Identifying and Removing Tilt Noise from Low-Frequency (0.1

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

Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seaﬂoor Vertical Seismic Data by Wayne C. Crawford and Spahr C. Webb

Abstract Low-frequency (Ͻ0.1 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 radians 4מ10 ן spectra measured on a seafloor seismometer leveled to within 1 (0.006 degrees) are up to 20 dB quieter than on a nearby seismometer leveled to radians (0.2 degrees). The noise on the less precisely leveled sensor 3מ10 ן within 3 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 Broadband seismology is moving into the oceans. As Collins et al., 1998) and as part of local seismic networks the recording capacities of ocean floor instrumentation im- (Romanowicz et al., 1998). A permanent broadband seismic prove and as broadband seismometers become smaller and station was installed on an underwater cable between Hawaii lower power, seismologists have begun measuring broad- and California as part of the Hawaii-2 seafloor global seismic band (0.001–50 Hz) seismic signals at the seafloor to answer observatory (Duennebier et al., 1998). Low-frequency seis- questions that cannot be addressed with land-based seismic measurements can also be combined with pressure mea- mometers. For example, researchers used a 320-km-wide ar- surements to study the oceanic crustal melt distribution ray of ocean-bottom seismometers to study the structure under spreading centers using the compliance method beneath the East Pacific Rise to 600-km depth using (Crawford et al., 1999). low-frequency teleseismic arrivals (the MELT experiment, Unfortunately, the typical background seismic-noise Forsyth et al., 1998). In another recent experiment, Laske et level is much higher at the seafloor than on land, especially al., (1998) measured Raleigh wave arrivals in the frequency at frequencies below 1 Hz. Although the noise levels ob- band between 0.014 and 0.07 Hz across an array of seafloor served over one week at the French OFM pilot seismic station differential pressure gauges to study lithosphere and upper (in a borehole beneath the Atlantic Ocean) approach the aesthenosphere structure beneath the Hawaiian Swell. Per- noise levels of good continental sites (Beauduin and Mon- manent broadband seafloor seismic stations are needed to fill tagner, 1996), most seafloor seismic measurements have in the gaps in global seismic networks (Montagner et al., much higher noise levels (Sutton and Barstow, 1990; Webb 1998), and several researchers have studied noise and the et al., 1994; Romanwicz et al., 1998). Some of the highest effects of seismometer emplacement for proposed perma- noise has a tidal signature (Romanwicz et al., 1998), indi- nent global seismic network stations (Montagner et al., cating that it is tied to currents. The noise may be diminished 1994; Webb et al., 1994; Beauduin and Montagner, 1996; by burying the sensor beneath the seafloor or placing it in a

952 Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 953 borehole (Montagner et al., 1994; Bradley et al., 1997; Col- stable if they tilt too far off of the long-axis center. On the radians 5מ10 ן lins et al., 1998), but this expensive option is probably only seafloor, the gravimeter levels to within 5 worthwhile for long-term or permanent stations. of a laboratory-determined center value. We calculate this In this article, we show how to reduce the vertical seis- center value by searching for the maximum apparent gravity mic noise level at frequencies below 0.1 Hz after the data as a function of the instrument cross level. The apparent are acquired, by subtracting out the coherent signal from gravity is gcos(h), where g is the local gravity (approxi- other channels such as the horizontal geophones. On the or- mately 9.8 m/sec2), and h is the cross-axis tilt from the מ der of 25 dB of the vertical seismic noise in the band from vertical. The deviation in measured gravity equals g(1 0.002 to 0.1 Hz can be caused by seafloor “compliance” or cos(h)) ϵ 2gsin2(h/2). The centering precision depends on by tilt noise caused by seafloor currents. This noise can be the microseism noise that overlies the gravity signal. In the removed in the frequency or time domain, by generalizing laboratory, we can distinguish changes in apparent gravity m/sec2, corresponding to a center value 8מ10 ן the technique described by Webb and Crawford (1999) to as small as 8 .radians 4מ10 ן remove compliance noise. uncertainty of approximately 1 3מ10 ן Long-period vertical-component noise at the Pacific At the seafloor, the STS-2 levels to within 5 seafloor should in theory be dominated by the seafloor de- radians of its center value. We estimated the STS-2 center formation under the loading of very low-frequency ocean value in the laboratory using a manufacturer-installed bubble waves (infragravity waves). In the absence of other noise level mounted on the seismometer base. The STS-2 hori- sources, the pressure and vertical displacement are nearly zontal and vertical channels are electronically derived from perfectly coherent at frequencies below about 0.05 Hz (the measurements of three geophones aligned in a cube-corner frequency limit depends on the water depth), as the seafloor geometry, allowing the sensor to correct for slightly off-level deforms under pressure loading (Crawford et al., 1998). A emplacements. The sensor specifications suggest that the -radi 2מ10 ן differential seafloor pressure gauge is an indispensable part electronics correction is accurate to within 1 of a broadband seismic station, both to remove the defor- ans. We will show that this inaccuracy can introduce signifi- mation signal from the seismic background spectrum and to cant vertical channel noise at the seafloor. detect other noise sources. The coherence between the vertical seismic and pressure measurements indicates the qual- Seafloor Seismic Spectra ity of the low-frequency vertical-component data. Low coherence in the frequency band 0.002–0.04 Hz suggests that We estimate the background seismic-noise levels on other noise sources, such as tilting due to ocean currents, both instruments using spectra calculated from finite Fourier dominate the “background” noise level. transforms (FFT) (Bendat and Piersol, 1986) of data windows visually inspected to avoid seismic events. The gra- The Experiment vimeter and STS-2 background vertical seismic spectra include a microseism peak at frequencies above 0.1 Hz, a We deployed two pressure-acceleration sensors in 900- “compliance” peak centered at 0.02 Hz, and a red noise spec- m-deep water at 31Њ24ЈN, 118Њ42ЈW, at the outer edge of trum at lower frequencies (Fig. 1a, b). the California Continental borderlands. The sediments there The STS-2 vertical channel is significantly noisier than are about 1-km thick, and the seafloor is relatively flat. The the gravimeter at frequencies below 0.05 Hz. The STS-2 instruments, deployed 1-km apart, collected data from 10 horizontal channels are more than 45 dB noisier than the September to 24 September 1998. vertical channel at frequencies below 0.1 Hz, but the vertical Both instruments carry a differential pressure gauge spectrum slope below 0.05 Hz is similar to the horizontal (Cox et al., 1984)) and a seismometer. In one instrument, spectrum slopes (Fig. 1a). We will show that the STS-2 the seismometer is a Lacoste-Romberg gravimeter (Lacoste, vertical-component noise below 0.05 Hz is caused by “leak- 1967), in the other, a Streckeisen STS-2 three-component age” of the horizontal noise due to the geophone being tilted broadband seismometer. The gravimeter acts as a single- from the vertical. We show how to remove this noise from channel (vertical) long-period seismometer (Agnew et al., the vertical data using its coherence with the horizontal- 1976). Both instruments sample twice per second, giving an component noise. upper (Nyquist) frequency limit of 1 Hz. The important dif- ferences between the two instruments are that (1) the STS- The “Unavoidable” Noise Source: 2 records horizontal and vertical motions, whereas the gra- Seafloor Compliance vimeter measures only in the vertical, and (2) the gravimeter The spectral peak centered at 0.02 Hz on the vertical is much more precisely leveled than the STS-2. seismometer channels comes from the seafloor “compli- Both the gravimeter and the STS-2 are leveled using ance”, which is simply the seafloor deformation under pres- motorized gimbals to center positions determined in the lab- sure forcing from linear surface gravity waves. This pressure oratory. We use a precise leveling system for the gravimeter signal from these waves is only significant at frequencies because the measured gravity is very sensitive to cross-axis corresponding to wavelengths longer than the water depth ס m, below 0.04 Hz for H 100 ס tilt and because Lacoste-Romberg gravimeters become un- H: below 0.12 Hz for H 954 W. C. Crawford and S. C. Webb

STS-2 Gravimeter -80 a -80 b /Hz) 2

) -100 -100 2 X Y -120 Z -120

-140 -140 PSD (dB rel (m/s -160 -160

-3 -2 -1 0 -3 -2 -1 0 10 10 10 10 10 10 10 10 1 1 c d 0.8 0.8

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0 0 -3 -2 -1 0 -3 -2 -1 0 10 10 10 10 10 10 10 10 Frequency (Hz) Frequency (Hz) Figure 1. “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 three- component, 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. m. The compli- compliance signal is much stronger at a sedimented site than 4000 ס m, and below 0.02 Hz for H 1000 ance signal jumps up rapidly below this frequency and then at a hard-rock site (Crawford et al., 1998). The compliance decreases approximately proportionally to the frequency signal can be used to study the shear modulus or shear- (Crawford, 1994). The compliance signal disappears behind velocity structure of the sediments and crust (Crawford et noise from other sources at a low-frequency limit that de- al., 1999), or it can be removed to allow easier detection of pends on this noise level. other seismic signals (Webb and Crawford, 1999). In our data, the compliance peak rises above vertical The compliance signal is not seen on the horizontal background levels at frequencies between 0.004 and 0.05 channels. In theory, the horizontal compliance signal is 2–4 dB referenced to 1 (m/ times smaller than the vertical signal, but this is well below 130מ Hz, peaking at approximately sec2)2/Hz, near 0.02 Hz. The compliance amplitude depends the measured horizontal background spectral levels. Not sur- mostly on the strength of the pressure signal (which is ap- prisingly, the horizontal-component data are incoherent with proximately constant in the Pacific Ocean, but which may the pressure data. be weaker and more variable in the Atlantic; Webb, 1998), We can use seafloor compliance to evaluate the vertical and the shear modulus of the underlying basement. For a seismic data quality in the frequency band between 0.001 given pressure signal, the deformation is approximately in- and 0.03 Hz. If there are no other significant noise sources, versely proportional to the basement shear modulus, so the the pressure-acceleration coherence amplitude will be 1. A Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 955

2 2 [( O(e ם (e sin u0 cos(2xt ם (cos u0 cos(xtמ]Lx e ס decrease in the coherence indicates that there is another noise ax 2 2 [( O(e ם (e cos u0 cos(2xt ם (Lx e[sin u0 cos(xt ס source; coherence less than 0.5 indicates that the other noise az source is stronger than the compliance signal. (2) The pressure-gravimeter coherence has a larger amplitude and spans a larger frequency range than the STS-2 and (2) a “rotation” term that comes from the change in the pressure-vertical coherence, indicating that the STS-2 ver- gravitational acceleration on the geophones: tical senses more noncompliance noise than the gravimeter (Fig. 1c, d). The pressure-gravimeter coherence is above 0.9 [sinh מ ( ␾ ם g[sin(h ס h from 0.005–0.03 Hz, with a maximum coherence amplitude g t e [(O(e2 ם (sin h cos2(xt מ (ge[cos h cos(xt ס Ͼ0.999. On the STS-2, the pressure-vertical coherence is only above 0.9 from 0.01–0.03 Hz, and the maximum co- 2 [cos h מ (␾t ם g[cos(h ס herence amplitude is 0.98. The smaller amplitude and the vg higher cut-off frequency of the STS-2 pressure-vertical co- e [(O(e2 ם (cos h cos2(xt ם (ge[sin h cos(xtמ ס herence indicates an additional low-frequency-noise source 2 that increases with decreasing frequency. (3)

The “Extraneous” Noise Source: Seafloor Currents where g is the gravitation acceleration (approximately 9.8 2 Several lines of evidence indicate that the STS-2 vertical m/sec ). spectral levels below 0.01 Hz (and the horizontal spectra The total tilt-generated acceleration felt by the sensors levels below 0.1 Hz) are dominated by tilting due to currents. is First, the noise levels vary in sync with ocean tides. Second, hg ם az sinh ם ax cos h ס the slope of the low-frequency noise is the same as that ob- ht served for seafloor currents. Third, the horizontal and ver- ((e sin u cos(2xt ם (cos u cos(xtמ)Lx2e[cos h ס tical spectra have similar slopes and are coherent, with much 0 0 larger noise levels on the horizontals. Finally, the noise is [((e cos u0 cos(2xt ם (sinh(sinu0 cos(xt ם not seen on the precisely leveled gravimeter. The STS-2 background noise below 0.1 Hz fluctuates e (O(e2 ם [(sin h cos2(xt מ (ge[cos h cos(xt ם with the tides. The noise is maximum when the first time 2 derivative of the local ocean tides is maximum, and mini- (4) vg ם ax sin h ם az cos h ס mum when the first time derivative of the local ocean tides vt is maximum (Fig. 2). The pressure-vertical coherence is ((e cos u cos(2xt ם (Lx2e[cos h(sin u cos(xt ס weakest when the noise levels are highest. Seafloor currents 0 0

[((e sin u0 cos(2xt מ (sinh(cos u0 cos(xt מ are primarily tidally driven although near-inertial motions can contribute significantly (e.g., Thomson et al., 1990; Brink, 1995). e (O(e2 ם [(cosh cos2(xt ם (ge[sinh cos(xt מ Current-induced tilt noise is caused by seafloor currents 2 flowing past the instrument and in eddies spun off the back of the instrument (Webb, 1988; Duennebier and Sutton, In general, h, e K 1 and the geophone is not perfectly above

,0 ס np| Ͼ e, n מ We can model the effect of seismometer tilting on or to the side of the center of mass (|␾0 .(1995 the acceleration signal by assuming that the geophones at 1, 2, 3), simplifying equation 4 to: rest are rotated by an angle h from the vertical and are offset 2 [(g cos h cos(xt ם (Lx cos h cos(u0) cos(xtמ]e ס from the instrument center of rotation (usually close to the h center of mass) by a distance L and an angle h0 (Fig. 3) 2 (g(sin h cos(xt מ (e[Lx cos h sin(u0) cos(xt ס v (Duennebier and Sutton, 1995). Current forcing rotates the e 2 [((cos(h) cos (xt ם ם u0 ס geophones around the center of mass by u ⑀(x)cos(xt). This rotation creates acceleration signals on the 2 (5) geophone by two processes: (1) a “displacement” term that 2 is the second derivative of the geophone position: The “displacement” (Lx . . . ) terms have positive amplitude slopes and dominate at higher frequencies. The “rotation” terms (g . . . ) are independent of frequency and dom- 2x inate at lower frequencies (Fig. 4). The rotational term isץ (L cos(␾)z (1 ם L sin(␾)x ס t, x ס a t2 t generally much larger on the horizontal channels than on theץ m vertical, so low-frequency tilt noise is much larger on the horizontals than on the vertical. The vertical rotational term is sinh) times the horizontal rotational ם leading to approximately (e/2 956 W. C. Crawford and S. C. Webb

-140 -110 -80 -160 -140 -120 0.5 1

d(Ocean tide)/dT X spectra (dB ref (m/s2)2/Hz)) Z spectra (dB ref (m/s2)2/Hz)) P-Z coherence 264

263 original

262 Julian Day 1998

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10-3 10-2 10-1 10-3 10-2 10-1 Frequency (Hz) Frequency (Hz) Figure 2. 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.

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 2 1.5מ 2מ f lradian /Hz and a geophone tilt 10 ן 1.3 ס (Se(f 1.5מ radians (0.2 degrees) (Fig. 5). The f 3מ10 ן 3 ס h 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 sim- ple 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 background- noise sources. At frequencies above 0.1 Hz, the seismic Figure 3. Schematic drawing of the geometry used to calculate the effect of tilt on the geophone channels are all dominated by microseism energy, so they signal. The square represents the geophone, and C is are partly coherent with one another. At frequencies below the center of rotation. 0.1 Hz, the horizontals are dominated by tilt noise, and any Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 957

θ=0 θ=3x10-5 radians θ=3x10-2 radians 5 10

0 10 φ0≈0

4 2 4 2 4 2 Sε=10 µrad /Hz Sε=10 µrad /Hz Sε=10 µrad /Hz -5 2 2 2 10 Sε=1 µrad /Hz Sε=1 µrad /Hz Sε=1 µrad /Hz 5 10

0 10 φ0=π/4

4 2 4 2 4 2 Sε=10 µrad /Hz Sε=10 µrad /Hz Sε=10 µrad /Hz -5 2 2 2 10 Sε=1 µrad /Hz Sε=1 µrad /Hz Sε=1 µrad /Hz

5 10

0 10 φ0=π/2

4 2 4 2 4 2 Sε=10 µrad /Hz Sε=10 µrad /Hz Sε=10 µrad /Hz

-5 2 2 2 10 Sε=1 µrad /Hz Sε=1 µrad /Hz Sε=1 µrad /Hz 10-3 10-1 101 10-3 10-1 101 10-3 10-1 101

Frequency (Hz) Figure 4. 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 signifi- The thinnest horizontal lines show .(0 ס cant if the geophones are perfectly leveled (h and 1 ס (the transfer functions due to this nonlinear term, for constant tilt spectra Se(f 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, except that it can reveal and remove other horizon- vertical. This coherence is high except over peaks in the tal/vertical noise coupling not accounted for by our tilt vertical seismic energy (the “infragravity wave” peak at model. This is the same technique we use to remove the 0.01–0.04 Hz and the small peak at 0.07 Hz, Fig. 1). There pressure signal from the verticals (Webb and Crawford, are no corresponding dips in the coherence between the two 1999), and can be generalized to remove vertical noise due horizontal channels, confirming that the horizontal seismic to other measured environmental variables such as tempera- signal below 0.1 Hz is dominated by tilt noise. ture. 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 in- Removing Tilt Noise from the Vertical Channel significant compared to instrument noise levels and to the We remove the tilt-generated seismic background noise continental low-noise-level Model (Fig. 5). To subtract the by calculating the transfer function between the horizontal tilt noise from the vertical component, we first estimate and vertical channels, and then subtracting the coherent hor- the noise using the vertical-horizontal transfer functions. We izontal energy from the vertical channel. For small geophone can also estimate the vertical tilt noise in the time domain tilts this is equivalent to rotating the geophone back to the using digital filters calculated from these transfer functions 958 W. C. Crawford and S. C. Webb

= = /2 φ0 0 φ0 π

-80 -80 /Hz) 2 ) a b 2 -100 -100

-120 -120

-140 -140

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-180 -180 Acceleration (dB ref (m/s

-3 -2 -1 0 1 -3 -2 -1 0 10 10 10 10 10 10 10 10 10 10 Frequency (Hz) Frequency (Hz) Figure 5. Modeled acceleration signals (Grey lines) versus seaﬂoor STS-2 spectra (black lines). Dashed lines show the horizontal components, solid lines show the ver- 2 1.5מ 2מ ס f lradian /Hz, L 10 ן 1.3 ס (tical component. Assumed tilt spectrum ␾t(f 0.5 m. The upper solid gray line is the modeled vertical acceleration for a geophone -radians, and the lower solid gray line is the modeled vertical accel 3מ10 ן tilt of 3 eration for a perfectly leveled geophone. (a) Assuming the geophone is directly above b) assuming the geophone is to the side of the center) ;(0 ס the center of rotation (␾0 .(p/2 ס of rotation (␾0

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). To remove the low-frequency tilt and compliance noise Removing the noise in the time domain is useful for picking from the vertical channel, we assume the horizontal channels seismic arrivals and modeling waveforms, whereas the are completely controlled by tilt below 0.1 Hz and that the frequency-domain method is useful for spectral techniques infragravity signal is only on the pressure and vertical chan- such as normal mode analysis or seafloor compliance mea- nels (in other words, the horizontal components and pressure surements. signal are incoherent). Clearly some component of any ver- Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 959 tical seismic signal will be coherent with the horizontal chan- already removed, adding noise to the vertical channel. For nels, however by a very large factor the horizontal channels example, the two STS-2 horizontal channels are correlated, below 0.1 Hz on the seafloor are dominated by tilt. Because so we first apply equation 1 to remove the correlated part of the horizontal-vertical transfer function is much smaller than X from both the Z and Y components, forming ZЈ and YЈ, unity, the corrected vertical signal is unaffected by any real then apply equation 1 to ZЈ and YЈ. To subtract the coherent seismic signal on the horizontals. This method does not work pressure signal, we calculate the transfer function between above 0.1 Hz because the seismometer channels are all dom- P and ZЉ (Z with the X and Y effects removed). This noise inated by the seismic “microseism” signal. suppression could also be done using multiple coherence We first calculate frequency-domain transfer functions techniques, which perform an equivalent set of operations. between the different channels. To calculate the transfer We also check to make sure the transfer functions don’t functions, we estimate the one-sided autospectral density change with time. If they do change (for example, if the functions Gss and Grr from the Fourier transforms of win- instrument tilt changes during an experiment), we would dowed sections of data for variables s and r, (where s is the have to calculate and apply different transfer functions be- “source” channel (X, Y, or P) and r is the “response” channel fore and after the change. (Z or Y)) and the one-sided cross-spectral density function An Example of Noise Removal Grs to obtain the coherence function crs(f): in the Frequency Domain

nd 2 2 N To remove the vertical tilt-induced noise in the fre- -quency domain, we first calculated the transfer functions be , . . . ,0,1 ס ͚ |Si(fj)| , j ס (Gss(fj 2 1סndNDt i 2 nd N tween the seismic channels (Fig. 7) in the relatively quiet time interval from 9 a.m. UMT 16 September to 1 a.m. UMT , . . . ,0,1 ס R*(f )S (f ), j ס ( G (f rs j n NDt ͚ i j i j 2 September 1998, skipping all time intervals containing 20 1סd i Grs(f) noise spikes or clipped horizontals. The transfer functions (6) 1/2 ס (crs(fj [Grr(f)Gss(f)] between the vertical and horizontal components are roughly nd 2 2 N constant below 0.01 Hz where tilt noise dominates the ver- -tical spectrum, and noisy and poorly resolved at higher fre , . . . ,0,1 ס ͚ |Ri(fj)| , j ס (Grr(fj 2 1סndNDt i quencies where the compliance signal dominates the vertical spectrum. The near constant values at long period are con- where Si(f) and Ri(f) are fast Fourier transforms of data win- sistent with a 0.003 radian vertical component tilt from the dow i for the source and response channels, nd is the number of data windows, N is the length of each data window, and true vertical in x direction and a 0.001 radian tilt in the y Dt is the sampling interval (Bendat and Piersol, 1986). Each direction. The magnitudes of the horizontal-to-vertical trans- window is tapered using a 4-pi prolate spheroidal function fer functions are small, so we are subtracting only a tiny to reduce broadband spectral leakage. The transfer function fraction (less than 1 part in 300) of the horizontal channels from the vertical channel. The effect of contamination of Ars(f) is: vertical-component seismic waveforms by horizontal-component seismic motions caused by this processing is there- Grr(f) fore small. (crs(f) (7 ס (Ars(f ΊGss(f) The transfer function between horizontal components is a measure of the interaction of the two components due to In the frequency domain the noise seen in component r the flow noise and varies between 0.2 and 1.2. It is presum- is linearly related to the s component through the transfer ably a complicated function of the site response and the noise function. The Fourier transform RЈ representing R corrected source. for the noise in S is then: Using these transfer functions, we removed the coherent horizontal data from the vertical as described previously. To -Ar*s(f)Si(f). (8) confirm that all the coherent noise was removed, we recal מ (Ri(f ס (RЈi (f culated the coherence between the three seismic channels. We calculate the various transfer functions between Z, The corrected Z channel is incoherent with the X and Y X, Y, and P and correct the vertical component for noise seen channels for all frequencies below 0.1 Hz. The corrected in each of the other components in turn. We only want to vertical spectral noise levels (solid black line, Fig. 8a) are subtract the part of the source channel that is noise on the up to 20 dB lower than in the original spectrum. The coher- for frequencies above 0.1 Hz ence between pressure and the corrected STS-2 vertical is 0 ס (vertical so we set A(f before applying equation 8. now higher than and spans a larger frequency range than the Since the source channels may be coherent with one pressure-gravimeter coherence (Fig. 8b). Even small im- another, we must subtract out the coherent effect from all provements in pressure-acceleration coherence are important previous “sources” before applying equation 8. Otherwise, when using seafloor compliance to study crustal structure. the transfer function will include information about signals The corrected spectra significantly reduce the tidal ef- 960 W. C. Crawford and S. C. Webb

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.

-100 a STS -110 STS minus coh X & Y

/Hz)) STS minus coh X, Y, & P 2 )

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-160 1 b 0.8

0.6

0.4 P-Z Coherence STS 0.2 STS minus coh X&Y L&R 0 -3 -2 -1 0 10 10 10 10 Frequency (Hz) Figure 8. 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 cor- but the smallest corrected pressure-acceleration coherence is rected data are still slightly correlated with tides, but the larger than the largest uncorrected acceleration-pressure co- corrected vertical spectral noise levels are always lower than herence. noise levels from the same time in the original data. The Finally, to determine the effective noise floor for long- corrected coherence also fluctuates slightly with the tides, period seismic observations in this area, we removed the Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 961 coherent pressure signal from the vertical spectrum (dash- dB below the horizontal noise level. The gravimeter spectral 154מ) dotted line, Fig. 8a). The new noise floor is 10–30 dB lower level is up to 67 dB below the STS-2 horizontal level dB at 0.004 Hz), and the gravimeter noise 79מ than in the original data at all frequencies below 0.04 Hz. dB versus slope below 0.004 Hz is much steeper than the STS-2 hor- An Example of Noise Removal in the Time Domain izontal noise slope (Fig. 1). This very low frequency gravimeter noise probably comes from temperature fluctuations, We applied the time-domain correction (see Appendix, since Lacoste-Romberg gravimeters are much more tem- and Webb and Crawford, 1999) to a section of data contain- perature sensitive than STS-2 seismometers. ing the arrivals from a magnitude 6.2 earthquake 45.2Њ away (Aleutian Islands, 14 September 1998, Fig. 9). The earthquake energy is mostly above 0.01 Hz, so the compliance Discussion correction is most noticeable, but the tilt correction is sig- We have shown how to remove tilt noise from low- nificant, particularly for waveform modeling. The horizontal frequency vertical-seismic data. This noise can be reduced correction will be more important at sites with low compli- by carefully leveling seismometers and by burying them in ance (such as a hard-rock seafloor), larger currents, and/or a sediments (Duennebier and Sutton, 1995) or perhaps by more tilted geophone. placing in boreholes, although long-period seismic data from seafloor boreholes up until now have been noisy, probably Other Noise Sources due to convection currents (Webb, 1998). In addition, buried Below 0.003 Hz, the corrected STS-2 spectrum is lower installations are often impossible or economically unfeasi- and its pressure-vertical coherence is higher than on the gra- ble. The technique we outline can transform a marginal data vimeter. The higher gravimeter noise probably isn’t caused set into a useful one, and is easily modified to account for by currents. The gravimeter leveling uncertainty of approx- other noise sources, even when their origin is not well un- .radians predicts a vertical noise level 76 derstood 4מ10 ן imately 1

.(44.2Њ ס Figure 9. STS-2 vertical seismic record of a magnitude 6.2 earthquake (D 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. 962 W. C. Crawford and S. C. Webb

In the measurements shown here, the compliance noise References is generally larger than the tilt-induced noise, but this is not Agnew, D., J. Berger, R. Buland, W. Farrell, and F. Gilbert (1976). Inter- generally the case. We designed our seafloor sensors to mea- national deployment of accelerometers: a network for very long pe- sure seafloor compliance (Crawford et al., 1998) and so we riod seismology, EOS Trans. Am. Geophys. Union 57, no. 4, 180– level them more precisely than typical seafloor seismome- 187. ters. Low-frequency vertical-seismic data from other sea- Agnew, D. C. (1997). NLOADF: a program for computing ocean-tide load- floor experiments such as MOISE (Romanowicz et al., 1998) ing, J. Geophys. Res. 102, no. 3, 5109–5110. Beauduin, R., and J. P. Montagner (1996). Time evolution of broadband and OSN-1 (Stephen et al., 1999) have red low-frequency seismic noise during the French pilot experiment of OFM/SISMOBS, background noise with the same slope as the horizontal Geophys. Res. Lett. 23, no. 21, 2995–2998, 1996. noise, indicating that they are dominated by tilt-generated Bendat, J. S., and A. G. Piersol (1986). Random Data: Analysis and Mea- noise. Even the very quiet OFM site appears to be dominated surement Procedures, John Wiley and Sons, New York, 566 pp. by tilt noise at low frequencies, probably because of a much Bradley, C. R., R. A. Stephen, L. M. Dorman, and J. A. Orcutt (1997). Very low frequency (0.2–10.0 Hz) seismoacoustic noise below the weaker compliance signal due to smaller infragravity waves seafloor, J. Geophys. Res. 102, no. 6, 11,703–11,718. in the Atlantic Ocean (Webb, 1998). Brink, K. H. (1995). Tidal and lower frequency currents above Fieberling We can not remove the tilt noise from the horizontal Guyot, J. Geophys. Res. 100, no. C6, 10,817–10,832. component because it isn’t possible to construct a suffi- Collins, J. A., F. L. Vernon, J. A. Orcutt, R. A. Stephen, J. R. Peal, J. A. ciently accurate vertical reference (tilt sensor) that is also Hildebrand, and P. N. Spiess (1998). Relative performance of the borehole, surficially-buried, and seafloor broadband seismographs on insensitive to horizontal acceleration. Direct current mea- the Ocean Seismic Network pilot experiment: frequency-domain re- surements may be of little value since the horizontal tilt is sults, EOS Trans. Am. Geophys. Union 79, no. 45, 661. caused by the turbulent interaction of the current with the Cox, C. S., T. Deaton, and S. C. Webb (1984). A deep sea differential sensor case and surrounding seafloor. On sedimented sea- pressure gauge, J. Atmos. Oceanic Technol. 1, 237–246. floors the tilt noise can be significantly reduced by burying Crawford, W. C., S. C. Webb, and J. A. Hildebrand (1998). Estimating shear velocities in the oceanic crust from compliance measurements the sensors a short distance below the seafloor. The theo- by two-dimensional finite difference modeling, J. Geophys. Res. 103, retical horizontal compliance signal is 2–4 times smaller no. 5, 9895–9916. than the vertical compliance peak but measured horizontal Crawford, W. C., S. C. Webb, and J. A. Hildebrand (1999). Constraints on spectra, even in buried and borehole sensors, are almost al- melt in the lower crust and Moho at the East Pacific Rise, 9Њ48ЈN, ways larger than vertical spectra (Montagner et al., 1994; using seafloor compliance measurements, J. Geophys. Res. 104, no. 2, 2923–2939. Collins et al., 1998). The horizontal compliance peak in our Duennebier, F. K., D. Harris, J. Jolly, K. Stiffel, J. Babinec, and J. Bosel data set would only be visible if the tilt spectrum is less than (1998). The Hawaii-2 observatory seismic system, EOS Trans. Am. .lradians2/Hz (dynamic tilts smaller than 0.03 Geophys. Union 79, no. 45, 661 1.5מ f 6מ10 lradians near 0.01 Hz). Data from the recently emplaced Duennebier, F. K., and G. H. Sutton (1995). Fidelity of ocean bottom seis- Hawaii-2 seafloor seismic observatory shows the first evi- mic observations, Mar. Geophys. Res. 17, 535–555. Forsyth, D. W., D. S. Scheirer, S. C. Webb, L. M. Dorman, J. A. Orcut, dence for tilt levels this low (F. Duennebier, personal com- A. J. Harding, D. K. Blackman, J. P. Morgan, R. S. Detrick, Y. Shen, munication, 1999). C. J. Wolfe, J. P. Canales, D. R. Toomey, A. Sheehan, S. C. Solomon, Seafloor noise levels can probably be reduced further. and W. S. D. Wilcock (1998). Imaging the deep seismic structure The vertical seismic-noise level after removing compliance beneath a mid-ocean ridge; the MELT experiment, Science 280, and tilt effects is still well above the instrument noise floor, 1215–1218. Lacoste, L. J. B. (1967). Measurement of gravity at sea and in the air, Rev. the predicted tilt noise, and the continental Low Noise Level Geophys. 5, 477–526. Model (Peterson, 1993). The vertical-component noise be- Laske, G., J. P. Morgan, and J. Orcutt (1998). Results from the Hawaiian low 0.004 Hz is probably caused by temperature variations; SWELL experiment, EOS Trans. Am. Geophys. Union 79, no. 45, adding sensitive temperature sensors to the instrument 662. should allow us to further reduce this noise. Simultaneous Montagner, J.-P., J.-F. Karczewski, B. Romanowicz, S. Bouaricha, P. Log- nonne, G. Roult, E. Stutzmann, J. L. Thirot, J. Brion, B. Dole, D. recordings of other environmental variables such as currents Fouassier, J.-C. Koenig, J. Savary, L. Floury, J. Dupond, A. Echar- and the magnetic field may allow us to identify and remove dour, and H. Floc’h (1994). The French pilot experiment OFM-SIS- further noise sources from seafloor seismic stations. MOBS; first scientific results on noise level and event detection, Phys. Earth Plan. Int. 84, no. 1–4, 321–336. Montagner, J.-P., P. Lognonne, R. Beauduin, G. Roult, J.-F. Karczewski, and E. Stutzmann (1998). Towards multiscalar and multiparameter networks for the next century; the French efforts, Phys. Earth Plan. Acknowledgments Int. 108, no. 2, 155–174. Peterson, J. (1993). Observations and modeling of seismic background The seafloor measurements and data analysis were funded by U.S. noise, U.S. Geol. Surv. Open-File Rept., Albuquerque. Navy ARL Grant N00014-96-1-0297. We thank Jacques Lemire and Tom Romanowicz, B., D. Stakes, J. P. Montagner, P. Tarits, R. Urhammer, M. Deaton for their help in developing and preparing the seafloor seismometer- Begnaud, E. Stutzmann, M. Pasyanos, J.-F. Karczewski, S. Etche- pressure sensors. We also thank Charles Golden, Alexandra Sinclair, Chris mendy, and D. Neuhauser (1998). MOISE: A pilot experiment to- Halle, Tony Aja, Bill Gaines, and the crews of the R/P FLIP and the USNS wards long term sea-floor geophysical observatories, Earth Planets Navajo for their help deploying and recovering the sensors. Space 50, 927–937. Identifying and Removing Tilt Noise from Low-Frequency (Ͻ0.1 Hz) Seafloor Vertical Seismic Data 963

Stephen, R. A., J. A. Collins, J. A. Hildebrand, J. A. Orcutt, K. R. Peal, We calculate the inverse Fourier transforms (IFT) of these F. N. Spiess, and F. L. Vernon (1999). Seafloor seismic stations per- various transform functions as shown below to derive digital form well in study, EOS Trans. Am. Geophys. Union 80, no. 49, 592. Sutton, G. H., and N. Barstow (1990). Ocean bottom ultra-low frequency impulse filters relating z to the x, yЈ and p components after (ULF) seismo-acoustic ambient noise: 0.002–0.4 Hz, J. Acoust. Soc. filtering the transform functions to frequencies below 0.1 Hz. Am. 87, 2005–2012. We subtract the noise in z due to these components by sub- Thomson, R. E., S. E. Roth, and J. Dymond (1990). Near inertial motions tracting out the convolution of these digital filters with the over a mid-ocean ridge: effects of topography and hydrothermal driving channels (Webb and Crawford, 1999). For example, plumes, J. Geophys. Res. 95, no. C5, 7261–7278. Webb, S. C., W. C. Crawford, and J. A. Hildebrand (1994). Long period to remove the current and compliance noise from the STS- seismometer deployed at OSN-1, OSN Newsletter: Seismic Waves 3, 2 vertical channel, calculate: no. 1, 4–6. Webb, S. C. (1988). Long-period acoustic and seismic measurements and ((IFT(AЈzx(f ס (azx(t ((IFT(AЈ (f ס (ocean floor currents, IEEE J. Ocean Eng. 13, no. 4, 263–270. a (t Webb, S. C. (1998). Broadband seismology and noise under the ocean, Rev. yx yx ((IFT(AЈzЈyЈ(f ס (Geophys. 36, no. 1, 105–142. azЈyЈ(t ((IFT(AЈzЉp(f ס (Webb, S. C., and W. C. Crawford (1999). Long period seafloor seismology azЉp(t and deformation under ocean waves, Bull. Seis. Soc. Am. 89, no. 6, :The corrected time-domain vertical data zٞ(t) is then .1542–1535

(y(t] מ (x(t)*azx(t מ (z(t ס (Appendix zٞ(t

(p(t)*azЉp(t מ (x(t)*ayx(t)]*azЈyЈ(t מ Removing Coherent Noise in the Time Domain To remove the coherent noise from the vertical com- where x(t)*a(t) stands for the convolution of the data channel ponent in the time domain, we first calculate the transfer x(t) with the filter a(t). Note the quantity in brackets is yЈ(t), functions as described in the text. Here again, we assume the y component corrected for x. 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 Scripps Institution of Oceanography University of California, San Diego y components and compliance noise resolved on the pressure La Jolla, CA 92093-0205 component. The x and y components are partly coherent, so [email protected] we first correct the z and y components for the effect of x (labeled zЈ and yЈ) and then correct zЈ for the effect of yЈ. Manuscript received 19 August 1999.