour intervals. More northern buoys off the New England coast are on the left (a–e from top to bottom), while those progressively further south (f–j from top to bottom) are on the right. See Figure 1 for locations. Dashed lines overlaying a–c and h–j are estimated swell arrival lags, with the shallower slope at h–j reflecting the greater propagation distance between those buoys.

[7] In contrast to local sea development, swell results when waves propagate out of the wave generation region and is characterized by the lowest frequency energy arriving first as a consequence of gravity wave dispersion. Long period swell arriving after 10/30 1200 UT is inferred to have a dominant east-to-west propagation direction from successive arrival lags of the lowest frequency energy between 44011, 44008, and 44013, (indicated by the dashed line overlaying Figures 2a–2c), and lags of peak wave height at these buoys (see Figure 4a below). Similarly, general north-to-south swell propagation along the East Coast for swell originating near the location of the Perfect Storm peak is inferred from successive arrival lags between 41001, 41002, and 41010 (indicated by the dashed line overlaying Figures 2h–2j) on 10/31. Much lower wave energy is observed at 44025 (at about the same distance from the storm track and in similar water depth as 44013) and 44009 (Figures 2e and 2f, respectively), probably related to swell beam width and fetch orientation since 44014 to the south of 44025 has substantially higher wave energy (Figure 2g and see Figure 4 below). Wave energy from Hurricane Grace must also have contributed to the wave heights observed on October 30, although, comparing wave spectra, northward propagating wave energy from Hurricane Grace cannot be identified.

Figure 4.

Band-limited significant wave height, Hs, determined from wave spectra during the Perfect Storm measured at buoys along (a) the New England coast and (b) the mid-Atlantic coast. (c) Corresponding seismic Hs determined for the vertical seismometer at HRV (green line) and ANMO (brown line). Respective Hs integration bands are indicated. All Hs data were low-pass filtered to remove data glitches and other noise. Note the similarity of Hs variation for buoy 44014 in (Figure 4b, blue line) with those in Figure 4a. Cross correlation of these data give the R2 functions in Figure 5.

[8] The general relationships between the wave climate and the microseism spectrum can be identified by comparing the temporal variation in spectral levels. Vertical broadband seismometer data from seismic stations HRV, located about 150 and 60 km inland from the coast to the south and east, respectively, and ANMO, located at Albuquerque, New Mexico, about 3125 km from the New England coast, show the variation in microseism levels during the Perfect Storm (Figure 3). The seismometer data were processed using standard Fourier methods. Hourly averages of resulting power density spectral estimates were obtained to correspond to the buoy sampling interval. The seismic levels at HRV and ANMO show a primary microseism peak near 0.055 Hz (n1) and DF microseism peaks near 0.11 and 0.16 Hz (n2 and n22, respectively) at 10/30 1600 UT. Decreasing local wind speed and/or dispersed swell arriving from the east result in the wave spectrum shifting to higher frequencies, causing the DF energy to also trend to higher frequencies near n3. Annotations in Figure 3a also apply to Figure 3b at the same time-frequency locations.

Figure 3.

Microseism vertical component power spectral variation during the Perfect Storm at inland stations (a) HRV in eastern Massachusetts and (b) ANMO at Albuquerque, New Mexico. Spectral values outside the ranges shown are set equal to their respective bound. Temporal tickmarks are at 12 hour intervals. Arrows designated N (north) and S (south) in Figure 3a refer to inferred generation areas shown below in Figure 6. Energy concentrations in Figure 3a designated n1 and n2, and s1 and s2, identify primary and associated DF microseisms. These signals, and n22 and n3, are discussed in the text. Note that similar microseism energy concentrations to those identified in Figure 3a are also observed at ANMO in Figure 3b. Annotations in Figure 3a also apply to Figure 3b. The lower-frequency bound for relatively high DF energy from the local seas is indicated by the dashed lines.

[9] The pattern of spectral variation is very similar at HRV and ANMO, suggesting a common source. Decreased spectral levels at ANMO result from cylindrical spreading, scattering and intrinsic attenuation, with the relative drop in DF microseism levels greater than that of the primary microseisms consistent with frequency dependent attenuation. Although less distinct, energy concentrations corresponding to those identified at HRV are observed at the same time and frequency at ANMO. Wave–wave interactions from locally generated seas from the intensified northerly winds on October 30 most likely dominate energy near n22, with the arrival of long-period westward propagating swell from the Perfect Storm primarily causing the n1 and n2 energy concentrations. A rough estimate of the lower-frequency bound for DF energy from the locally generated seas is indicated by the dashed lines in Figure 3. Note the decrease in frequency from October 28 to 29 as the local seas develop. This bimodal distribution of DF energy from local seas and swell is clearly observed at ANMO. Because the primary microseism mechanism favors the generation of low-frequency signals [Hasselmann, 1963], primary microseisms associated with n22 DFs on October 30 have lower amplitudes than n1 and are not as clearly identifiable. Thus high primary microseism levels are more closely associated with the arrival of long-period swell than with locally generated seas.

[10] The spectral energy variation of DF microseisms at HRV (Figure 3a) closely follows the wave spectral density pattern at nearshore buoys 44011, 44008, and 44013 (Figures 2a–2c), with the seismic microseism levels at twice the ocean wave frequencies correlating with corresponding gravity wave energy. The highest wave energy levels along the New England coast have nearly a one-to-one correspondence with the highest microseism levels at both HRV and ANMO. Thus nearly all of the observed temporal variation of DF spectral levels during the Perfect Storm can be explained by wave activity on the New England continental shelf. Sustained winds near 20 m/s from a northerly direction persisted from October 29 0000 UT to October 31 0600 UT at open ocean buoys 44011 and 44008, requiring a fetch of about 400–500 km to generate 15 s waves [U.S. Army Corps of Engineers, 1984]. Longer fetches are required to generate longer-period waves at a given wind speed. Consequently, because both long-period wave development is fetch-limited to the west of 44011 and the wind direction was not favorable for generating eastward propagating swell, most wave energy opposing the dominant long period Perfect Storm swell propagating from the east (that generate n2 DF signals) must result from shore reflected/scattered wave energy. Similarly, because winds generating local seas were steady from the north and there is no coastline south of buoys 44011 and 44008, shore-reflected/scattered wave energy near Cape Cod (in addition to ambient seas) may also provide opposing components for nearshore generation of a substantial portion of the n22 DF energy associated with these shorter-period waves.

3. DF Microseism Source Area Localization

[11] Storm meteorological and wave propagation considerations suggest that it is unlikely that winds from the Perfect Storm itself could generate opposing waves for DF microseism generation in the open ocean having the spectral time histories observed in Figure 3. The absence of DF microseisms associated with wave activity near the location of Hurricane Grace prior to the development of the Perfect Storm supports this contention. Note that although Hurricane Grace's time history indicates that extreme waves must have been generated prior to October 28 1200 UT (Figure 1), elevated DF microseism levels comparable to those during the Perfect Storm were not observed at either HRV or ANMO when wave energy was comparatively low along the East Coast (compare Figures 2, 3, and 4 from October 28 0000 to 1200 UT). Also, because gravity waves are dispersive, it is unlikely that opposing wave energy from both the Perfect Storm and Hurricane Grace would generate DF microseisms in the open ocean that have the same spectral variation as that observed at the New England buoys and HRV. Thus, because primary microseisms can be generated only in shallow water, the concurrent observation of primary and associated DF microseisms (n1 and n2, respectively, Figure 3) having similar time histories indicates nearshore generation of both of these signals.

[12] The variable DF microseism source area, resulting from changing wave climate conditions coupled with gravity wave propagation characteristics, makes the temporal resolution of the inherently emergent microseism signal onset uncertain. Some of the DF energy observed at HRV likely results from DF microseisms generated at multiple New England near-coastal locations, with the expectation that DF generation at the nearest coastline, i.e., near buoy 44013, would most likely be dominant. However, the similarity in spectral variation at buoys 44008, 44011, and 44013 with DF energy at HRV makes the identification and the extent of a dominant near-coastal source area uncertain.

[13] To estimate the size and location of the dominant DF microseism source area, the temporal relationship between gravity wave and DF microseism spectra is first quantified by cross-correlating Hs determined for both seismic and wave data in associated spectral bands. Hs is obtained from 4 m01/2, where m0, the band-limited zeroth moment of the spectrum, S(f), is given by m0 = image The integration limits, [f1, f2], for the seismic data are chosen as [0.09, 0.35] Hz, double the gravity wave [0.045, 0.175] Hz band. This excludes most primary microseism signals from seismic Hs.

[14] In general, the time histories of Hs at 44011, 44008, and 44013 (Figure 4a) correspond closely to the time history of seismic Hs at HRV (Figure 4c). Note that the time of the peak of seismic Hs at HRV corresponds most closely with the wave Hs peak at 44008 (Figure 4a, red line). Figure 5a shows the correlation coefficient, R2, as a function of lag for seismic Hs from vertical seismometer data at HRV with Hs at all buoys shown in Figure 1. A positive lag indicates that microseism levels at HRV lead the associated buoy Hs. R2 functions in Figure 5 show that the energy in the DF microseism band at HRV is generally well correlated with the gravity-wave Hs, with peak R2 > 0.7 from Cape Hatteras northward (Table 1). The HRV–ANMO R2 function is nearly symmetric about zero lag (Figure 5a, green line), consistent with a common, dominant gravity wave source. Note that Hs at HRV lags buoys 44011 and 44008 and leads 44013. This indicates that the dominant DF microseisms are generated after the westward propagating swell passes buoys 44011 and 44008, but before the gravity waves reach 44013. Although DF microseisms are undoubtedly generated near 44013, these correlations and lags are consistent with the location of the dominant DF source area near the southern Massachusetts coast and not at the coast closest to HRV.

Figure 5.

The correlation coefficient, R2, as a function of lag between band-limited Hs at HRV and gravity wave Hs at (a) northern and (b) southern east coast buoys indicated in the legends. A positive lag implies that the DF microseism levels at HRV lead the buoy Hs. The R2 function between HRV and ANMO is shown in Figure 5a (green line).

Table 1. Peak R2 between HRV and each buoy in Figure 1 and their associated localizations, ℒ

[15] The peak R2 between HRV and all buoys in Figure 5 are used as control points at each associated buoy location to estimate the distribution of correlation contours along the East Coast for waves from the Perfect Storm. Although the sparseness of the buoy distribution (i.e. gravity-wave field sampling) causes the estimated contours in Figure 5 to be poorly constrained, general relationships can be identified. R2 contours (Figure 6, green lines) show that the gravity-wave field and the HRV DF microseism spectrum are highly correlated from the New England coast to Cape Hatteras. R2 contours also show the effective decorrelation of the gravity-wave field from the Perfect Storm as a result of wave front spreading and dispersion during southward propagation from the wave generation region in the north, with the cross-correlation lags related to propagation time. Decorrelation of R2 is also due in part to the increased importance of wave energy from other sources as swell from the Perfect Storm becomes less dominant.

Figure 6.

Peak R2 contours (green lines) between HRV and Atlantic buoys (see Figure 5) and associated microseism localization contours (red lines) have maximum values of 0.9 enclosing the location of buoy 44008. Contours were estimated using GMT routines [Wessel and Smith, 1991]. Only those portions of contours constrained by at least one buoy within about 300 km are shown. Localization contours west of 41001 are less than 0.5 and are not plotted. Locations of NOAA coastal buoys (solid circles) and the HRV seismometer site (solid triangle) are also shown. Shaded near-coastal boxes, designated N and S, indicate inferred dominant generation areas for correspondingly designated microseism signals in Figure 3. The single bathymetric contour (light dotted lines generally paralleling the coast) is at 200 m below sea level.

[16] Because Rayleigh waves propagate at velocities much greater than gravity waves, correlation lags (associated with high R2) between seismic and gravity wave Hs are thus a measure of the temporal (and therefore spatial) separation between the DF microseism source area and the wave spectrum measurement location. Consequently, the DF microseism source area can be localized by letting •i2 be the peak R2 at a particular buoy and τi be the magnitude of the lag at the peak. Then the localization, •i, is obtained from

equation image

and then

equation image

Localization contours are then obtained using the •i (Table 1) as control points at their respective buoy location. The normalization max(l), determined for all li, causes the dominant source area to be centered at the buoy with max(l).

[17] Localization contours (Figure 6, red lines) have a maximum centered at buoy 44008 (highest R2 and smallest lag, Figure 5). However, considering that the wave energy at 44008 leads (and 44013 lags) the DF energy at HRV and that the dominant swell propagation direction is westward, this suggests that the dominant DF source area is nearer the southern Massachusetts coast than is 44008 (estimated as the shaded region designated “N” in Figure 6). The high R2 between HRV and ANMO at zero lag suggests that broadband seismometers at other locations more distant from the New England coast than HRV would also give similar localizations, although associated contours would probably be more widely separated as a result of somewhat lower correlation resulting from attenuation of the DF microseism signal. Note that although R2 contours greater than 0.7 (Figure 6, green lines) are observed at 44011 and as far south as Cape Hatteras, DF localization contours along the coast that account for the time-lag are small and are not shown.

[18] Although DF energy near 0.16 Hz (n3, Figure 3) propagating from the northern source area still dominates the microseism spectrum on October 31 2000 UT, primary (s1) and associated DF (s2) energy are also clearly observed at both HRV and ANMO (Figure 3). Similar temporal variation of wave spectra at buoys 41002 and 41010 (Figures 2i and 2j) to these lower-frequency primary and DF microseisms, together with the absence of corresponding long period wave energy at buoys elsewhere at that time, suggests that the source area for this microseism energy is south of Cape Hatteras. Noticeably lower DF energy is observed at both HRV and ANMO when high seas were present along the coast near buoy 44014 at about October 31 0800 UT (between N and S, Figure 3a). Note that the shoreline near 44014 just north of Cape Hatteras (Figure 6) is exposed to swell from the northeast. This suggests that the swell propagation direction along the coast near Cape Hatteras is not the most critical factor that causes relatively low DF microseism energy generation near October 31 1200 UT in Figure 3. However, the comparatively low DF levels observed may result because the relatively linearshoreline near Cape Hatteras provides significantly less scattered opposing wave energy for DF generation than the more irregular coastline of New England. Considering this apparent importance of irregular coastlines for DF generation and the swell propagation time from the vicinity west of 41002 to the coast, the coastal region south of Cape Hatteras with the most irregular shoreline (designated “S” in Figure 6, with associated signals identified in Figure 3a) is estimated as the most likely southern microseism source region.

[19] Note that the spectral levels for the southern source DF signals (s2) are only slightly higher at HRV (Figure 3a) than at ANMO (Figure 3b). Also note that, at ANMO (Figure 3b), s1 levels (propagating from region S) are slightly higher than n1 levels (propagating from region N). These relative amplitude relationships are consistent with less attenuation for the shorter propagation distance for Rayleigh waves from region S to both HRV and ANMO (HRV is about 40% closer to region S than is ANMO; region N is about twice the distance of region S to ANMO). There is no evidence to suggest that any of the DF microseism energy observed at either HRV or ANMO during the Perfect Storm results from wave–wave interactions more than about 300 km from coastlines. Furthermore, because these signals can be clearly observed at distances of more than 3000 km from coastal generation areas at ANMO, coastal microseism source areas can contribute significantly to noise levels on the ocean bottom at mid-ocean locations when high seas occur at proximal shorelines.


[20] The California Department of Boating and Waterways supported this research. Thanks to Fred Duennebier at the University of Hawaii for suggesting to look at seismic data during the Perfect Storm and comments. Thanks also to Reinhard Flick and Bob Guza at SIO for helpful discussions and for reviewing the manuscript. An anonymous referee made several suggestions that helped clarify the manuscript.