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Journal of Geophysical Research: Solid Earth

RESEARCH ARTICLE Multisensor, Microseismic Observations of a Hurricane 10.1002/2017JB014885 Transit Near the ALOHA Cabled Observatory Key Points: Rhett Butler1 and Jérome Aucan2 • Microseisms are observed and mapped from the interaction of 1Hawai’i Institute of Geophysics and Planetology, University of Hawai’i at Mānoa, Honolulu, HI, USA, 2Laboratoire d’Etudes Hurricane Lester near Hawaii and Typhoon LionRock near Japan en Géophysique et Océanographie Spatiale, Institut de Recherche pour le Développement, Toulouse, France • Dominant radial-vertical and transverse-vertical motions show retrograde particle motions Abstract The generation of microseisms is investigated at the ALOHA Cabled Observatory (ACO) north characteristic of Rayleigh wave fl • Observed transverse motions may of Oahu during the close passage of Hurricane Lester in September 2016. Sensors include a sea oor arise from a broad source region with ALOHA pressure gauge at ACO, KIP seismic data on Oahu, and nearby wave buoys. Examination of local scattering in the crust emplaced frequency-direction spectra from wave buoys and numerical wave model outputs confirms two separate at the Pacific-Farallon ridge microseism generation processes: At frequencies <0.225 Hz, the microseisms are generated by swells from Hurricane Lester and Typhoon LionRock traveling in opposite directions in the vicinity of ALOHA. At higher frequencies >0.225 Hz, microseisms are dominated by waves originating from Hurricane Lester. The Correspondence to: cross-over frequency (0.225 Hz) occurs where the ocean wave group velocity matches the Hurricane storm R. Butler, [email protected] track speed. Correcting for impedance, the spectrogram for energy at ALOHA closely correlates with KIP. When opposing swells meet at a distance from the Hurricane Lester and ACO, the resulting microseisms also spread geometrically in propagation to ALOHA and KIP, effectively equivalent to 1/R2. At the microseism Citation: Butler, R., & Aucan, J. (2018). peak, 4 September, the dominant motions of KIP are observed with retrograde particle motion characteristic Multisensor, microseismic observations of Rayleigh modes, in both the radial-vertical and transverse-vertical sagittal planes at distances of ≲400 km of a hurricane transit near the ALOHA from the eye. Otherwise, the energy on the transverse component is comparable to the radial component. Cabled Observatory. Journal of Geophysical Research: Solid Earth, 123, We hypothesize that the observed transverse energy arises locally: (1) from the extended microseism source 3027–3046. https://doi.org/10.1002/ region near ACO and (2) and from scattering by dipping structure and anisotropy embedded in the crust 2017JB014885 during emplacement at the Pacific-Farallon ridge. Received 17 AUG 2017 Plain Language Summary The close passage of Hurricane Lester near the Hawaiian Islands in Accepted 23 FEB 2018 September 2016 afforded an in-depth, close-up study of storm generation of the largest background Accepted article online 28 FEB 2018 Published online 20 APR 2018 vibrations observed planet wide. The observations at the ALOHA Cabled Observatory on the seafloor below the Hurricane, coupled with seismic sensors on Oahu, and ocean wave buoys off shore, present a detailed picture connecting the storm to the ocean and Earth. Wave interactions from a distant typhoon near Japan play an important role. Vibration energy levels observed on Oahu closely match those on the sea floor 100 km north of Oahu, where ALOHA Cabled Observatory is the world’s deepest seafloor observatory at 4,728 m depth. Characteristic vibrations generated radially from the Hurricane were observed, along with unexpected transverse motions perpendicular to the radial waves. This latter observation is consistent with a broad source region extending from Hurricane Lester and generating the vibrations. Evidence for substantial scattering of the vibrations in the ocean crust is inferred, due to slanting layers and directionally varying velocities, dating back nearly 80 million years ago when the sea floor was being originally being emplaced at a Pacific mid-ocean ridge. This hurricane transit yields new knowledge on how storms vibrate the planet.

1. Introduction Microseismic noise (which has displacement amplitudes on the order of microns) is the principal seismic noise source on Earth. The largest (double frequency or secondary) microseism generation mechanism (Longuet-Higgins, 1950 in the deep ocean is from nonlinear, opposing wave-wave interaction that forces the seafloor at double the wave frequency, generating seismic body waves and Rayleigh waves that propa- gate from the seafloor and are observed even at the farthest reaches from the oceans in central Asia (e.g., Kedar et al., 2008, and Ardhuin et al., 2011, for recent reviews). Secondary microseisms can be partitioned into three classes depending on the wavefield generating them (see Ardhuin et al., 2011, for a complete descrip- tion): Class I microseisms when they are generated by a single storm with a broad directional wave spectrum, fl ©2018. American Geophysical Union. Class II microseisms when they are generated by the interaction of an ocean swell with its own re ection off a All Rights Reserved. nearby coastline, and Class III microseisms when they result from the interaction of two different swells of

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Figure 1. Path of Hurricane Lester in the eastern Pacific near the Hawaiian Islands in August–September 2016. Inset panel shows the total Pacific track. The circles correspond to the location of the storm’s eye; their color indicates the wind speeds (see legend). Locations are shown every 6 hr UTC. Four sites discussed in text are indicated by pins: ALOHA (orange), KIP (yellow), and Buoys (green) 106 and 098, respectively.

identical frequency but opposing directions. Class III microseisms can be further divided into Class IIIa when the two opposing swells are from the same rapidly moving storm and Class IIIb when the two opposing swells are from distinct storms. In August–September 2016, Hurricane Lester emerged from the tropical Pacific south of Mexico and approached the Hawaiian Islands. In this instance, the Hurricane veered north of the Islands, and in doing so the eye of the storm passed within 75 km of the ALOHA Cabled Observatory (ACO), where it was recorded in full-fidelity in real time by a nano-resolution pressure sensor at seafloor station ALOHA and by the broad- band seismic station, KIP Kipapa, on the Island of Oahu. The close proximity (Figure 1) of the Hurricane to both seafloor and island sensors, as well as ocean wave buoys off Oahu, provides an unusual opportunity to test and verify the generation of microseisms close to a known source. The research approach focuses first upon the time domain data filtered in the microseism band, correcting for site impedance, and then follows with time-frequency domain analysis. The ALOHA pressure and KIP three-component velocity (KIP3) are normalized to a common metric, m/s. We use the radial distance (i.e., the radially directed horizontal component of motion) from the eye of Hurricane Lester to observations at ALOHA and KIP as the primary basis for explaining the waxing and waning of microseism amplitude. The microseisms observed at KIP are analyzed for the directionality of Rayleigh wave arrivals (both propagating radially and transversely), as well as for transversely polarized Love waves. We examine the relationship between the observed microseisms at ACO and KIP, on one hand, and observed and modeled wave spectra on the other hand to investigate the different mechanisms for generating double-frequency microseisms. Mechanisms for the quasi-equal balance of radial and transverse energy seen at KIP consider (1) a broad microseism generation area near KIP and (2) strong shallow crustal scattering. Finally, we conduct an analysis as to where elements of the ALOHA microseism time-frequency spectrum are generated.

2. Data Set The Hurricane Lester data set includes pressure data (kPa) from the ACO ALOHA Paroscientific nano- resolution, Digiquartz® pressure sensor, and three-component (Z, N, and E) velocity data (m/s) from the Streckeisen STS-2® Global Seismographic Network station, KIP Kipapa, on Oahu. KIP is located about

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1400 120 150 km due South of ALOHA. The closest approach of Hurricane Lester

110 1200 to Oahu occurred around 4 September. Data have been corrected for instrument sensitivity and response to SI units. Note that over the fre- 100 1000 quency band considered (about 0.01 to 1 Hz), the instruments have a flat response. Data are reduced to a common sample rate of 1 sample/s. 90 800 Pressure and three-component velocity data were collected from 80 600 ALOHA and KIP, respectively, sampled at 1 s in the time window 25 70 August through 16 September 2016. The digital data were corrected

Wind Speed, kt 400 Winds for instrument response to velocity (m/s). This is the native format for 60 Pressure the KIP STS-2. For ALOHA, pressure was converted from pressure in Distance from Hurricane, km Atmospheric Pressure, kPa ALOHA 200 KIP kilopascal to its equivalent in particle velocity, vp in m/s, 50 Buoy-098 0 P 9/02 9/03 9/04 9/05 9/06 v p ¼ cρ SEPTEMBER, 2016 where c = 1,500 m/s and ρ = 1,000 kg/m3. To separate the single (1F) Figure 2. 2–6 September 2016 on horizontal axis. Basic parameters for hurricane and double-frequency (2F) microseism bands in the time domain, we wind speed and atmospheric pressure (left scale) are plotted with the distances band-pass filtered the data with fifth-order elliptical filters (Matlab® ellip (right scale) for ALOHA, KIP, and Wave Buoy-098 from the hurricane eye. NB function) with 50 dB attenuation, 2 dB passband ripple), implemented ALOHA is closer than Oahu to the eye of the hurricane. If the microseisms are fi generated proximal to the eye, then KIP will be smaller simply due to the 1/R as a zero-phase digital lter. The 1F band is (1/16 1/10) Hz, and the 2F geometric spreading effect. NB the wind speed is dropping by a factor of two as band is (1/10 1/2) Hz. Eventually, we focused only upon the 2F microse- the Hurricane approaches ALOHA. isms as the 1F signal was insubstantial. The Hurricane wind speed, barometric pressure, and location of the SEPTEMBER, 2016 eye were downloaded from National Oceanic and Atmospheric 9/02 9/03 9/04 9/05 9/06 Administration (Brown, 2017), and the relevant data are plotted in 35 Figures 2 and 3. Frequency-direction wave spectra from CDIP buoys Hurricane speed 098 and 106 were obtained from the Coastal Data Information Wave group velocity Wave phase velocity Program (cdip.ucsd.edu). We also used the frequency-direction spectral 30 output from IOWAGA numerical wave model, extracted at 158 W 22.7 N, near station ALOHA.

25 3. Geometric Spreading Twice The proximity of the path of Hurricane Lester to ALOHA and KIP illus- 20 trates geometric spreading relationships for understanding what are the principal contributions to the observed microseisms. As the ocean wave swell propagates to a distance R away from Hurricane Lester, its 15 energy spreads and decreases as 1/R, (1/sin Δ° at large angular dis- Velocity, m/sec tances Δ°). Upon interaction with an opposing swell at R, energetic Raleigh wave microseisms are generated that propagate back—also 10 decreasing as 1/R—to the observation sites, ACO and KIP. Hence, when the microseism source is close to the observation sites, the geometric 5 spreading to and from the excitation site at distance R, the energy effectively decreases as 1/R2. Therefore, in consideration these dual, multiplicative geometric spreading effects (ocean wave and microse- 0 ism), the interactions of ocean swells creating microseisms from 0 2 4 6 8 10 12 14 16 18 20 Hurricane Lester are dominated by nearby interactions and prejudiced Wave Period, sec against distant generation. Nonetheless, these geometric spreading effects are to be distinguished from possible, concomitant changes in Figure 3. Apparent velocity (blue) of the hurricane eye ranges from 6 to 8 m/s the excitation source strength with distance. approaching/departing from ALOHA (Figure 1) from 2–6 September 2016. Ocean gravity wave phase and group velocities in deep water (red) are plotted versus wave period. NB where the wave group velocity, Ug, crosses the Hurricane 4. Envelopes of Microseisms speed, VH, the ocean waves match the Hurricane speed. When Ug < VH, at short periods, the waves lag behind the faster moving storm front. For Ug > VH, The energy envelopes of the Hurricane Lester passage near ALOHA and the long period waves lead the storm. KIP are shown in Figure 4. The rapid increase in microseism energy

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AB 2 × 10 -9 × 10 -11 ALOHA 06h 26m KIP3 2 1.8 07h 17m 6 1/R 1/R

/sec 1.6 2 5 1.4 1.2 4 1 3 0.8 0.6 2 0.4 1 1 Hour RMS envelope, m 0.2

9/02 9/04 9/06 9/02 9/04 9/06 September, 2016 September, 2016

Figure 4. The plots show in black the 1 hr root-mean-square envelope of velocity squared between 2 September and 6 September 2016. At ALOHA this is the particle velocity u_ 2; at KIP it is comprised by the sum (KIP3) of Z, NS, and EW jj envelopes, v2 v2 v2 : The colored dashed lines are 1/R fall-off rates from the peak values scaled to closest approach to Z þ N þ E the hurricane eye. The arrows show that the energy maxima occur before the closest approach of the eye, indicating ÂÃ that the locus of microseismic noise generation takes place about 7 hr in advance of the eye. For Hurricane Lester traveling at about 25 km/hr, this is about 175 km ahead of the eye, or the distance between successive locations shown in Figure 1. The KIP peak occurs about 1 hr 8 min prior to ALOHA, consistent with the times of closest approach in Figure 2.

observed at both ALOHA and KIP occurs very near to the hurricane eye’s closest approach, confirming that radial distance is a primary factor. However, careful measurement of the relative time of maximal energy and radial distance of the eye from ALOHA and KIP shows that the energy maximum occurs before closest approach (Figure 2)—the difference is about 7 hr. Hence, the microseism generation precedes the

Hurricane eye by about ¼ day. Since the Hurricane speed is V ~ 7 m/s (see Figure 3), the group velocity Ug of the waves generating the predominant microseism energy must be faster still. Filtering the ALOHA data into high- and low-frequency (LF and HF) component envelopes in Figure 5, we see that the LF components arrives first, as expected from group velocity considerations. 4.1. Impedance

10-9 The ALOHA and KIP Z envelopes have a similar form, but differ in ampli- 1.2 ACO LF 2F envelope tudes due to the mismatch of impedance—ρc, the product of density ACO HF 2F envelope and velocity—between the two sites. Amplitude is inversely propor- 1/R 2 1 tional to impedance. The impedance at ALOHA is a ρwc, where

/sec 3 2 ρw = 1,000 kg/m and the sound speed, c = 1,500 m/s. At KIP the impe- 0.8 dance is less constrained, but we can use the background noise as a guide. In principle, the background noise levels at ALOHA and KIP 0.6 should be nearly the same in the absence of local sources and when corrected for impedance. Measuring the average power in the microse- 0.4 ism noise over three days prior to Hurricane Lester (25–27 August), the amplitude ratio ALOHA/KIP3 is ~√16.5 ≅ 4.1, the square root of the

60 minute RMS envelope m 0.2 envelope ratios.

For ALOHA the sound speed, cw ≈ 1,500 m/s, and density 0 ≈ 3 9/02 9/03 9/04 9/05 9/06 ρw 1,000 kg/m . At KIP the density ρKIP is between 2,000 and 3 September, 2016 2,600 kg/m (Moore, 2001), and the compressional velocity of the uppermost crust is vp~3,700 m/s (Watts & Ten Brink, 1989). Since the Figure 5. The 2F power envelopes (1 hr root-mean-square) for ALOHA are band- microseisms are composed predominantly of Rayleigh waves, which pass filtered into high- (HF, green, 0.23–0.5 Hz) and low-frequency (LF, red, are primarily sensitive to the shear wave speed, we assume a Poisson 0.1–0.23 Hz) bands. The band separation at 0.23 Hz corresponds with the solid with cKIP≈vp=p3 2;140 m=s . The impedance ratio is then observed spectral null (see Figure 11) where the group velocity of the ocean ¼ 6 waves matches the Hurricane speed (see Figure 3). The 1/R curve is plotted (ρc)KIP/(ρc)ALOHA = 4.1,ffiffiffi with (ρc)ALOHA = 1.5 × 10 rayl. Therefore 6 relative to closest approach. (ρc)KIP = 6.1 × 10 rayl. Using ρKIP = 2,600 and cKIP = 2,140,

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×10-9 6 (ρc)KIP = 5.5 × 10 rayl, which is within 10%. Correcting for impedance 2 ALOHA and distance, the ALOHA and KIP energies plotted in Figure 6 are KIP3 1.8 remarkably similar. This correspondence is all the more striking, since 2 1.6 KIP measures the propagating microseisms, whereas ALOHA measures /sec

2 both the propagating microseisms plus the in situ pressure exciting 1.4 the microseisms. 1.2 4.2. Energy Quaternion 1 At ALOHA, we have measured in Figure 6 the microseism energy of the 0.8 2 scalar pressure wavefield, P = ES, and at KIP the energy of the vector 0.6 2 2 2 wavefield, x_ !i y_ !j z_ !k EV , as observed on the 0.4 þ þ ¼ 1 Hour RMS Envelope, m  three-component vectors, i ; j ;!k. Both E and E have peak energies 0.2 ! ! S V 9 2 2 at ~2x10À m /s . In considering the total energy observed Eq (a frac- 9/02 9/04 9/06 tion of the total radiated power), we have the contributions of scalar September, 2016 and vector wavefields. Having corrected for impedance mismatch and using the same SI units, the underlying scalar versus vector founda- Figure 6. The power envelopes (1 hr root-mean-square) for ALOHA and KIP3 are tion remains and poses the question: does ES + EV = Eq or does plotted for the arrival and departure of Hurricane Lester. KIP3 data are corrected for impedance and for relative 1/R distance from a microseism source 7 hr ES = EV = Eq. In other words, if ACO had a collocated, broadband seism- ahead of the eye (see Figure 4). Within the uncertainty of impedance parameters, ometer, a scalar hydrophone/pressure gauge, and three orthogonal the radiated 2F microseism energy of Hurricane Lester as observed at both vector hydrophones, would some of the sensors be redundant? That ALOHA and KIP is comparable. is, given the presence of a scalar hydrophone, are only two compo- nents of the three vector hydrophones necessary? Vector calculus does not answer this question, but its progenitor, the quaternions (Hamilton, 1969), has a clear answer. Consider a quaternion q p x_ !i y_ !j z_ !k , which is the sum of a scalar pressure p and ¼ þ þ þ 2 2 2 three-component velocity vector, x_ !i y_ !j z_ !k , where !i !j !k !i !j !k = 1. The norm þ þ ¼ ¼ ¼ À (squared length) of q is N q p2 x_ 2 y_ 2 z_2 NSq NVq , where Sq is the scalar portion of ¼ þ þ þ ¼ þ    q , and Vq is the vector component of q . Thus, E NSq p2 and E NVq x_ 2 y_ 2 z_2 . S ¼ ¼ V ¼ ¼ þ þ   Therefore, N q E E E . This suggests that neither the pressure wavefield nor the seismic wave- ¼ q ¼ S þ V field solely represent the full energy, rather the sum of the two norms is required. Of course, we have not measured the scalar (ALOHA) wavefield at the same place as the vector wavefield (KIP). This would require the installation of a broadband seismometer co-located with ALOHA, which has been proposed.

Nonetheless, we have observed that ES ≅ EV, and hence, the total energy may be approximately twice that of either independent measure.

4.3. Rayleigh Waves Rayleigh waves have been linked to microseisms since Lee (1932) as attributed by Jeffreys’s (1976); Mitra (1957) noted, “It is now well established that these microseismic waves (at least most of them) are Rayleigh waves which originate in the sea and have periods mostly lying between 2 sec and 10 sec.” Roever et al., (1959) analyzed the wave propagation along a fluid-solid interface as Stoneley and pseudo- Rayleigh waves. We have sought definitive evidence for the Rayleigh wave contribution in the microseism field generated by Hurricane Lester over the 3 day of approach and departure. Several means were attempted. Segmenting the data into windows (e.g., 1 hr), we looked for radial polarization between the hurricane eye and KIP as the storm approached, using both principal component analysis and singular value decomposition methods without success. Plotting the envelopes for radial and transverse KIP energies as Hurricane Lester approaches KIP in Figure 7, both components essentially overlay on another whether near or far from the hurricane eye. Note also in Figure 7 that surface waves observed at KIP from distant earthquakes do not show equiva- lent radial and transverse motion, even though their frequency bands are the same as the Hurricane Lester microseisms.

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NI NZ BFZ OK 4.4. Transverse Microseisms 5 1.8 This observation that the transverse energy at KIP from Hurricane 4 Lester 92° azimuth 1.6 Lester in Figure 7 is comparable to the radial is difficult to reconcile. 3 1.4 At 3 September 18 hr the transverse is larger than the radial; this may 2 be explained by the generation of microseisms ahead of the eye, where 1.2 -11 the apparent radial direction to KIP swings from west to east. For a 1 1 short interval the “transverse” component is now radial, generating x10 0 2 the Rayleigh waves. 0.8 /s 2 m 0.6 In principle, the pressure source (Hasselmann, 1963; Longuet-Higgins, 1950; Miche, 1944) produces only vertical stresses on the seafloor, and 0.4 energy is radiated in the radial-vertical (sagittal) plane. Even though KIP Z 1F KIP R2 0.2 omnidirectional in exciting seismic waves, a simple vertical force from KIP T2 fl the water on the sea oor does not excite transverse seismic waves (SH 0 A30 A31 S01 S02 S03 S04 and Love waves), given the tangential stress discontinuity at the August-September, 2016 liquid-solid seafloor interface. Further, Juretzek and Hadziioannou (2016) note, “For the secondary microseisms, no direct generation Figure 7. The horizontal components at KIP are rotated into radial (R) and trans- mechanism of Love waves from ocean waves is presently known. verse (T) directions—aligned with the azimuth to the eye of Hurricane Lester (Figure 1). In this frame, the KIP radial points to the mean direction (±5°) of Indirect generation has been proposed, such as conversion from Lester’s approach. For the horizontals only, their energy envelopes (R2 and T2) Rayleigh waves on the propagation path between source region and are plotted (right axis). Superimposed in green is the KIP vertical (Z) velocity the point of observation (e.g., Toksöz & Lacoss, 1968).” Even when we component (left axis) in the 1F band (1/16 1/10) Hz to clearly show earthquakes. admit to a broadly distributed source region around KIP wherein the From 4 September forward (not plotted), the azimuth rapidly shifts to the “radial” arrives omnidirectionally, none of these paths contain trans- northwest as the Hurricane passes. The impulses are earthquakes that show starkly varying polarizations, contrasting the concurrent, homologous microse- verse horizontal energy. Furthermore, we observe in Figure 7 that both isms. Whereas the radial and tangential energies track closely together for the “radial” and “tangential” energies at KIP together grow as 1/R— mircroseism signals, the earthquake polarizations on the horizontals do not suggesting omnidirectionality even at a distance. show such equality—the ratio of R2 and T2 varies with earthquake source mechanism (“beachball” gCMT solutions are shown above event). The green 4.5. Transverse Rayleigh Waves arrows imposed on the beachball mechanisms show the radial direction for each earthquake from KIP). Earthquake and magnitude key: NI, New Ireland, Mw 6.8; Even though the microseism source cannot generate Love waves, the NZ, New Zealand, Mw 7.1; BFZ, Blanco Fracture Zone, Mw 5.6; OK, Oklahoma, broader source region generating the microseism can admit transver- Mw 5.8. sely propagating Rayleigh waves arriving from back azimuths not radial to Hurricane Lester; that is, Rayleigh waves in the vertical-transverse sagittal plane. At the peak of the microseism KIP three-component signal in Figure 4, we plotted for the largest arrivals the apparent orbits of vertical-radial and vertical-transverse (sagittal) motion. Figure 8a shows the characteristic retrograde elliptical orbit characteristic of a Rayleigh wave. The polarization is “tilted” from the vertical, likely due to lateral variation in the crustal structure between KIP and the hurricane source, as well as lateral gradients (e.g., Yanovskaya & Roslov, 1989) and anisotropy (e.g., Crampin, 1975; Kobayashi et al., 1997). Retrograde-elliptical Rayleigh wave orbits are also seen in the vertical-transverse sagittal plane observed in Figure 8b but lack the distinctly inclined orbits seen in the vertical-radial sagittal plane.

π By correcting for the Rayleigh wave =2 phase shift between vertical and horizontal, the elliptical motions are transformed into rectilinear motion, as shown in Figure 9a. In order to localize when the microseisms show the characteristic Rayleigh wave polarization at KIP, we segment the KIP record into 30 min windows during the approach and departure of Hurricane Lester and perform linear model regressions on the orthogonal radial and transverse data sets. This analysis is shown in Figure 9b. The correlation coefficient r2 serves as the measure of polarization, with r2 = 1 being perfectly correlated in the sagittal plane. High values of cor- relation (r2 > 0.5) are observed only near closest approach. Only when the Hurricane eye is near to KIP does the sagittal motion manifest clearly: for the radial motion, at a distance R ≤ 300 km, and for transverse motion, R ≤ 400 km. However, unlike the radial motions, the sign of the transverse correlation coefficient changes near closest approach to KIP. This sign change may be ascribed to the change in propagation direc- tion for the transverse data from Figure 9a. As Hurricane Lester makes closest approach, the radial correla- tion is maximum, and the transverse motions swing from propagation in the ( ) transverse to (+) direction À

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AB1.5 8 1

-5 4 0.5 x 10

0 0

-4 -0.5 KIP Z m/sec

Propagation -8 -1 Propagation

-8 -4 0 4 8 -1.5 -1 -0.5 0.50 1 1.5 KIP Radial, m/sec x 10 -5 KIP Transverse, m/sec x 10 -5

Figure 8. Polarization of the Hurricane-generated microseisms observed at KIP plotted near closest approach—times indi- cated in the figure that follows. (a) The radial and vertical components of motion (30 s duration) exhibit the retrograde elliptical particle motions characteristic of Rayleigh waves—a clear example of Rayleigh wave motion being generated by the Hurricane. The radial (+) direction “points” toward the hurricane eye near closest approach and maximum power. The four orbits in 30 s correspond to a period of ~7 s. (b) The transverse and vertical components of motion at KIP also show the retrograde elliptical particle motions characteristic of Rayleigh waves. These motions orbit in the vertical-transverse sagittal plane and are not Love waves. Rather, propagation is transverse (+), orthogonal to the radial direction and toward a southeast azimuth. The eight orbits in 30 s correspond to a period of ~4 s. The nearly simultaneous observations of Rayleigh-wave microseisms from orthogonal directions are strong indication of an extended area of microseism generation proximal to Oahu. NB other examples also show significant inclination of the Z-radial Rayleigh orbits, and smaller inclination for Z-transverse orbits.

(facing the radial direction, transverse is positive to the right and negative to the left). Before this phase change, the transverse motion followed the same trajectory as the radial in Figure 8a.

4.6. Scattered Love Waves We have not observed actual Love waves in this study, as Rayleigh waves contribute in all directions. Nonetheless, we cannot rule out their presence, since horizontal transverse energy is substantial from dis- tances beyond about 400 km. Love waves attributable to microseisms have been clearly observed before. Tanimoto et al. (2015) note, “Using a colocated ring laser and an STS-2 seismograph, we estimate the ratio of Rayleigh-to-Love waves in the secondary microseism at Wettzell, Germany, for frequencies between 0.13 and 0.30 Hz. Rayleigh wave surface acceleration was derived from the vertical component of STS-2, and Love wave surface acceleration was derived from the ring laser. Surface wave amplitudes are compar- able; near the spectral peak about 0.22 Hz, Rayleigh wave amplitudes are about 20% higher than Love wave amplitudes, but outside this range, Love wave amplitudes become higher. In terms of the kinetic energy, Rayleigh wave energy is about 20–35% smaller on average than Love wave energy. The observed secondary microseism at Wettzell thus consists of comparable Rayleigh and Love waves but contributions from Love waves are larger. This is surprising as the only known excitation mechanism for the secondary microse- ism, described by Longuet-Higgins (1950), is equivalent to a vertical force and should mostly excite Rayleigh waves.” If we cannot change the source excitation to produce the horizontal transverse energy, we must consider the path from the source to KIP. The lack of distinguishable contrast between radial and transverse motions (for R ≳ 400 km) suggests that there may be substantial scattering of the energy. Nonetheless, the earthquakes in Figure 7 do not show a similar character, even though (1) the frequency bands (0.1–0.5 Hz) are the same and (2) the earthquake paths are much longer (hence, more scattering). This suggests that the microseism scatter takes place near the source. Two issues are unclear: (1) even though the frequency bands are the same, the wavelengths may be different, depending upon the group velocity, and (2) the microseism arrivals likely contain both fundamental and

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π Figure 9. (a) For Rayleigh waves the vertical component is =2 phase-shifted from the horizontal components (blue radial and red transverse). By correcting this phase shift via Hilbert transform, the retrograde-elliptical particle motion seen in Figure 8 is converted to rectilinear motion, and measured by regression of independent Z and Hilbert (R) variables. Similarly, Rayleigh motions in the transverse-vertical sagittal plane are measured (red). The 30 min time window at the peak correlation time (green dot for radial, green circle for transverse) contains the Rayleigh wave orbits in Figure 8. Propagation directions are indicated for the radial and transverse coordinate system. The radial component is directed 6 hr in advance of the hurricane eye (see Figure 4) where microseisms appear to be generated. (b) The temporal variations of the correlation coefficient, r2, for vertical-transverse and vertical-radial sagittal motions. For the radial (blue) the correlation increases rapidly from 3 September at 18 hr, and is maximal at closest approach, but the Z and radial components become effectively uncorrelated (r < 0.2) before 3 September and on 5 September. The transverse correlation also grows as the Hurricane approaches. However, near closest approach the direction of transverse propagation swings rapidly from westward to eastward when the radial correlation is peaking.

higher overtone modes (e.g., Brooks et al., 2009; Toksöz & Lacoss, 1968), and may be dominated by Stoneley/Scholte interface waves (Schreiner & Dorman, 1990). Butler and Lomnitz (2002) proposed that T-phases at the H2O site are seismoacoustically coupled to the seafloor via low, shear-wave-velocity (ß < 1,500 m/s) sediments. Hence, the microseisms may reflect branches of the system of normal modes that differ from the fundamental modes (Rayleigh and Love) associated with global earthquake surface waves. Measurement of the microseism group velocity at ALOHA would be very helpful in sorting this out.

4.7. Transverse Hypothesis: SV-SH Scatter in the Oceanic Crust Whether as Rayleigh or Scholte-Rayleigh modes, the excitation of 2F microseisms at the seafloor nevertheless

generates only motion in the sagittal plane. The scatter of energy from SV (vertical) into SH (horizontal) requires either dipping structure (i.e., surface normal is not vertical) or anisotropic structure or both (e.g., Langston, 1977; Levin & Park, 1997). A possible explanation may be found looking 85 Myr ago when the crust of the lithosphere was being emplaced at the now-subducted Pacific-Farallon ridge. The crust is emplaced and extended in normal faults that result in faulted crustal structure dipping (generally) toward the spreading axis, and a system of abyssal hills parallel to the axis. Detachment normal faults are clearly observed in marine seismic surveys (e.g., Ranero & Reston, 1999; Reston & McDermott, 2011; Reston & Ranero, 2011), and their origin and generation have been broadly discussed (e.g., Carbotte et al., 2003; de Martin et al., 2007; Gudmundsson, 1992; Han et al., 2016; John & Cheadle, 2010; Schouten et al., 2010; Schroeder et al., 2007; Searle et al., 1998; Singh et al., 2006; Thatcher & Hill, 1995; White et al., 1990). The range of fault dips varies substantially: dips range from less than 20° to more than 40° where the majority dip toward the ridge crest (White et al., 1990), to 60°–>80° (Carbotte et al., 2003). Buck et al. (2005) state, “Abyssal-hill-bounding faults that pervade the oceanic crust are the most com- mon tectonic feature on the surface of the Earth.” Similarly, seismic anisotropy of P waves (up to 9%; Barclay & Wilcock, 2004) and S waves (up to 30%; Barclay & Toomey, 2003) near the ridge has also been well documented (e.g., Barclay & Toomey, 2003; Barclay & Wilcock, 2004; Dunn, 2015; Dunn et al., 2005; Dunn & Toomey, 2001). Furthermore, Butler (2003) observed

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Figure 10. (A) Cartoon showing the propagation of a microseism event at 34° to the strike of the upper crustal structure, and through the nonplanar, dipping (30–60°), anisotropic structure (8–30%). As the energy propagates through the lateral heterogeneity, SV is continuously converting into SH motions, and vice versa. After sufficient distance (≳400 km), the transverse and sagittal motions are homogenized into an amalgam of randomized polarizations. Only at close distances (R ≲ 400 km) from the apparent source can the “native” polarization excited by the pressure be observed (Figures 6–8). Illustration adapted from Olive et al., 2015. (b) Hurricane Lester’s path (dotted black-orange arrow) is superimposed on the paleo-spreading axis orientation (double white lines). The updip directions of paleo-faults created during spreading associated with the emplacement age of the Pacific plate are orthogonal to the paleo-spreading axis.

shear wave birefringence indicating polarization anisotropy of about 3%, with SV faster than SH in the uppermost crust at a 45° strike between abyssal hills at the H2O site (45 Myr crust) 1,900 km east of ACO. Over time, the crust “freezes” in place, leaving the dipping, (and possibly) anisotropic structure manifest, the seismic lithosphere thickens with age anisotropically (e.g., Blackman et al., 2002; Harmon et al., 2009), and the seafloor is covered with sediments (Figure 10a). Near Hawaii the seafloor age is ~85 Myr, with a half- spreading rate of 30–60 mm/year at its formation (Müller et al., 2008). In Figure 10b the paleo-spreading axis near ACO is shown (parallel to the double lines); the updip (ridge facing) directions of the buried abyssal hill faults—remnant from their formation at the Pacific-Farallon ridge—are orthogonal. We see that sagittal-

oriented Scholte waves (SV) will propagate both at large angles to the spreading fabric and internal anisotro- pic dipping structure (Figure 10a). Both of these features will scatter SV into SH. The observation of transverse energy in the Hurricane Lester microseisms, and this structural interpretation, may also serve as a hypothesis for understanding other transverse energy observations in the oceans, for example, seismoacoustic T waves (Butler, 2006) and Po/So lithosphere propagation (Butler & Duennebier, 2000; Cessaro & Butler, 1987).

4.8. Geometric Spreading Redux We conclude our envelope analyses by comparing the observed peak power at KIP with other Global Seismographic Network (Butler et al., 2004) stations in the mid-Pacific: MIDW Midway Atoll, AFI Western Samoa, JOHN Johnston Atoll, and XMAS Kiritimati Atoll. Other island sites both south and west of these are dominated by closer, southern hemisphere storms. Each site has nearly identical STS-2 seismometers, which are corrected for instrument response to m/s. No correction is made for impedance; instead we measure the background noise levels at each site following the window of Hurricane Lester, subtracting from each site the energy not associated with Hurricane Lester. This yields a measure of the power fall off of the microseismic noise propagating from a source near Oahu. The envelope peaks decrease with distance. A linear regression 1.25 of the log energy with log distance gives indicates a fall off slope of about RÀ , slightly faster than 1/R. In principle, we might derive attenuation Q from the marginally faster fall off of the energy. However, we do not have a good constraint on the group velocity. Based upon theoretical models of Ewing et al. (1957) and Bagheri et al. (2015), respectively, the group velo- cities appropriate for 2–10 s Scholte waves (fundamental and first overtone) should be in the range ~0.75α to

α, where α = 1500 m/s and β =2α (i.e., Ug = 1,125 to 1,500 m/s); ~0.6β to β where β = 2,000 m/s (i.e., Ug = 1,200 to 2,000 m/s). Here α is the water velocity and β is an anisotropic shear velocity in the uppermost crust. By timing the maximum peak at the island sites, it is clear that the apparent group velocities from a source near KIP are significantly slower than 1,125 to 2,000 m/s—from 15 to 53 m/s at AFI and XMAS, respectively. The

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0.5 -2

0.45 AB -4

0.4 -6 0.35 / Hz ] -8 2 0.3 / s 2 0.25 -10 [ m

0.2 10 -12

Frequency, Hz 0.15 -14 0.1 Power, log -16 0.05

0 -18 A25 A27 A29 A31 S02 S04 S06 S08 S10 S12 S14 S16 A25 A27 A29 A31 S02 S04 S06 S08 S10 S12 S14 S16 Time (Month/Day/2016)

2 Figure 11. Spectrograms are displayed for (a) ALOHA and (b) KIP3. Both figures use identical colors in units of log10([m/s] /Hz). The KIP3 spectrogram sums the PSD contributions from the KIP vertical and two horizontal components, showing that the power measured on the seafloor at ALOHA is comparable to that measured at KIP on Oahu. KIP3 amplitudes are adjusted for impedance relative to ALOHA. Frequencies are shown from 0 to Nyquist (0.5 Hz), and the data are shown from 25 August through 16 September 2016. Hurricane Lester has its closest approach to Oahu around 4 September. Leftmost 1 ½ days of each display a pre-event “noise” sample. To the right of this noise sample, only data with signal to noise >2 are plotted; that is, the dark blue background encompasses all data with signal to noise ≤ 2. The sample bins are 512 s, and overlap by 50%. The correlation coefficient between ALOHA and KIP3 evaluates to r2~ 0.83 in the 2F frequency band (0.5–0.1 Hz) and time window 3–5 September. The ALOHA data show energy in the 1F band (1/16 to 1/10 Hz) that starts abruptly near 31 August, continuing una- bated through 16 September, but not observed in the KIP data.

sites closer to Typhoon LionRock, MIDW, and JOHN, have apparent group velocities of 180 and 380 m/s. This latter observation further suggests (1) possible distance dependence in the apparent group velocities or (2) Lester-LionRock ocean wave interactions west of KIP. The apparent group velocities may suggest the coupling of Scholte waves to very slow shear wave velocities in the sediments (e.g., Butler, 2003; Butler & Lomnitz, 2002).

4.9. Time-Frequency Analysis Having reviewed the time domain microseism data we turn to the time-evolution in the frequency domain through spectrograms. Figure 11 plots the entire time window from 28 August through 16 September. Key features are as follows: (1) KIP and ALOHA look very similar overall and are highly correlated (r2~0.83) in the 2F band near Hurricane Lester’s closet approach, (2) the low-frequency (<0.2 Hz) component in the 2F band shows velocity-dispersion of energy for 1–6 September, (3) the 2F band is separated by noise near 0.23 Hz, (4) the upper 2F range (>0.23 Hz) has its energy peak later than the lower 2F range, (5) the 1F band (<0.1 Hz) shows earthquakes (vertical lines) on both ALOHA and KIP data sets, whereas ALOHA shows an additional signal component starting at 31 August not observed at KIP; (6) a clear 1F microseism arrival is not evident above the pre-Lester noise level, 10–11.65 m2/s2/Hz.

5. Oceanic Origin of the Observed Microseisms Double frequency microseisms are generated by opposing wave trains so we investigate the different wave events that occur during our observation period.

5.1. Buoy Data We first analyze data from two directional wave buoys off the coast of the island of Oahu (Figure 1). The first buoy off Waimea Bay is open to waves coming from the west and north, while the other buoy, off Kailua Bay, is open to waves from the east and north. The data from the Waimea Bay directional wave buoy (CDIP 106; Figure 12a), shows a low-frequency (0.05 Hz) swell starting 1 September. The temporal increase of energy peak frequency is a typical sign of the arrival of a distantly generated swell. We attribute this swell to Typhoon LionRock near the Japanese coast (see Figure 13). The higher frequency (0.1–0.2 Hz) waves

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Figure 12. (a and b) Wave buoy spectrograms for locations near Oahu (Waimea and Kailua). Both data sets show ocean wave velocity dispersion. For Waimea with line-of-sight access to the swell coming from the north and west, the disper- sion is manifest starting at about 1 September at 0.05 Hz. For Kailua, the largest energy arrives with Hurricane Lester (closest approach September 4) and is dispersed after its passage. The frequency axis for the wave buoy data corresponds to the ocean wave swell. The locus of wave power at the Kailua wave buoy (0.125 Hz) nearly matches the loci of double-frequency microseism power seen at ALOHA (0.146 Hz) and KIP3 (0.142 Hz). (c) Spectrogram detail for ALOHA (Figure 11) is shown for the time window 2 September at 0 hr to 6 September at 0 hr UTC, plotting only data with signal to noise > 2. The double-frequency axis here corresponds to the microseisms and is aligned with the ocean wave frequency 2 2 axis. The color bar shows the PSD scale in log10([m /s ]/Hz). The arrow points out the correlation of the peak Kailua ocean wave energy with the peak ALOHA microseism energy.

observed from A31 to S03 at the buoy are from the local trade-winds. Waves generated by Hurricane Lester are observed at the Kailua Bay buoy CDIP 098, Figure 12b, starting September 03—well before the actual arrival of Hurricane Lester in the vicinity of the Island. Since both buoys are respectively close to the Western and Eastern shores of Oahu, they cannot individually measure two opposing swells trains of ocean origin. The Waimea buoy does, however, show a small amount of shore-reflected energy from the Typhoon LionRock swell. This interaction of the swell with its reflection of the North Shore of Oahu could generate Class II microseisms (Ardhuin et al., 2011).

5.2. Wave Model Results No in situ directional wave buoy is available at ACO so we used the out- put of a wave model (Rascle & Fabrice, 2013) to investigate the wave component in the open ocean directly over ACO (Figure 14) from the directional wave energy variance, F(f, θ). Consistent with observations at both Kailua and Waimea wave buoys, we can identify between S01 and S03 a low-frequency swell (13–17 s) from the WNW (attributed to Typhoon LionRock), and higher frequency waves (8–10 s) from a broad eastern quadrant (Figure 14). An easterly low frequency swell (13–17 s) is also observed (Figure 14) and attributed to waves gener- ated under Hurricane Lester that traveled outside the storm because their group velocity exceeded the storm translation speed. Figure 13. Path of Typhoon LionRock in August 2016. Dates where the eye is centered are noted. Red circles: typhoon winds ≥65 kt; yellow: tropical storm The bottom pressure fluctuations that generate microseisms can be winds ≥50 kt. The sea swell generated by Typhoon LionRock propagates east, calculated from frequency-direction wave spectra using equations 2 meeting the swell from Hurricane Lester near the ALOHA Cabled Observatory. and 3 in Ardhuin et al. (2011). Here we chose to calculate and display From 23 August until the typhoon’s eye crosses the Japanese coast, low fre- quency components of the swell that are less than 0.23 Hz meet and interact the microseism generation term, G(f, θ)=f · F(f, θ)·F(f, θ + π), to identify from Hurricane Lester near ALOHA. [Image: Digital Typhoon, National Institute of which frequency-direction bins are most responsible for microseisms Informatics, http://agora.ex.nii.ac.jp/digital-typhoon/]. generation (Figure 15). From S01 to S03, the microseism would be

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Figure 14. Polar representation of the ocean wave directional variance spectral density F(f, θ) in m2s/radian, from the IOWAGA numerical wave model, extracted at 158°W, 22.7°N, near station ALOHA (file http://glob_30m.w1580n227_2016_spec.nc). Azimuth is the direction (θ) that the waves are coming from, and the radial distance is the wave period (1/f). Low spectral colors are largest. As indicated by dots on each plot, the decreasing radii are at 8 s (outermost), 10, 13, 17, and 25 s. The F(f, θ) are plotted by date and time from the upper left corner—time increases from left to right, and date increases downward. The vertical axis label is the date (day/month) and time (hours GMT). In general, energy arising in the west-northwest comes from Typhoon LionRock, whereas the eastern quadrant arises from Hurricane Lester.

predominantly generated by opposing wave at ~17 s (~0.06 Hz) from a narrow range of directions around ESE and WNW. On S04, microseisms would be generated by waves <8s(>0.125 Hz) from a broad range of directions. The value of the second order pressure term (Fp3D) responsible for microseism generation (equation 2 in Ardhuin et al., 2011) is also available from the WWIII model. Near ACO (Figure 16a), the integrated low-frequency pressure spectrum is elevated both under and away from the Hurricane Lester toward ACO, while the high-frequency pressure spectrum (Figure 16b) is only elevated directly under the hurricane. The discrepancy in timing between model simulations and in situ data at ACO, KIP, and the buoy is likely due to the difficulties of the model to adequately reproduce the Hurricane Lester wavefield.

5.3. Wave Group Velocities and Storm Speed From Figure 3, the group velocity of ocean waves at 0.05 Hz (or 20 s) is ~15 m/s. On 27 August, the Waimea Buoy was ~7,000 km from Typhoon LionRock. At this distance, the swell would take about 5.4 days to get to Oahu, as observed in Figure 13. From this point forward, the swell from Typhoon LionRock—the typhoon now moving east and northward—continues supplying ocean wave energy to Oahu from the west at

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Figure 15. Polar representation of the microseism generation term G(f, θ)=f · F(f, θ)·F(f, θ + π), where F(f, θ) is the direc- tional variance spectral density in m2s/radian (i.e., Figure 14). The sources are periodic in π radians, representing contri- butions of the opposing azimuths in Figure 14. In this symmetry, we see the joint contribution of ocean waves interacting at ACO from Hurricane Lester and Typhoon LionRock. Plot labels and axes are same as Figure 14.

wave frequencies from 0.05 to 0.1 Hz. This is the primary source of waves opposing Hurricane Lester’s locally generated ocean wavefield in the same frequency band near station ALOHA. For higher wave frequencies (> 0.1 Hz), the Typhoon LionRock swell arrives too late. For these frequencies, the microseisms are locally generated or by the interaction of the swell from an earlier NE Pacific storm. We overlaid on the ALOHA spectrogram the times of arrival of waves from Lester and LionRock (Figure 17), in each frequency range, based on the respective storm position and wave frequency group velocities. We also sketched the microseism contributions (Figure 17) from six different wave-interaction geometries, illustrated in Figure 18. A common feature in this mapping (Figure 18i–vi) is the radial distance from the eye of Hurricane Lester (recalling prior geometric spreading considerations), where the storm’s velocity V > Ug, the ocean wave group velocity. Each time-frequency location in this mapping (ƒ < 0.225; Figure 17) represents (1) the ocean swell generated by Typhoon LionRock’s eye, (2) the ocean swell generated by Hurricane Lester’s eye, (3) the same ocean wave group velocity from each respective eye, and (4) either meeting at ALOHA or radially close to ALOHA. For Figure 18i, the symbols indicate the spread of times when the lower frequency components of the ocean swell interact nearest to ALOHA. At ~0.225 Hz V~Ug (Figure 18iv), the storm speed V equals the ocean wave group velocity Ug. In higher frequency bands, the waves from LionRock have not yet arrived, and there is little opposing wavefield, leaving a null in the microseism spectrum at ALOHA and KIP. As Hurricane Lester passes

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closest approach to ALOHA, the ocean waves now race ahead of the storm, creating the opposing wavefield increasingly distant radially from ALOHA (and KIP). For case Figure 17ii, the Typhoon LionRock and Hurricane Lester swells meet west of ALOHA; for case Figure 17iii, the opposing wave interaction occurs near the eye of Hurricane Lester (minimum distance, R) where the swell from Hurricane Lester is maximum. These interactions explain the dominant features of the microseisms for f < 0.23 Hz. In the case of the higher frequency (f > 0.23) Hz components of the microseisms, these are primarily generated by Hurricane Lester, since the slower group velocity ocean waves have not yet arrived from Typhoon LionRock. Here (Figure 18v) Hurricane Lester outraces its own ocean waves projecting forward (in the storm V direction), then creating an opposing wavefield projecting backward from the Hurricane. In addition, there are waves generated by Pacific storms to the northeast in mid-August and earlier that are only now arriving due to their slow group velocities (Figure 18vi). This ocean wave energy is also observed in the ocean wave azimuthal spectrum at both the Waimea (CDIP 106) and Kailua (CDIP 098) wave buoys. These different scenarios of microseism generations correspond with 2 2 Figure 16. Power spectral density of second order pressure (MPa m ), which other classification schema. The separation of the 2F (double fre- contributes to acoustic and seismic noise, integrated from (a) 0.04 to 0.11 Hz quency) band into short-period and long-period bands, SPDF and and (b) from 0.11 to 0.3 Hz. From the IOWAGA numerical wave model, LPDF (Bromirski et al., 2005; Davy et al., 2016), herein reflects ocean with seismic source terms (file GLOBAL05_2016_REFMAP/WW3-GLOB- 30M_201609_p2l.nc). The black line is the 7 m significant wave height contour, wave group velocities that are less than (cases v and vi), equal to (case which indicates the position of Hurricane Lester. The red line represents the iv), or greater than the storm velocity (cases i–iii). In the classification Hawaiian Islands’ coastlines; the black symbol is the location of station ALOHA. schema of Ardhuin et al. (2011), the interaction of swells generated by a single storm (Class I or IIIa) corresponds to our case v, whereas their interaction of swells from two different storms (Class IIIb) corresponds to our cases i, ii, iii, and vi. 5.4. Summary of Microseisms Origin The results above combine to support the existence of two nearly coincident mechanisms that explain the observed microseisms. First the interaction of long waves from Hurricane Lester with long waves (0.05– 0.1 Hz) from Typhoon LionRock generates microseisms in the 0.1–0.2 Hz band, between S03 and S05, with a peak early on S04 (Figure 5). This mechanism is described as class IIIb Microseism in Ardhuin et al. (2011). During the passage of Hurricane Lester over ACO, the ocean waves generated by Hurricane Lester alone excite microseisms in the 0.2–0.5 Hz band—either through the interaction of broadly directional wave gen- eration (Class I microseism) or through the interaction of opposing waves under a fast-moving storm where the storm speed matched the wave group velocity (Class IIIa microseisms). Further, the directional wave spec- trum of ocean wave buoys off shore of Oahu shows ocean waves arriving from NE Pacific with higher fre- quencies (>0.15) and slow group velocities (<5 m/s), which also interact with Hurricane Lester.

6. Discussion of Results in the Context of Prior Studies In this paper, we observe the microseism generation by an unusual interaction of waves from two tropical cyclones on opposite sides of the Pacific Ocean, with a unique combination of deep seafloor high-frequency pressure measurements, seismic data, and ocean wave data, all within ~100 km of the Hawaiian Hurricane Lester. Several microseism studies of cyclones been based upon waveforms recorded thousands of kilo- meters from a cyclone (e.g., Bromirski et al., 2005; Sutton & Barstow, 1990, 1996; Zhang et al., 2010). In relation to Hurricane Lester, the observation of separate long-period and short period band within the double- frequency microseism (Bromirski et al., 2005) is seen herein as the effect of the separation of the storms’ ocean wavefields being segregated into ocean wave group velocities either slower than or faster than the storm track speed. Applying our analysis approach, we offer a different perspective and interpretation of four prior studies of microseisms generated within the proximity of a cyclone,

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Chen et al. (2015) analyzed USArray seismic data (vertical component only) in the eastern United States from Hurricane Sandy propagating along the Atlantic coast through landfall near New Jersey in the frequency band of 0.1–0.25 Hz. The land-sited seismic stations ranged from ~350 km (closest approach to Florida) to 1,900 km (U.S. Midwest). The water depth along the east coast continental shelf (100 to 3,000 m) is substan- tially shallower that the Pacific. In discussing the microseism observations, Chen et al. (2015) invoke a model of the barometric pressure fluctuation just above the sea surface (generated by the hurricane), balanced by sea surface fluctuation of the two radially symmetric ocean waves traveling in opposite directions (outward and inward). In this physical mechanism, “the pressure at the bottom of the ocean is not the direct result of surface barometric pressure variation across the eyewall of the hurricane. Rather, it is caused by the nonlinear interactions of the ocean waves that are generated by surface barometric pressure variations across the hur- ricane eyewall.” However, there is another plausible source: the ocean swell generated by Hurricane Raphael east of Hurricane Sandy during the prior week as a source region of the opposing ocean wavefield. Sufri et al. (2014) studied the three-component USArray data set for Hurricane Sandy and offer additional insights. These include an apparent microseism source in the North Atlantic (Hurricane Rafael). However, they also concluded that “the microseisms from Sandy were generated mainly by a class-I mechanism,” that is, “ocean waves generated by a rapidly moving storm interact with trailing waves in the opposite direction.” However, whereas this mechanism (Figure 18v) for Hurricane Lester is observed for microseism frequencies >0.25 Hz, Sufri et al. (2014) invoke this for frequencies at 0.2 and 0.125 Hz (periods of 5 to 8 s). Measuring the storm track speed of Sandy (in deep water), the apparent velocity is ~4.9 to 5.3 m/s between 000 UTC 27 and 29 October. From Figure 3, we see that the ocean wave group velocity in deep water (>3,000 m) is ~7.8 to 12.5 m/s at 10 to 16 s period, respectively—significantly faster than the storm track. For the double-frequency mechanism, the ocean wave periods correspond to 5 and 8 s microseisms. This apparent contradiction sug- gests that wave-wave interactions between Hurricane Sandy and Hurricane Raphael contribute. Chi et al. (2010) studied Typhoon Shanshan—which approached Taiwan in deep water from the east before sharply both veering northward into the shallow waters (100 to <1,500 m) of the East China Sea—using land seismometers (TATO), ocean bottom seismometers (OBSs), and a wave buoy). The closest deep-water approach of the typhoon to an OBS was about 140 km. The velocity of the storm at closest approach (to OBS S004) was 3 to 4.2 m/s; hence, most of the generated wave energy (>5 s) traveled faster than the storm. Therefore, the interaction of leading and trailing waves (e.g., Figure 18v) suggests microseism energy >0.4 Hz. However, the closest OBS shows substantial microseism energy <0.4 Hz (peaked at ~0.28 Hz or 3.5 s), and maximum power when the typhoon enters shallow water. Typhoon Ioke had its closest approach to the Taiwan coast on at ~1800 UTC on 4 September at a distance of ~2,700 km. The ocean swell traveling at a group velocity 3.4 m/s would then be opposing the swell of Typhoon Shanshan. In deep water, this corre- sponds to a wave period of ~5 s (0.2 Hz) with double-frequency microseism frequency at 0.4 Hz. Therefore, the long-period component of Typhoon Ioke’s ocean swell arrived near Taiwan before Typhoon Shanshan’s arrival. The mean wave period of the nearby wave buoy OBS S004 peaks near closest approach at 8.6 s—cor- responding to a microseism double-frequency of 0.23 Hz. As there is no clear source of opposing wave energy for the Typhoon Shanshan low-frequency 2F microseisms, it seems reasonable to ascribe an apparent source due to Taiwan coastal reflection or propagation/reflection from the continental shelf of the East China Sea. Davy et al. (2014) and Davy et al. (2016) show observations of microseisms and ocean swell generated by tro- pical cyclones around Reunion Island in the Indian Ocean. In the 2F microseism band (3–10 s), normally attrib- uted to the interaction of broadly directional waves directly from typhoons, Davy et al. (2016) found lower frequency microseisms (7–10 s) attributed to the interaction of a swell with its own coastal reflection (com- pare with results of Chi et al., 2010, in prior paragraph). In one instance (during Tropical Cyclone Dumille in January 2013), Davy et al. (2016) describe the interaction between waves from the nearby Tropical Cyclone Dumille, with waves generated by a distant extra-tropical storm in the Southern Indian ocean.

7. Summary for the ALOHA Cabled Observatory Duennebier et al. (2012) suggested that the “background” microseismic level at frequencies below 0.4 Hz at Station ALOHA is (1) uncorrelated to local wind speeds and (2) attributed to the double-frequency microse- isms due to incident long period swells interacting with their nearby coastal reflection. Furthermore,

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Figure 17. The shaded portion of the microseism spectrogram for ALOHA during the arrival and departure of Hurricane Lester maps out the apparent generation mechanism and geometry with respect to ACO. The annotated symbols (Roman numerals keyed to Figure 18) outline the edges of characteristic regions connected in time by light shading. The basis for the opposing swell interaction (i–iii) is illustrated in the lower right inset: ocean wave group velocities, Ug, are matched between Lester and LionRock, linking the generation of the swell near its respective eye with the frequency and time observed at ACO. For the lowest frequencies (i–iii), the ocean wave group velocity exceeds the storm-track speed of Hurricane Lester, and opposing wavefields are generated by Hurricane Lester vis-á-vis Typhoon LionRock. The case (i) arrivals show energy converging at ALOHA from Hurricane Lester ( ) and from Typhoon LionRock ( ). For case (ii), microseisms propagating to (=>) ALOHA after Hurricane Lester’s closest approach are generated by LionRock–Lester interactions (-><-) both near to Hurricane Lester’s eye ( ) and in the Pacific west of ALOHA ( ). At a frequency of about 0.23 Hz for case (iv), the speed of Hurricane Lester matches the ocean wave group velocity at ALOHA, and no opposing wavefield is generated—hence the lack of microseism energy. The highest frequency arrivals (v and vi) are generated nearby Hurricane Lester, as the swell from Typhoon LionRock arrives at ALOHA after that from Hurricane Lester.

Duennebier et al. (2012) stated that opposing offshore long-period swell energy from different systems was a rare event, and should it happen, it would be due to the interaction of trade wind swell with an extratropical winter storm swell:

“Storms generate long-period swell that can propagate across the Pacific Ocean, and such swell from remote storms can oppose Hawaii regional swell energy (Ardhuin et al., 2011). This is rare, however, given the climatological winter storm tracks and trade wind patterns of the subtropics. Storm

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Figure 18. Cartoon illustrations show six cases for generating microseisms observed at ALOHA (red ), for a storm-track speed of Hurricane Lester (arcuate arrows, V ~ 7 m/s) and ocean wave group velocity Ug, at times T1 and T2. The circles represent Hurricane Lester’s eye. Waves (|||||) from Hurricane Lester are red (at T1) and blue (T2), whereas ocean waves (|||||) from Typhoon LionRock are black. Cases: (i) ocean waves converge on ALOHA simultaneously from both storms; (ii) after passing ALOHA, Hurricane Lester generates waves propagating into the Pacific, meeting the swell from Typhoon LionRock; (iii) the swell from Typhoon LionRock meets at Hurricane Lester’s eye after passing ALOHA; (iv) the group velocity Ug equals the storm-track speed V of Hurricane Lester—the wave energy “piles up” near the eye but there is no opposing wavefield as the swell from Typhoon LionRock arrives too late to interact; (v) when Ug < V, ocean waves generated by Hurricane Lester at T1 meet opposing waves generated by Hurricane Lester at T2; (vi) the swell from a storm in the northeast Pacific (|||||) meets with the swell from Hurricane Lester near ALOHA, similar to case (iii), but from a different direction. Cartoons were inspired by Obrebski et al. (2013).

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centers, where opposing wave energy at frequencies <0.1 Hz is most probable, rarely pass within 1000 km of the main Hawaiian Islands.” For example, since 1950, there have been only three hurricanes that traversed the proximal path of Hurricane Lester north of Oahu. These are Hurricanes Hiki in 1950, Jova in 1963, and Gil in 1983. In this study, we captured a possibly even rarer event where a strong local tropical cyclone—Lester—swell interacts with another long period swell generated by a tropical cyclone—LionRock—halfway across the ocean. Furthermore, since single frequency microseisms are generated at the coast, their apparent absence therefore further confirms our hypothesis of deep ocean generation of double-frequency microseisms. In this study the concomitant measurement of seafloor water pressure fluctuation, and the resulting microseismic waves, during this interaction episode between two tropical cyclones presents a close-up, new perspective of double-frequency microseism generation.

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