Identifying and Removing Tilt Noise from Low-Frequency (0.1 Hz ...

Bulletin of the Seismological Society of America, 90, 4, pp. 952–963, August 2000

Identifying and Removing Tilt Noise from Low-Frequency (!0.1 Hz) Seafloor Vertical Seismic Data by Wayne C. Crawford and Spahr C. Webb

Abstract Low-frequency (!0.1 Hz) vertical-component seismic noise can be reduced by 25 dB or more at seafloor seismic stations by subtracting the coherent signals derived from (1) horizontal seismic observations associated with tilt noise, and (2) pressure measurements related to infragravity waves. The reduction in effective noise levels is largest for the poorest stations: sites with soft sediments, high currents, shallow water, or a poorly leveled seismometer. The importance of precise leveling is evident in our measurements: low-frequency background vertical seismic spectra measured on a seafloor seismometer leveled to within 1 ! 10"4 radians (0.006 degrees) are up to 20 dB quieter than on a nearby seismometer leveled to within 3 ! 10"3 radians (0.2 degrees). The noise on the less precisely leveled sensor increases with decreasing frequency and is correlated with ocean tides, indicating that it is caused by tilting due to seafloor currents flowing across the instrument. At low frequencies, this tilting generates a seismic signal by changing the gravitational attraction on the geophones as they rotate with respect to the earth’s gravitational field. The effect is much stronger on the horizontal components than on the vertical, allowing significant reduction in vertical-component noise by subtracting the coherent horizontal component noise. This technique reduces the low-frequency vertical noise on the less-precisely leveled seismometer to below the noise level on the precisely leveled seismometer. The same technique can also be used to remove “background” noise due to the seafloor pressure field (up to 25 dB noise reduction near 0.02 Hz) and possibly due to other parameters such as temperature variations. Introduction Collins et al., 1998) and as part of local seismic networks (Romanowicz et al., 1998). A permanent broadband seismic station was installed on an underwater cable between Hawaii and California as part of the Hawaii-2 seafloor global seismic observatory (Duennebier et al., 1998). Low-frequency seismic measurements can also be combined with pressure measurements to study the oceanic crustal melt distribution under spreading centers using the compliance method (Crawford et al., 1999). Unfortunately, the typical background seismic-noise level is much higher at the seafloor than on land, especially at frequencies below 1 Hz. Although the noise levels observed over one week at the French OFM pilot seismic station (in a borehole beneath the Atlantic Ocean) approach the noise levels of good continental sites (Beauduin and Montagner, 1996), most seafloor seismic measurements have much higher noise levels (Sutton and Barstow, 1990; Webb et al., 1994; Romanwicz et al., 1998). Some of the highest noise has a tidal signature (Romanwicz et al., 1998), indicating that it is tied to currents. The noise may be diminished by burying the sensor beneath the seafloor or placing it in a

Broadband seismology is moving into the oceans. As the recording capacities of ocean floor instrumentation improve and as broadband seismometers become smaller and lower power, seismologists have begun measuring broadband (0.001–50 Hz) seismic signals at the seafloor to answer questions that cannot be addressed with land-based seismometers. For example, researchers used a 320-km-wide array of ocean-bottom seismometers to study the structure beneath the East Pacific Rise to 600-km depth using low-frequency teleseismic arrivals (the MELT experiment, Forsyth et al., 1998). In another recent experiment, Laske et al., (1998) measured Raleigh wave arrivals in the frequency band between 0.014 and 0.07 Hz across an array of seafloor differential pressure gauges to study lithosphere and upper aesthenosphere structure beneath the Hawaiian Swell. Permanent broadband seafloor seismic stations are needed to fill in the gaps in global seismic networks (Montagner et al., 1998), and several researchers have studied noise and the effects of seismometer emplacement for proposed permanent global seismic network stations (Montagner et al., 1994; Webb et al., 1994; Beauduin and Montagner, 1996; 952

Identifying and Removing Tilt Noise from Low-Frequency (!0.1 Hz) Seafloor Vertical Seismic Data

borehole (Montagner et al., 1994; Bradley et al., 1997; Collins et al., 1998), but this expensive option is probably only worthwhile for long-term or permanent stations. In this article, we show how to reduce the vertical seismic noise level at frequencies below 0.1 Hz after the data are acquired, by subtracting out the coherent signal from other channels such as the horizontal geophones. On the order of 25 dB of the vertical seismic noise in the band from 0.002 to 0.1 Hz can be caused by seafloor “compliance” or by tilt noise caused by seafloor currents. This noise can be removed in the frequency or time domain, by generalizing the technique described by Webb and Crawford (1999) to remove compliance noise. Long-period vertical-component noise at the Pacific seafloor should in theory be dominated by the seafloor deformation under the loading of very low-frequency ocean waves (infragravity waves). In the absence of other noise sources, the pressure and vertical displacement are nearly perfectly coherent at frequencies below about 0.05 Hz (the frequency limit depends on the water depth), as the seafloor deforms under pressure loading (Crawford et al., 1998). A differential seafloor pressure gauge is an indispensable part of a broadband seismic station, both to remove the deformation signal from the seismic background spectrum and to detect other noise sources. The coherence between the vertical seismic and pressure measurements indicates the quality of the low-frequency vertical-component data. Low coherence in the frequency band 0.002–0.04 Hz suggests that other noise sources, such as tilting due to ocean currents, dominate the “background” noise level.

The Experiment We deployed two pressure-acceleration sensors in 900m-deep water at 31"24#N, 118"42#W, at the outer edge of the California Continental borderlands. The sediments there are about 1-km thick, and the seafloor is relatively flat. The instruments, deployed 1-km apart, collected data from 10 September to 24 September 1998. Both instruments carry a differential pressure gauge (Cox et al., 1984)) and a seismometer. In one instrument, the seismometer is a Lacoste-Romberg gravimeter (Lacoste, 1967), in the other, a Streckeisen STS-2 three-component broadband seismometer. The gravimeter acts as a singlechannel (vertical) long-period seismometer (Agnew et al., 1976). Both instruments sample twice per second, giving an upper (Nyquist) frequency limit of 1 Hz. The important differences between the two instruments are that (1) the STS2 records horizontal and vertical motions, whereas the gravimeter measures only in the vertical, and (2) the gravimeter is much more precisely leveled than the STS-2. Both the gravimeter and the STS-2 are leveled using motorized gimbals to center positions determined in the laboratory. We use a precise leveling system for the gravimeter because the measured gravity is very sensitive to cross-axis tilt and because Lacoste-Romberg gravimeters become un-

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stable if they tilt too far off of the long-axis center. On the seafloor, the gravimeter levels to within 5 ! 10"5 radians of a laboratory-determined center value. We calculate this center value by searching for the maximum apparent gravity as a function of the instrument cross level. The apparent gravity is gcos(h), where g is the local gravity (approximately 9.8 m/sec2), and h is the cross-axis tilt from the vertical. The deviation in measured gravity equals g(1 " cos(h)) # 2gsin2(h/2). The centering precision depends on the microseism noise that overlies the gravity signal. In the laboratory, we can distinguish changes in apparent gravity as small as 8 ! 10"8 m/sec2, corresponding to a center value uncertainty of approximately 1 ! 10"4 radians. At the seafloor, the STS-2 levels to within 5 ! 10"3 radians of its center value. We estimated the STS-2 center value in the laboratory using a manufacturer-installed bubble level mounted on the seismometer base. The STS-2 horizontal and vertical channels are electronically derived from measurements of three geophones aligned in a cube-corner geometry, allowing the sensor to correct for slightly off-level emplacements. The sensor specifications suggest that the electronics correction is accurate to within 1 ! 10"2 radians. We will show that this inaccuracy can introduce significant vertical channel noise at the seafloor.

Seafloor Seismic Spectra We estimate the background seismic-noise levels on both instruments using spectra calculated from finite Fourier transforms (FFT) (Bendat and Piersol, 1986) of data windows visually inspected to avoid seismic events. The gravimeter and STS-2 background vertical seismic spectra include a microseism peak at frequencies above 0.1 Hz, a “compliance” peak centered at 0.02 Hz, and a red noise spectrum at lower frequencies (Fig. 1a, b). The STS-2 vertical channel is significantly noisier than the gravimeter at frequencies below 0.05 Hz. The STS-2 horizontal channels are more than 45 dB noisier than the vertical channel at frequencies below 0.1 Hz, but the vertical spectrum slope below 0.05 Hz is similar to the horizontal spectrum slopes (Fig. 1a). We will show that the STS-2 vertical-component noise below 0.05 Hz is caused by “leakage” of the horizontal noise due to the geophone being tilted from the vertical. We show how to remove this noise from the vertical data using its coherence with the horizontalcomponent noise. The “Unavoidable” Noise Source: Seafloor Compliance The spectral peak centered at 0.02 Hz on the vertical seismometer channels comes from the seafloor “compliance”, which is simply the seafloor deformation under pressure forcing from linear surface gravity waves. This pressure signal from these waves is only significant at frequencies corresponding to wavelengths longer than the water depth H: below 0.12 Hz for H $ 100 m, below 0.04 Hz for H $

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W. C. Crawford and S. C. Webb

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“Background” seismic autospectral densities and pressure-vertical coherence from two seafloor seismometer/pressure gauge packages deployed 1-km apart on the 900-m-deep seafloor. The shaded region in the spectra shows the bounds of seismic noise observed on land stations (Peterson, 1993). One sensor contains a threecomponent, Streckeisen STS-2 broadband seismometer (left panels). The other sensor contains a Lacoste-Romberg one-component (vertical) gravimeter (right panels). (a) STS-2 vertical and horizontal spectra. (b) Gravimeter vertical spectrum. (c) STS-2 pressure-vertical coherence. (d) Gravimeter pressure-vertical coherence.

1000 m, and below 0.02 Hz for H $ 4000 m. The compliance signal jumps up rapidly below this frequency and then decreases approximately proportionally to the frequency (Crawford, 1994). The compliance signal disappears behind noise from other sources at a low-frequency limit that depends on this noise level. In our data, the compliance peak rises above vertical background levels at frequencies between 0.004 and 0.05 Hz, peaking at approximately "130 dB referenced to 1 (m/ sec2)2/Hz, near 0.02 Hz. The compliance amplitude depends mostly on the strength of the pressure signal (which is approximately constant in the Pacific Ocean, but which may be weaker and more variable in the Atlantic; Webb, 1998), and the shear modulus of the underlying basement. For a given pressure signal, the deformation is approximately inversely proportional to the basement shear modulus, so the

compliance signal is much stronger at a sedimented site than at a hard-rock site (Crawford et al., 1998). The compliance signal can be used to study the shear modulus or shearvelocity structure of the sediments and crust (Crawford et al., 1999), or it can be removed to allow easier detection of other seismic signals (Webb and Crawford, 1999). The compliance signal is not seen on the horizontal channels. In theory, the horizontal compliance signal is 2–4 times smaller than the vertical signal, but this is well below the measured horizontal background spectral levels. Not surprisingly, the horizontal-component data are incoherent with the pressure data. We can use seafloor compliance to evaluate the vertical seismic data quality in the frequency band between 0.001 and 0.03 Hz. If there are no other significant noise sources, the pressure-acceleration coherence amplitude will be 1. A

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decrease in the coherence indicates that there is another noise source; coherence less than 0.5 indicates that the other noise source is stronger than the compliance signal. The pressure-gravimeter coherence has a larger amplitude and spans a larger frequency range than the STS-2 pressure-vertical coherence, indicating that the STS-2 vertical senses more noncompliance noise than the gravimeter (Fig. 1c, d). The pressure-gravimeter coherence is above 0.9 from 0.005–0.03 Hz, with a maximum coherence amplitude $0.999. On the STS-2, the pressure-vertical coherence is only above 0.9 from 0.01–0.03 Hz, and the maximum coherence amplitude is 0.98. The smaller amplitude and the higher cut-off frequency of the STS-2 pressure-vertical coherence indicates an additional low-frequency-noise source that increases with decreasing frequency. The “Extraneous” Noise Source: Seafloor Currents Several lines of evidence indicate that the STS-2 vertical spectral levels below 0.01 Hz (and the horizontal spectra levels below 0.1 Hz) are dominated by tilting due to currents. First, the noise levels vary in sync with ocean tides. Second, the slope of the low-frequency noise is the same as that observed for seafloor currents. Third, the horizontal and vertical spectra have similar slopes and are coherent, with much larger noise levels on the horizontals. Finally, the noise is not seen on the precisely leveled gravimeter. The STS-2 background noise below 0.1 Hz fluctuates with the tides. The noise is maximum when the first time derivative of the local ocean tides is maximum, and minimum when the first time derivative of the local ocean tides is maximum (Fig. 2). The pressure-vertical coherence is weakest when the noise levels are highest. Seafloor currents are primarily tidally driven although near-inertial motions can contribute significantly (e.g., Thomson et al., 1990; Brink, 1995). Current-induced tilt noise is caused by seafloor currents flowing past the instrument and in eddies spun off the back of the instrument (Webb, 1988; Duennebier and Sutton, 1995). We can model the effect of seismometer tilting on the acceleration signal by assuming that the geophones at rest are rotated by an angle h from the vertical and are offset from the instrument center of rotation (usually close to the center of mass) by a distance L and an angle h0 (Fig. 3) (Duennebier and Sutton, 1995). Current forcing rotates the geophones around the center of mass by u $ u0 % !(x)cos(xt). This rotation creates acceleration signals on the geophone by two processes: (1) a “displacement” term that is the second derivative of the geophone position:

am $

leading to

%2xt , xt $ L sin(")x % L cos(")z %t2

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ax $ Lx2e["cos u0 cos(xt) % e sin u0 cos(2xt) % O(e2)] az $ Lx2e[sin u0 cos(xt) % e cos u0 cos(2xt) % O(e2)]

(2) and (2) a “rotation” term that comes from the change in the gravitational acceleration on the geophones: hg $ g[sin(h % "t) " sinh] e $ ge[cos h cos(xt) " sin h cos2(xt) % O(e2)] 2 vg $ g[cos(h % "t) " cos h] e $ "ge[sin h cos(xt) % cos h cos2(xt) % O(e2)] 2

(3) where g is the gravitation acceleration (approximately 9.8 m/sec2). The total tilt-generated acceleration felt by the sensors is ht $ ax cos h % az sinh % hg $ Lx2e[cos h("cos u0 cos(xt) % e sin u0 cos(2xt)) % sinh(sinu0 cos(xt) % e cos u0 cos(2xt))] % ge[cos h cos(xt) "

e sin h cos2(xt)] % O(e2) 2

vt $ az cos h % ax sin h % vg

(4)

$ Lx2e[cos h(sin u0 cos(xt) % e cos u0 cos(2xt)) " sinh(cos u0 cos(xt) " e sin u0 cos(2xt))] " ge[sinh cos(xt) %

e cosh cos2(xt)] % O(e2) 2

In general, h, e K 1 and the geophone is not perfectly above or to the side of the center of mass (|"0 " np| $ e, n $ 0, 1, 2, 3), simplifying equation 4 to: h $ e["Lx2 cos h cos(u0) cos(xt) % g cos h cos(xt)] v $ e[Lx2 cos h sin(u0) cos(xt) " g(sin h cos(xt) e % cos(h) cos2(xt))] 2 (5) The “displacement” (Lx2 . . . ) terms have positive amplitude slopes and dominate at higher frequencies. The “rotation” terms (g . . . ) are independent of frequency and dominate at lower frequencies (Fig. 4). The rotational term is generally much larger on the horizontal channels than on the vertical, so low-frequency tilt noise is much larger on the horizontals than on the vertical. The vertical rotational term is approximately (e/2 % sinh) times the horizontal rotational

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STS-2 horizontal and vertical spectra and pressure-vertical coherence versus time and tides. Periods of high spectral noise are correlated with a high first derivative of the ocean tide amplitude (calculated using the method of Agnew 1997). Top row, uncorrected vertical channel; bottom row, vertical channel from which coherent horizontal signals have been removed.

Figure 3.

Schematic drawing of the geometry used to calculate the effect of tilt on the geophone signal. The square represents the geophone, and C is the center of rotation.

term. It is very small if the instrument is perfectly leveled, but it increases greatly if the geophone is even slightly off level. The STS-2 low-frequency horizontals and vertical-noise levels are well fit using equation 3 or 4 with a tilt spectrum Se(f ) $ 1.3 ! 10"2f "1.5 lradian2/Hz and a geophone tilt h $ 3 ! 10"3 radians (0.2 degrees) (Fig. 5). The f "1.5 slope of the tilt spectrum is the same as the observed seafloor current spectrum (Duennebier and Sutton, 1995; Webb, 1998). The displacement of the geophone from the instrument center of mass, which plays a large role at higher frequencies, has no effect at frequencies below 0.1 Hz. A simple rotation of the geophones to the vertical should reduce the vertical tilt noise level to near or below the continental low-noise levels (Peterson, 1993). The coherence between the three seismometer components (Fig. 6) help to illuminate the different backgroundnoise sources. At frequencies above 0.1 Hz, the seismic channels are all dominated by microseism energy, so they are partly coherent with one another. At frequencies below 0.1 Hz, the horizontals are dominated by tilt noise, and any

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Tilt-acceleration transfer functions, assuming the geophone is 0.5 meters from the center of rotation. Thick lines show the overall transfer function, and thin lines show the “rotation” (zero slope) and “displacement” (positive slope) components. The only important nonlinear term is the vertical acceleration due to rotation, which is significant if the geophones are perfectly leveled (h $ 0). The thinnest horizontal lines show the transfer functions due to this nonlinear term, for constant tilt spectra Se(f) $ 1 and 104 lradian2/Hz. Each row has the same angle between the geophone and the center of rotation ("0) and each column has the same geophone tilt from the vertical (h).

horizontal-vertical coherence comes from tilt noise on the vertical. This coherence is high except over peaks in the vertical seismic energy (the “infragravity wave” peak at 0.01–0.04 Hz and the small peak at 0.07 Hz, Fig. 1). There are no corresponding dips in the coherence between the two horizontal channels, confirming that the horizontal seismic signal below 0.1 Hz is dominated by tilt noise.

Removing Tilt Noise from the Vertical Channel We remove the tilt-generated seismic background noise by calculating the transfer function between the horizontal and vertical channels, and then subtracting the coherent horizontal energy from the vertical channel. For small geophone tilts this is equivalent to rotating the geophone back to the

vertical, except that it can reveal and remove other horizontal/vertical noise coupling not accounted for by our tilt model. This is the same technique we use to remove the pressure signal from the verticals (Webb and Crawford, 1999), and can be generalized to remove vertical noise due to other measured environmental variables such as temperature. Our technique is inferior to rotation if nonlinear terms are important, but we prefer it because of its more general applicability and because nonlinear terms are generally insignificant compared to instrument noise levels and to the continental low-noise-level Model (Fig. 5). To subtract the tilt noise from the vertical component, we first estimate the noise using the vertical-horizontal transfer functions. We can also estimate the vertical tilt noise in the time domain using digital filters calculated from these transfer functions

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Modeled acceleration signals (Grey lines) versus seafloor STS-2 spectra (black lines). Dashed lines show the horizontal components, solid lines show the vertical component. Assumed tilt spectrum "t(f) $ 1.3 ! 10"2f "1.5 lradian2/Hz, L $ 0.5 m. The upper solid gray line is the modeled vertical acceleration for a geophone tilt of 3 ! 10"3 radians, and the lower solid gray line is the modeled vertical acceleration for a perfectly leveled geophone. (a) Assuming the geophone is directly above the center of rotation ("0 $ 0); (b) assuming the geophone is to the side of the center of rotation ("0 $ p/2).

Figure 6.

Coherence between STS-2 seismometer channels. Upper plots show amplitude; lower plots show phase. Z is the vertical channel, X and Y are the horizontal channels. The dotted line in the amplitude plots marks the 95% significance level.

(see Appendix or Webb and Crawford, 1999, for details). Removing the noise in the time domain is useful for picking seismic arrivals and modeling waveforms, whereas the frequency-domain method is useful for spectral techniques such as normal mode analysis or seafloor compliance measurements.

To remove the low-frequency tilt and compliance noise from the vertical channel, we assume the horizontal channels are completely controlled by tilt below 0.1 Hz and that the infragravity signal is only on the pressure and vertical channels (in other words, the horizontal components and pressure signal are incoherent). Clearly some component of any ver-


tical seismic signal will be coherent with the horizontal channels, however by a very large factor the horizontal channels below 0.1 Hz on the seafloor are dominated by tilt. Because the horizontal-vertical transfer function is much smaller than unity, the corrected vertical signal is unaffected by any real seismic signal on the horizontals. This method does not work above 0.1 Hz because the seismometer channels are all dominated by the seismic “microseism” signal. We first calculate frequency-domain transfer functions between the different channels. To calculate the transfer functions, we estimate the one-sided autospectral density functions Gss and Grr from the Fourier transforms of windowed sections of data for variables s and r, (where s is the “source” channel (X, Y, or P) and r is the “response” channel (Z or Y)) and the one-sided cross-spectral density function Grs to obtain the coherence function crs(f ): n

d 2 N |S ( f )|2, j $ 0,1, . . . , nd NDt i$1 i j 2 nd 2 N Grs( fj) $ R*( i fj)Si( fj), j $ 0,1, . . . , nd NDt i$1 2 Grs( f ) crs( fj) $ [Grr( f )Gss( f )]1/2 nd 2 N Grr( fj) $ |Ri( fj)|2, j $ 0,1, . . . , nd NDt i$1 2

Gss( fj) $

! !

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!

where Si(f ) and Ri(f ) are fast Fourier transforms of data window i for the source and response channels, nd is the number of data windows, N is the length of each data window, and Dt is the sampling interval (Bendat and Piersol, 1986). Each window is tapered using a 4-pi prolate spheroidal function to reduce broadband spectral leakage. The transfer function Ars(f ) is: Ars( f ) $ crs( f )

"G ( f ) Grr( f )

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ss

In the frequency domain the noise seen in component r is linearly related to the s component through the transfer function. The Fourier transform R# representing R corrected for the noise in S is then: R#( i f ) $ Ri( f ) " A*( rs f )Si( f ).

(8)

We calculate the various transfer functions between Z, X, Y, and P and correct the vertical component for noise seen in each of the other components in turn. We only want to subtract the part of the source channel that is noise on the vertical so we set A(f ) $ 0 for frequencies above 0.1 Hz before applying equation 8. Since the source channels may be coherent with one another, we must subtract out the coherent effect from all previous “sources” before applying equation 8. Otherwise, the transfer function will include information about signals

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already removed, adding noise to the vertical channel. For example, the two STS-2 horizontal channels are correlated, so we first apply equation 1 to remove the correlated part of X from both the Z and Y components, forming Z# and Y#, then apply equation 1 to Z# and Y#. To subtract the coherent pressure signal, we calculate the transfer function between P and Z& (Z with the X and Y effects removed). This noise suppression could also be done using multiple coherence techniques, which perform an equivalent set of operations. We also check to make sure the transfer functions don’t change with time. If they do change (for example, if the instrument tilt changes during an experiment), we would have to calculate and apply different transfer functions before and after the change. An Example of Noise Removal in the Frequency Domain To remove the vertical tilt-induced noise in the frequency domain, we first calculated the transfer functions between the seismic channels (Fig. 7) in the relatively quiet time interval from 9 a.m. UMT 16 September to 1 a.m. UMT 20 September 1998, skipping all time intervals containing noise spikes or clipped horizontals. The transfer functions between the vertical and horizontal components are roughly constant below 0.01 Hz where tilt noise dominates the vertical spectrum, and noisy and poorly resolved at higher frequencies where the compliance signal dominates the vertical spectrum. The near constant values at long period are consistent with a 0.003 radian vertical component tilt from the true vertical in x direction and a 0.001 radian tilt in the y direction. The magnitudes of the horizontal-to-vertical transfer functions are small, so we are subtracting only a tiny fraction (less than 1 part in 300) of the horizontal channels from the vertical channel. The effect of contamination of vertical-component seismic waveforms by horizontal-component seismic motions caused by this processing is therefore small. The transfer function between horizontal components is a measure of the interaction of the two components due to the flow noise and varies between 0.2 and 1.2. It is presumably a complicated function of the site response and the noise source. Using these transfer functions, we removed the coherent horizontal data from the vertical as described previously. To confirm that all the coherent noise was removed, we recalculated the coherence between the three seismic channels. The corrected Z channel is incoherent with the X and Y channels for all frequencies below 0.1 Hz. The corrected vertical spectral noise levels (solid black line, Fig. 8a) are up to 20 dB lower than in the original spectrum. The coherence between pressure and the corrected STS-2 vertical is now higher than and spans a larger frequency range than the pressure-gravimeter coherence (Fig. 8b). Even small improvements in pressure-acceleration coherence are important when using seafloor compliance to study crustal structure. The corrected spectra significantly reduce the tidal ef-

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Figure 7.

Magnitude of transfer functions between the seismic channels (the phase is the same as in Figure 6). The complex transfer function is used to subtract the effect of the horizontal channels on the vertical.

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Vertical spectra and vertical-pressure coherence before and after removing coherent noise from STS-2 horizontals. (a) Autospectral densities; (b) pressure-vertical coherence.

fect on vertical seismic data (Fig. 2, bottom row). The corrected data are still slightly correlated with tides, but the corrected vertical spectral noise levels are always lower than noise levels from the same time in the original data. The corrected coherence also fluctuates slightly with the tides,

but the smallest corrected pressure-acceleration coherence is larger than the largest uncorrected acceleration-pressure coherence. Finally, to determine the effective noise floor for longperiod seismic observations in this area, we removed the


coherent pressure signal from the vertical spectrum (dashdotted line, Fig. 8a). The new noise floor is 10–30 dB lower than in the original data at all frequencies below 0.04 Hz. An Example of Noise Removal in the Time Domain We applied the time-domain correction (see Appendix, and Webb and Crawford, 1999) to a section of data containing the arrivals from a magnitude 6.2 earthquake 45.2" away (Aleutian Islands, 14 September 1998, Fig. 9). The earthquake energy is mostly above 0.01 Hz, so the compliance correction is most noticeable, but the tilt correction is significant, particularly for waveform modeling. The horizontal correction will be more important at sites with low compliance (such as a hard-rock seafloor), larger currents, and/or a more tilted geophone. Other Noise Sources Below 0.003 Hz, the corrected STS-2 spectrum is lower and its pressure-vertical coherence is higher than on the gravimeter. The higher gravimeter noise probably isn’t caused by currents. The gravimeter leveling uncertainty of approximately 1 ! 10"4 radians predicts a vertical noise level 76

Figure 9.

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dB below the horizontal noise level. The gravimeter spectral level is up to 67 dB below the STS-2 horizontal level ("154 dB versus "79 dB at 0.004 Hz), and the gravimeter noise slope below 0.004 Hz is much steeper than the STS-2 horizontal noise slope (Fig. 1). This very low frequency gravimeter noise probably comes from temperature fluctuations, since Lacoste-Romberg gravimeters are much more temperature sensitive than STS-2 seismometers.

Discussion We have shown how to remove tilt noise from lowfrequency vertical-seismic data. This noise can be reduced by carefully leveling seismometers and by burying them in sediments (Duennebier and Sutton, 1995) or perhaps by placing in boreholes, although long-period seismic data from seafloor boreholes up until now have been noisy, probably due to convection currents (Webb, 1998). In addition, buried installations are often impossible or economically unfeasible. The technique we outline can transform a marginal data set into a useful one, and is easily modified to account for other noise sources, even when their origin is not well understood.

STS-2 vertical seismic record of a magnitude 6.2 earthquake (D $ 44.2"). All traces are bandpass-filtered between 0.001 and 0.05 Hz. (a) Original vertical trace; (b) vertical trace after subtracting coherent pressure signal; (c) vertical trace after subtracting coherent pressure and horizontal signals.

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In the measurements shown here, the compliance noise is generally larger than the tilt-induced noise, but this is not generally the case. We designed our seafloor sensors to measure seafloor compliance (Crawford et al., 1998) and so we level them more precisely than typical seafloor seismometers. Low-frequency vertical-seismic data from other seafloor experiments such as MOISE (Romanowicz et al., 1998) and OSN-1 (Stephen et al., 1999) have red low-frequency background noise with the same slope as the horizontal noise, indicating that they are dominated by tilt-generated noise. Even the very quiet OFM site appears to be dominated by tilt noise at low frequencies, probably because of a much weaker compliance signal due to smaller infragravity waves in the Atlantic Ocean (Webb, 1998). We can not remove the tilt noise from the horizontal component because it isn’t possible to construct a sufficiently accurate vertical reference (tilt sensor) that is also insensitive to horizontal acceleration. Direct current measurements may be of little value since the horizontal tilt is caused by the turbulent interaction of the current with the sensor case and surrounding seafloor. On sedimented seafloors the tilt noise can be significantly reduced by burying the sensors a short distance below the seafloor. The theoretical horizontal compliance signal is 2–4 times smaller than the vertical compliance peak but measured horizontal spectra, even in buried and borehole sensors, are almost always larger than vertical spectra (Montagner et al., 1994; Collins et al., 1998). The horizontal compliance peak in our data set would only be visible if the tilt spectrum is less than 10"6 f "1.5 lradians2/Hz (dynamic tilts smaller than 0.03 lradians near 0.01 Hz). Data from the recently emplaced Hawaii-2 seafloor seismic observatory shows the first evidence for tilt levels this low (F. Duennebier, personal communication, 1999). Seafloor noise levels can probably be reduced further. The vertical seismic-noise level after removing compliance and tilt effects is still well above the instrument noise floor, the predicted tilt noise, and the continental Low Noise Level Model (Peterson, 1993). The vertical-component noise below 0.004 Hz is probably caused by temperature variations; adding sensitive temperature sensors to the instrument should allow us to further reduce this noise. Simultaneous recordings of other environmental variables such as currents and the magnetic field may allow us to identify and remove further noise sources from seafloor seismic stations.

Acknowledgments The seafloor measurements and data analysis were funded by U.S. Navy ARL Grant N00014-96-1-0297. We thank Jacques Lemire and Tom Deaton for their help in developing and preparing the seafloor seismometerpressure sensors. We also thank Charles Golden, Alexandra Sinclair, Chris Halle, Tony Aja, Bill Gaines, and the crews of the R/P FLIP and the USNS Navajo for their help deploying and recovering the sensors.

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We calculate the inverse Fourier transforms (IFT) of these various transform functions as shown below to derive digital impulse filters relating z to the x, y# and p components after filtering the transform functions to frequencies below 0.1 Hz. We subtract the noise in z due to these components by subtracting out the convolution of these digital filters with the driving channels (Webb and Crawford, 1999). For example, to remove the current and compliance noise from the STS2 vertical channel, calculate:

Appendix

z&(t) $ z(t) " x(t)*azx(t) " [y(t) " x(t)*ayx(t)]*az#y#(t) " p(t)*az &p(t)

Removing Coherent Noise in the Time Domain To remove the coherent noise from the vertical component in the time domain, we first calculate the transfer functions as described in the text. Here again, we assume that P is incoherent with X and Y and that noise on the vertical component is because of tilt noise resolved on the x and y components and compliance noise resolved on the pressure component. The x and y components are partly coherent, so we first correct the z and y components for the effect of x (labeled z# and y#) and then correct z# for the effect of y#.

azx(t) $ IFT(A#zx( f ))

ayx(t) $ IFT(A#yx( f )) az#y#(t) $ IFT(A#z#y#( f )) az&p(t) $ IFT(A#z&p( f )) The corrected time-domain vertical data z&(t) is then:

where x(t)*a(t) stands for the convolution of the data channel x(t) with the filter a(t). Note the quantity in brackets is y#(t), the y component corrected for x. Scripps Institution of Oceanography University of California, San Diego La Jolla, CA 92093-0205 [email protected] Manuscript received 19 August 1999.