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Page 1: Fidelity of ocean bottom seismic observations

Fidelity of Ocean Bottom Seismic Observations

FRED K. D U E N N E B I E R I and G E O R G E H. SUTTON 2

School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, US.A. 2 5 Pelican Ct., Palmyra, VA 22963, US.A.

(Received 12 December 1994; accepted 18 October 1995)

Key words: Ocean bottom seismometer, coupling to the ocean floor, seismic noise.

Abstract. The often poor quality of ocean bottom seismic data, particularly that observed on horizontal seismometers, is shown to be the result of instruments responding to motions in ways not intended. Instruments designed to obtain the particle motion of the ocean bottom are found to also respond to motions of the water. The shear discontinuity across the ocean floor boundary results in torques that cause package rotation, rather than rectilinear motion, in response to horizontal ground or water motion. The problems are exacerbated by bottom currents and soft sediments. The theory and data presented in this paper suggest that the only reliable way of obtaining high fidelity particle motion data from the ocean floor is to bury the sensors below the bottom in a package with density close to that of the sediment. Long period signals couple well to ocean bottom seismometers, but torques generated by bottom cur- rents can cause noise at both long and short periods. The predicted effects are illustrated using parameters appropriate for the opera- tional OBS developed for the U. S. Office of Naval Research. Ex- amples of data from ocean bottom and buried sensors are also presented.

1. Introduction

Very little published literature is available on particle motion obtained from three-component ocean bottom seismometers (OBS), although many such instruments have been placed on the ocean floor during the past twenty or more years (e.g., Au and Clowes, 1984; Bratt and Solomon, 1984; Trehu, 1984; Barstow et al., 1989; Sutton and Barstow, 1990; Lindholm and Marrow, 1990). We suspect that one reason for this lack of reporting is that the quality of data recovered, particu- larly on the horizontal components, is often so poor that authors tend to ignore them, rather than waste time with poor data or publication of negative results. Horizontal geophone data from the ocean floor are often characterized by "ringy" wave forms and noise levels 20 dB or more higher than levels observed on vertical sensors (e.g., Hyndman et al., 1978; Jacobson et al., 1987). Data observed at nearby sites from iden-

Marine Geophysical Researches 17" 535-555, 1995. © 1995 Kluwer Academic Publishers. Printed in the Netherlands.

tical instruments often change character considerably from one instrument to the other (Ostrovsky, 1989), and horizontal particle motion, while yielding reason- able directions for water waves from explosives, can yield unreasonable results for seismic waves (Bratt and Solomon, 1984). In their paper, refracted arrivals from orthogonal source directions yielded particle motion in the same direction, i.e. one horizontal always :fielded larger signals than the other. Similar particle motions are observed by Trehu, 1984.

This presumed !ack of fidelity in recording ground motion is a serious problem in that a principal reason for placing three-component sensors rather than a single vertical seismometer and/or a hydrophone on the bottom is to obtain the vector motion of the ocean floor, making it possible to identify the various types of seismic waves based on their particle motion and providing additional constraints on the velocity-depth function. While some information can be obtained even from poor horizontal data, such as arrival times of shear waves, much is being lost and considerable effort is being wasted if these data are not being ob- tained with reasonable fidelity. While it is possible that horizontal noise levels on the ocean floor are larger than vertical levels, and that the horizontal signals are truly ringy in some places, we will show that these characteristics - high horizontal noise and ringy sig- nals - are expected if coupling to the bottom is poor. We suggest that a well controlled experiment would verify these findings.

In this paper, we continue theoreticai work on the coupling of OBSs to the ocean floor, expanding earlier work (e.g., Sutton and Duennebier, 1987) to horizontal motions. Whereas vertical particle motion caused by seismic waves is continuous across the ocean bottom interface, horizontal response is complicated by the discontinuity in particle, motion. In addition, an OBS responds differently to input of horizontal motion of the water or bottom. This relative motion ger~Lerates torques on packages that cross this boundary. Data from the 1991 ULF/VLF Experiment (Ultra Low Fre-

Page 2: Fidelity of ocean bottom seismic observations

536 F. K. DUENNEBIER AND G. H. SUTTON

TABLE I Constants and parameters used. Numbers in parentheses are used in model calculations except when noted. Instrument parameter values for the ONR OBS package are shown in plain text;

environmental and model parameter values are shown in italicized text

Independent variables: y,: horizontal displacement of ocean floor relative to inertial reference frame y~: - water relative to inertial reference frame Yc: - calibration mass relative to the CM (center of mass) z~: vertical displacement o f - ocean floor relative to inertial reference frame zc: calibration mass relative to CM s: Laplace variable (i~o for a sinusoidal input) a: dimensionless frequency (mr0/v,)

Dependent variables: u: horizontal CM displacement from equilibrium relative to the moving bottom w: vertical CM displacement from equilibrium relative to moving bottom 0: clockwise rotation angle of the package from equilibrium

Frequency dependent soil parameters: ko: spring constants - rotational motion kx: - horizontal motion k~: vertical motion do: damping constants - rotational motion dx: - horizontal motion d~: vertical motion

Instrumental and other environmental constants: MI

M~: m~

,~t~ Mw: b: r0~ r,: C: zl x~

he: hw: /: p:

Pw:

v,:

g:

total mass of instrument plus virtual mass mass of instrument package alone (38 kg) virtual mass (10.3 kg for sphere, 54.2 kg for base) internal calibrator mass (0.005 kg) buoyant mass of transient calibration float (1.82 kg) mass of water displaced by the instrument (20.58 kg) height of CM above base (0.15 m) radius of base (assuming circular base) (0.25 m) radius of sphere (0.17 m) drag coefficient (0.4 for a spherical package) geophone height above CM (upper horiz.: 0.02 m; lower horiz.: -0.06 m) geophone distance horizontally from CM (vert: 0.057 m) height of calibrator above CM (0.05 m) effective height of force couple above CM (0.05 m) moment of inertia of the package about the CM (0.44 kg m 2) sediment density (1600 kg/m 3) water density (1000 kg/m 3) sediment rigidity (~p) sediment shear velocity (20 m/s) Poisson's ratio (0.5) acceleration of gravity (9.8 m/s 2)

quency/Very Low Frequency, usually considered below and above 1 Hz, respectively), where two b road -band

seismic packages were buried in sediment 200 m apart in 600 m of water, are presented where appropriate to display the predict ions of the theory. We use parame- ters appropriate for the operat ional U.S. Office of

Naval Research ocean b o t t o m seismometer (ONR OBS) as an example for our numerical calculations

based on the theory presented. Relevant parameters for this OBS and envi ronmenta l parameters are listed in Table I, and the mechanical model is shown in

Figure 1.

Dur ing operat ion of the O N R OBS, the seismometer sensor package is separated by about 1 m from a power

and recording system conta in ing the floatation needed for recovery. Gimbaled 3-component geophones are conta ined in an a luminum quasi-sphere moun t ed on a light fiberglass circular base plate with or thogonal radial vertical strips for stiffening and to aid bo t tom

coupling (Jacobson et al., 1991). Barash et al. (1994) show a photograph and sketches of the sensor package and the geophone gimbal mount ing , and provide a detailed description including dimensions consistent with those listed in Table I.

Page 3: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 537

% i i Ii % ii %

%%

%%

°i 6 N ~xE

Ys

Yw

Ihw

g e o p h o n e

Iz

\

\ u+ o l ' , - i ' . . . . . . " , ._ ._ _ L N

t \ r s

T I - - - - A A A A I ro .. 2

) l ~ I w+w° .o T 1 -'x-I= :> k o I ~ 2 -

o . I I

• ~-N /

Fig. 1. Sketch of the mechanical parameters used in the coupling theory. Symbols shown are explained in Table I.

The sediment shear velocity chosen (v~ = 20 m/s) for the theoretical examples we present, while low in order to demonstrate possible problems, is appropriate for near-bottom high-porosity marine sediments. Ewing et al. (1992) observed 37 m/s; Schreiner and Dorman (1990) obtained 40 m/s; Tuthill et aI. (1981) obtain 15-20 rrds in the upper few meters. Results from OBS coupling tests, where the uppermost tens of cm are most important, indicate relevant shear speeds of 10-15 rn/s (Sutton et al., 1981; Zelikovitz and Prothero, 1981; Trehu, 1985a). Although marine sediments gen- erally exhibit a strong increase in shear velocity with depth near the bottom, the theory presented here as- sumes a simple uniform half space.

2. Theory

In our earlier paper, theory was presented that covered the case of vertical particle motion recorded by a ver- tical geophone (Sutton and Duennebier, 1987). While some statements were made concerning horizontal in- put to the system, the theory was mainly applicable to vertical input. As there is continuity of vertical particle motion across the ocean floor-water interface, the theory is relatively straightforward, although an inherent problem exists because of the differences in density among the water, the sediment, and the instru- ment. These density differences demand that a package which intersects a compliant boundary has some

Page 4: Fidelity of ocean bottom seismic observations

538 F. K . D U E N N E B I E R A N D G . H . S U T T O N

differential motion with respect to the bottom (Sutton and Duennebier, 1987). Good response for a vertical motion sensor requires package symmetry about the vertical axis and near zero horizontal offset of the sensor from the horizontal axis of any signal-induced rotations (Sutton and Duennebier, 1987). The mechan- ical coupling between the sensor package and the com- pliant sediment has a low-pass response with a "corner" frequency that is determined by the package mass and configuration and the rigidity of the sedi- ment. At frequencies well below the corner, the pack- age follows the ground motion with high fidelity for vertical seismic input.

In contrast, horizontal ground motion is discontinu- ous across the ocean floor boundary, thus motion of the water with respect to the bottom will necessarily generate torques in packages that intersect the bound- ary. The horizontal response includes two coupled modes of oscillation, translation and rocking, each with its own "corner" frequency. It is desired to have these frequencies well above the band of interest, but the equations and examples presented here demon- strate the difficulty of obtaining high fidelity horizontal response for existing instruments resting on the ocean floor. It is possible to conduct field measurements for determining the extent of these problems using an in- ternal shaker, transient tests, and/or by recording mul- tiple collinear sensors within the package, but inversion of field data from a poorly coupled instrument to ob- tain ground motion is difficult because many of the coupling parameters are environmental and difficult to estimate.

Several types of input to the seismic package are considered: (1) horizontal and vertical seismic motion of the ocean bottom, (2) horizontal motion of the water, both acoustic and bottom-current generated, (3) internal calibrator input, and (4) transient test input generated by releasing a float from the package. A calibrator is a device that moves a mass inside the package producing motion of the package detected by the sensors. Calibration forces and forces caused by relative motion of the water and the OBS are similar, in that they both can be modeled as point forces ap- plied to the package.

We assume that the package, including the base plate, is completely rigid. The ONR OBS has a fiber- glass disk base which may flex in response to motion, but this issue will be ignored in this paper. We also assume that the package does not sink into the sedi- ment to any significant depth, allowing us to ignore the buoyancy effects of the buried section.

3. Horizontal Theory

The equation of rectilinear horizontal motion of the CM is

M ( f s + f i ) + d x ( f t - b O ) + k x ( u - b O ) = f ( t ) , (1)

wheref(t) is the sum of all horizontal forces acting on the package in addition to that produced by motion of the bottom. In Laplace notation

( m s 2 + d x s + k x ) u - b ( d x s + k x ) O = F s + F (2)

where

F, =-Ms2ys, and F may be a w of the following forces: (3)

Fc = -ms2yc, force generated by calibration input (4)

3 2 F,,=SMws y~+Fd, force on a spherical package generated by water motion, including buoyant and drag components (5)

1 2 r 2 Fa =~ Cp~ (sy~) ~z ~, drag force on a spherical package from currents (6)

F, = gM,, step of force generated by releasing S

buoyant mass, 214,. (7)

The buoyancy term of Fw comes from the equations for the oscillatory motion, q, of a sphere in water (Batchelor, 1983, page 454):

q 3Mw and

y w - 2 m i + mw '

Fw=Ms2q= M~+-- 2- s2q. (8)

The drag component of Fw, obtained from Batchelor (1983, page 233), is not important at seismic particle velocities, but it will be discussed later in regard to current noise.

The package also undergoes rotation with a second coupled equation of motion given by

IO + dorZ O + korg O + d~b(bO- ft ) + k~b(bO- u )

+ gO(M~ h~ - M~ b) = Zh, f (t). (9)

The last term on the left represents the gravitational and buoyancy torques, and Zh~f(t) is the sum of the external torques acting on the package. The motion of the bottom acts on the soil around the package, and torques for this motion are included in the left

Page 5: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 539

side of the equation. Rearranging, and using Laplace notation

[ IS2 "~- (do r~ + d~ b 2 )s

+ (kor2 + k~b2 + gM,~h~-gM~b)]O

-b(d~s + k~)u= Y,h~F~. (10)

We can rewrite equations (2) and (10) using notation similar to Hsieh (1962). From equation (2)

A1u-AaO=F~+F, (11)

and from equation (10):

where

( 0: ground motion only . . . . J h~(F~ or Ft): calibrator or

- - / ~ 4 L / t L-~ 3 U = ~ transient input

hwF,~: water motion input (12)

A~ = Ms2 + Gs + G (13)

~2=A4=b(dxs-}-kx) ( 1 4 )

A3 = Is2 + (dor2 q- d~b2)s

+ (ko r 2 + k~ b 2 + gM~ h,~ - gM~ b). (15)

Commonly, we are interested in cases where only the ground and/or water are moving, or where the ground and water are assumed to be still and a calibration source is being used. Solving (11) and (12) for water and ground motion input

a n d

hi--

F~+F~ - A 2

hwFw ~3 ~3(Fs+E~)+~2hwFw

A 1 - z~ 2

- - A 4 A 3

A 1 A 3 - A 2 A 4

& F~+Fw

-A4 hwF~. Alh~F~+A4(Fs+F~)

(16)

0 - - (17) A 1 - - A 2 A1A3 - - A2A 4

- - A 4 A 3

Similarly, when the ground is not moving,

F(A3 + hA2) U = A1A3 _ A2A4 , (18)

and

F(hA1 + A4) 0 - (19)

A1A3- AzA4"

In equations (18) and (19) Fis taken to be Fw, F~, or F~ only, and h is the height of the force application above the CM. The total horizontal displacement of the CM relative to inertial space is given by

T= u +ys, (20)

and the horizontal acceleration and tilt input at the location of the horizontal sensor are given by:

l h =- S 2 T-~- gO + s2Oz. (21)

The equation of motion for equivalent displacement input for a horizontal sensor becomes

,h ~ = y , + u + O z+ . (22)

The transfer function for equivalent displacement in- put for a horizontal sensor to actual ground displace- ment input (with or without water motion) where u and 0 are obtained from equations (16) and (17) is thus

- 1 + ( 2 3 ) Ys Ys

This transfer function should equal 1.0 when fidelity is perfect. For the case of water motion (only) or shaker calibration input u and 0 are obtained from equations (18) and (19) yielding

- - - ( 2 4 ) Yc,w Yc,w

Since y~ are all zero for the transient calibrator input, Ft, equations (18) and (19) and (21) or (22) are used directly to evaluate the coupling response.

For a relatively simple OBS consisting of a sphere rigidly attached to a thin circular base plate of small mass,

m,,, M = M ~ + 2 ' (25)

the effective mass of the instrument, where M~,/2 is the virtual mass of the sphere (BatcheloL 1983, page 453), and the moment of inertia is estimated by

2 2 I = ~ M~ rs, (26)

Page 6: Fidelity of ocean bottom seismic observations

540 F. K. DUENNEBIER AND G. H. SUTTON

which is the moment of inertia of a uniform sphere (assuming that the fiber glass base plate of the ONR OBS adds little to the moment); more detailed calcula- tions indicate that the uniform density approximation is reasonable for the sphere•

4. Vertical Theory

The derivation of vertical motion is similar to that for horizontal, although continuity requires that the vertical water motion is the same as the motion of the ocean floor. Unlike the case for horizontal motion, we assume that the package is symmetric around a vertical axis, and that no rotations occur:

(M~-Mw)Z~+M~+d~vg+k~w=f(t) (or zero)

(27)

(msZ+dj+k~)w= -(Mi-mw)sZG+F. (28)

This yields the transfer function for vertical ground motion:

w+Z~=z~ 1 \Ms2+Gs+k~ j, (29)

and the transfer function for a shaker calibration force

w( 1) Fc = Ms2q-dzsq -k

o r

W ( mS2 ) (30) ~= Ms2+d~s+k~ •

For the transient calibrator, Fc is replaced by F, in the top version of equation (30). The above transfer functions for vertical input are the same as those found in Sutton and Duennebier (1987) with appropriate changes in notation M = Mff, and (z~ + w = I), and with their value Ms = 0. We will use the Sutton and Duen- nebier (1987) approximation for the virtual mass:

My = 4(p, + p~) r3/3, (31)

assuming that essentially all of the virtual mass is asso- ciated with the circular base plate of the OBS for ver- tical motion. Equation (31) is the relationship for water motion normal to a thin circular disk in water (Batch- elor, 1983, page 458) with water density replaced by the average of water and sediment densities. This should be a good approximation for marine sediments with Poisson's ratio near 0.5.

5. Cross Coupling

If no rotations occur around a horizontal axis in re- sponse to vertical ground motion, then there will be no cross coupling from vertical ground motion to hori- zontal geophones (unfortunately, this may not be the case in certain expected situations). Horizontal motion of the package, however, can generate rotations about horizontal axes which produce signals on the vertical geophone given by

w = Ox. (32)

This "cross talk" on the vertical sensor generated by horizontal motion can be significant and will be discus- sed in a later section.

6. Frequency Dependent Bottom Parameters

The damping and spring constants (see Figure 1) are given by the following equations (Hsieh, 1962; Luco and Westman, 1971; Veletsos and Wei, 1971):

8~ro f~t k ~ = 2 _ a ~ +g21 , (33)

8#r 2 gll 4 = - - - ; (34) av, ( 2 - rr) ~1 + g~l

8#r0 2 - a f22 k°=2-a 3(1 -o 9 Y~22-k-g22 ; (35)

8#r~ 2 - - O" g22

d°=aVs(2-a) 3(1-cr) f~2+g2a ; (36)

@r0 f00 k z - 1 - a f~00+g02' and (37)

4/~r~ g00 dz = av~ (1 - a) j~20 + g020 " (38)

The values off~ and g,~ in these equations are ob- tained from curves for a = 0.5 presented in Luco and Westman (1971) and Veletsos and Wei (1971). Values of the above parameters are shown in Figure 2. A Poisson's ratio of just under 0.5 implies that the shear velocity is much less than the compressional velocity, as is appropriate for soft sediments in the ocean• In our previous paper (Sutton and Duennebier, 1987), the values of dimensionless frequency were limited by approximations to values of less than 2.0 (Hsieh, 1962), limiting the results to packages with small radii and large shear velocities (Trehu, 1985a). In this paper we use the solutions of Luco and Westman (1971) and Veletsos and Wei (1971) to expand the applicability

Page 7: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 541

Z

106

5 xl05

-5 xlo -s-

.lo6. i

iq

\

20 40 60 80

Frequency, Hz

2a: Effective spring coefficients for horizontal and rocking motion.

\ 100

~ 6,000-

4,000-

8

J

/ 0 2O 40 60

Frequency, HZ

N

80 100

2b: Effective damping coefficients for horizontal and rocking motion.

O- E

g ~ -4 x 10 6-

~ -8 X I 0 B-

Y~

80 100

18,000-

E

=

8 16,000-

"~.

_~

uJ 14,000- c"

d z j

J 20 40 60 20 40 60 80

FrezlUency, Hz F ~ c y , Hz

2c: Effective spring coefficient for 2d: Effective damping coefficient for vertical motion, vertical motion.

Fig 2. Effective spring and damping coefficients for the O N R OBS resting on a material with a density of 1600 kg/m 3, a shear velocity of 20 m/s, and with ¢ ~ 0.5. To apply these curves for different parameter values, note that the vertical scales are proportional to # = ~ p , and that

the frequency scale is proportional to v,/ro.

f 100

to values of dimensionless frequency (a) up to 8.0 assuming that the energy is radiated away from the package as Rayleigh waves (no water). Estimates sug- gest that the change to radiation as Scholte waves with water covering the instrument differ by no more than 10% from the values given by Luco and Westman, 1971 (C. Bradley, pers. commun.). Note that the values of two of the spring constants change to negative values at high frequencies, implying that the springs stretch when pushed upon. Luckily, however, this curiosity is not important in this paper, as the effects of the spring constant at high frequencies are negligible.

Theory presented above assumes that the wave- lengths of input motion are large compared to the dimensions of the OBS, in particular the base diameter for seismic motion of the sediment, and the sphere diameter for bottom current eddies and for seismic motion of the water. High frequency inputs with low horizontal phase velocity violate this assumption, and the package itself acts as a low pass filter. We approxi- mate these effects with appropriate package transfer functions obtained in a manner analogous to that for tapered geophone arrays (e.g. Waters, 1981). For the sphere we assume a spatial force window shape propor-

Page 8: Fidelity of ocean bottom seismic observations

542 F. K. DUENNEBIER A N D G. H . S U T T O N

tional to the area of small circles perpendicular to the path through the sphere and obtain a Fourier integral transform:

S(co) = ~ a ~ rc(aZ--tZ)exp[-icot] dt a

(39)

where 2a = 2rs/v~ is the travel time across the sphere and V(a) = 43 rca3.

Equation (39) has the closed-form solution:

3 S(co) = ~ [sin(aco) - aco cos(aco)]. (40)

ta~)-

Later, when we consider the effect of bot tom current eddies, we replace vs with an appropriate, lower, current speed.

For the base plate, we assume a force window shape proportional to the chord length perpendicular to the path across the base plate and obtain the t ransform

1 f~ 2 ~ e x p [ - i c o t ] d t o

(41)

where 2a = 2ro/vs is the travel time across the base plate, and A(a) = rc a 2. We can integrate equation (41) numeri- cally to obtain the transfer function.

For the ONR OBS with a shear speed of 20 m/s, the base plate low pass filter is 3 dB down at 20 Hz, and its first null is at 49 Hz; the sphere filter is 3 dB down at 35 Hz, and its first null is at 85 Hz.

7. Response of the ONR OBS

The ONR OBS is currently used for a wide range of applications in ocean bottom seismology, from earth- quake studies to seismic refraction. It is generally as- sumed by users that signals recorded by the sensors, when corrected for the sensor response, reflect.the mo- tion of the ocean floor in the direction of sehsitivity. In this section we will show that this is not the case in situations where the ocean floor is soft.

Seismic response. Seismic motion includes cases where the ocean floor and/or water are moving with respect to the inertial reference frame, normally at very small particle velocities and displacements, but with relatively high propagation velocities, from 20 m/s or less for shear waves in soft sediments to kilometers per second for compressional waves. The vertical com- ponent of ground motion must be the same as the vertical component of water motion at the ocean floor to preserve continuity. The horizontal component of

motion may be decoupled, however, between the water and the bottom sediments. Thus we expect the vertical response to vertical motions to be relatively good, as no torques are likely to be generated, and the bottom and top of the sensor package should move with the surroundings. This can be seen in the solid curves of Figure 3, where the transfer function for vertical seis- mic motion is shown vs. frequency. Even near 100 Hz, the package is expected to move only slightly less than (about 0.7) and in phase with the ocean floor.

If the bot tom is moving horizontally then the vertical sensor will respond to package tilt as "cross cou- pling", unless the sensor is located in the vertical plane of the tilt axis. In Figure 3, we show the theoretical response of a vertical sensor in the ONR OBS for the case where the bottom is being seismically displaced horizontally and the water is still, such as for Sh motion. The theory (equations (17) and (32)) predicts that the vertical ONR OBS sensor in its normal location in the package will detect the horizontal motion at a level of about - 12 dB, or one fourth of the horizontal signal amplitude, near 18 Hz. The dashed curve in Figure 3 implies that an Sh signal ten times the size of any vertical motion would be detected with equal or greater amplitude by the vertical sensor on the ONR OBS from about 12 Hz to 90 Hz. A vertical sensor located near the edge of the base plate would detect the hori- zontal motion at an amplitude almost as large as the motion itself near 18 Hz. The situation would be worse for a softer sediment, a more buoyant sphere, or a higher center of mass.

Predicted horizontal seismic response to horizontal input motion detected at the location of the lower horizontal sensor in the ONR OBS is shown in Figure 4 from equation (23). Four limiting examples are shown, with no attempt to model particle motion from true seismic waves. When the ground and water are moving together, the predicted amplitude response is quite good at all frequencies (within a few dB of input levels up to 80 Hz). However, there is a 4 dB change in level and a maximum phase error of about 25 ° near 18 Hz. When the water is not moving, or when the water and bot tom are moving out of phase (as can occur for horizontally polarized shear waves and vertically po- larized body and boundary waves), the response to ground motion becomes seriously distorted (ampli- tudes in error by more than 3 dB and large phase errors) above about 10 Hz. The package is attempting to follow the motion of the water rather than the mo- tion of the ocean floor at high frequencies. This can be seen in the thin solid curves of Figure 4, showing the horizontal response to seismic motion of the water with the bot tom still.

Page 9: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 543

-20

E,

-40 .,-4

- 6 o

180

1 2

P h a s e 90 -

5 10. 20.

Frequency, Hz

50.

' ~

I

100.

©

t-

-90

-180

% \

\ \

\

% %

1 2 5 10. 20. 50. 100.

Frequency, Hz

Fig. 3. Cross Coupling. Vertical seismic input to an ONR OBS package yields the solid curves at the location of the vertical geophone in the ONR OBS (using equation 29). If the same amplitude seismic motion were present in the horizontal direction with no water mo~-ion, the vertical geophone would see cross-coupled motion at the level shown in the dashed curves (using equations 32 and 17) in the worst case

where the motion is in the direction of the horizontal offset of the vertical geophone.

As an example of how particle motion can be dis- ~ted, we show in Figure 5 the response of the ONR

sensor package to circular wave motion at 18

Hz, where the horizontal water motion is equal but opposite in direction to the horizontal ground motion. The theoretical recorded particle motion is heavily dis-

Page 10: Fidelity of ocean bottom seismic observations

544 F. K. DUENNEBIER AND G. H. SUTTON

10

-5

-10

-15

-20 1 2 5 10. 50. 100.

Frequency , H z

180

Igl

I])

t -

90

-90

¢-,

~5

O

-180 1 2 5 10. 50. 100.

Frequency , H z

Fig. 4. ONR OBS transfer functions for horizontal motion at the location of the lower geophone. In the cases where both the ground and water are moving, they are modeled to have the same displacement amplitude, and the dB reference input is the ground motion. When only

the water is moving, the reference input is the water motion.

torted from the true (circular) particle motion, and the cross coupling term leads to a range of possible responses depending on the sense and orientation of the input rotation relative to the horizontal offset direc- tion of the vertical sensor.

Shaker response. The desired response of the pack- age to an internal shaker is a small rectilinear motion. I f a shaker consists of an offset cam spinning at a known frequency, then the displacement of the cam is independent of frequency, and the velocity response of

Page 11: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 545

<;ii ..............................................

============================================= ":'~";:"::';:x:,,::.;:..::..;:.;:,.::,.::..;:x::.;;:..::..::r.::, C

......................................... ........................... 1-11 .......................... I -2 -1 ~':" ................ ;:~i:":% %;:i::":" ~

horizontal

e,. ~I

1 I

B

ID

-1

C

-2

I ~ i - - I I

0.01 0.0½ 0.0t 0.04 0.05

t ime , s

Fig. 5. Theoretical 'displacement' output for boundary wave input at 18 Hz as predicted for an ONR OBS. See text for parameters. In part A, the input ground particle motion (dark circle) is shown with output motion in the sagittal plane. The two lighter ellipses show the limiting particle motions that could be observed depending on the sense of the input rotation relative to the direction of horizontal offset of the vertical geophone. The input particle motion is shown vs time in part B. The dark solid curve represents horizontal ground motion, the light curve vertical motion, and the dashed curve shows the horizontal motion of the water. The output 'displacement' is shown in part C; the

horizontal (solid dark) and vertical output (light) for both limiting cases (as in A) are shown.

a sensor to shaker d i sp lacement should have a posi t ive s lope o f 18 dB/octave i f coupl ing is good, i.e. no signi- ficant t i l t ing and coupl ing resonan t frequencies above the f requency o f the ca l ib ra to r (see, for example, equa- t ion (30)). H o r i z o n t a l response to the m o t i o n o f an

in ternal shaker loca ted at the center of the sphere is ident ical in shape to the response of the package to hor i zon ta l water m o t i o n (equat ions (4) and (5)) if d rag is ignored and if the ocean f loor is no t moving (Ys = 0). Ca l ib r a to r m o t i o n and water m o t i o n exert equal

Page 12: Fidelity of ocean bottom seismic observations

546 F. K. DUENNEBIER AND G. H. SUTTON

-20

-60

o~

"~ -100

-140

-180 0.1 0.5 1 5 10. F requency , H z

50. 100.

It I1

180

9O

-90 _I/±W kk

-180 0.1 0.5 1 5 10.

i I !

50. 100.

F requency , H z

Fig. 6. Theoretical amplitude and phase response of O N R sensors to an internal shaker. The shaker is an offset cam rotating near the center of the gimbal. Good coupling is present where the slope of the amplitude curve is 18 dB/oct.

Page 13: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 547

force on the package (E =F~.) if, for example, m = 0.005 kg and M,~ =20.6 kg for the ONR OBS, and the displacement of the calibrator (Yc) is 6000 times the displacement of the water (2~). Figure 6 shows the predicted horizontal and vertical velocity response to a 0.005 kg shaker with 0.005 m displacement located at the gimbal pivot for the ONR OBS resting on soft sediment from equations (4), (24), and (30). Notice that the horizontal response to horizontal shaking is larger than the vertical response to vertical shaking, and that the response becomes less than optimum above about 12 Hz. The horizontal response is modi- fied below about 1 Hz by the gravity term in equation (24) for package tilt generated by the shaker mass. Figure 6 also shows the response of the vertical sensor to the horizontal component of shaker motion from equations (19) and (32). Ideally, this response (heavy dashed curve) would be well below noise level, but the theory suggests that this cross coupling response is only a few dB less than the response to the vertical component of shaker motion at about 18 Hz, and never more than 12 dB below this curve. This implies that severe distortion of shaker results could result from cross coupling. Relating response to shaker input to seismic response is not a simple task, as the shaker response depends on the height of the shaker in the package and seismic response depends on motion of the water as well as that of the bottom. While a shaker can indicate regions of the spectrum where coupling may be poor, it would be difficult to use shaker results to remove the effects of poor coupling from data.

Shaker Calibration Data. Sauter and Dorman (1986) reported on using an internal calibrator to obtain transfer functions for an OBS, but they did not report on ocean bottom data. Results from such data have not been published for the ONR OBS although an internal calibrator is present in the package. Dodds et al. (1994) used a small vibrator in their sensor pack- age to assess coupling to the ocean floor. Their results yield curves similar to those in Figure 6. A 3-compo- nent instrument package designed for burial below the ocean floor (Duennebier and Harris, 1989) is equipped with a shaker consisting of an offset cam attached to a motor that can be driven at frequencies from about 5 to 70 Hz. The cam rotates in a vertical plane oriented at 45 ° to the axes of the horizontal sensors producing equal horizontal inputs 0.7 times the vertical input and 90 ° different in phase. The shaker is placed in the center of a pressure case (55 kg mass, 0.38 m high by 0.3 m diameter with a density of 1800 kg/m3), with signals detected by the geophones located near the center of the package just below the shaker. The pack- age has been tested in air on a concrete slab, in shallow

(5 m deep) water with a sandy bottom (both on the bottom and buried), and in 620 m water depth buried in a muddy bottom. Results from these tests are shown in Figure 7, and details of each curve are given in Table II. The spectral levels are referred to the geo- phone output voltage (proportional to velocity from 6 to 50 Hz), and the relative signal levels are correct to within about 3 dB. Good coupling, recognized by an 18 dB/oct slope (shown as the gray parallel lines in the figure), was observed on the vertical components in all situations, including when the package was resting on the seismic pier, on the ocean floor, and buried below the ocean floor. Good response was also observed on the horizontal geophones in every case where the instrument package was buried below the bottom. These curves are shown in Figure 7a. Note that the package motion in response to the shaker is larger on the buried horizontal sensors than on the vertical sensors, implying that the horizontal soil spring parameters are weaker than those of the vertical. The response of the buried package to seismic waves is excellent because the package density is nearly the same as that of the sediment in which it is buried (Sutton and Duennebier, 1987). Comparing the hori- zontal shaker response levels when the package is on the cement slab (Figure 7b) with the horizontal re- sponse when the instrument is buried shows that the buried package is as well coupled to the bottom in this frequency range as when resting on a concrete slab. The large deviations from slopes of 18 dB/oct of the other curves in Figure 7b imply that considerable signal distortion could be expected if this package were used on the ocean floor, rather than buried.

Transient Test Response. It is possible to assess the fidelity of OBS response to seismic signals by noting the response to impulsive signals applied to the OBS package. Transient calibration signals were applied to OBSs for this purpose as part of the Lopez Island OBS Calibration Experiment (Sutton et al., 1981; Zeli- kowitz and Prothero, 1981), and more recently on the ONR OBS by Trehu and Sutton (1994). Transient sig- nals are applied by releasing floats attached by string to the packages in both the vertical and, using a pulley, in the horizontal direction. The signals obtained are the equivalent of a step of acceleration applied to the packages at the point of attachment. As shown earlier with the response equations, the response to transient tests are not the same as the response to seismic waves. A sensor package which couples perfectly to the ocean floor (transfer function of 1.0) will still respond to a shaker or to a transient pull, even though the ground is not moving. Theoretical frequency domain examples of the geophone velocity response (displacement re-

Page 14: Fidelity of ocean bottom seismic observations

548 F. K. DUENNEBIER AND G. H. SUTTON

2 4 [ I 1 I I I I I I I

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• """~** " * ' i . ' ' " '.""'" " ' " " " ' *~. " " " -. '"" " " H13 ~ ~ ~ ......... • .......... . . . . . . . . . . . . ........ ...,...,, . . . . . ." ...... . ........ . .........

~ - " ~ . ....... ...t'*,.'."~. *,*Z ~ ........ , ~ " ~ , * . ...... . . O 1 t .,"'" -- ~"4~_ ..~,**" ..~ ........ "~,;" "-~_,...'M*-..~,-....,~...-- y'.;L~,,C .:- ..... - -

• " " , . , - ~ : : , " ~ - - . " - . . . . . . . " . j ~ ' , ~ , ~ z . ~ ' ' 7 ~ " , .~ ...... : " . ...... % .,.-~.~ ~ ....... ,~..,.:,-~. ........ ........ ~ ...... ,.. .......

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F r e q u e n c y , H z Fig. 7. Comparison of geophone responses to an internal shaker for various situations. The sensors are located inside a package described in the text. The light parallel diagonal lines show the slope expected when coupling is good (18 dB/oct). The response of vertical geophones in all situations, and buried horizontal geophones are shown in 7A; the response of horizontal geophones when the sensor package was on the ocean bottom and on a concrete slab in air are shown in 7B. The only acceptable response in Figure 7B is when the package was resting

on the concrete slab (curve H15). Data for each curve are given in Table II.

Page 15: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS

TABLE II Shaker data information. Shaker test data for the ULF/VLF Experiment sensor package. Data above the heavy

line are displayed in Figure 7a while those below the line are shown in Figure 7b.

549

Curve label Sensor Date Depth, location Comments

HI, H2 (2 curves) H geophones 7/17/91 620 m, off Oregon H3, H4 (2 curves) H geophones 12/90 5 m, off Oahu H5, H6 (2 curves) H geophones 6/13/90 5 m, off Oahu H7, H8 (2 curves) H geophones 6/13/90 5 m, off Oahu V1 V geophone 6/13/90 5 m, off Oahu V2 V geophone 6/13/90 5 m, off Oahu V3 V geophone 6/13/90 5 m, off Oahu V4 Vertical accel 7/17/91 620 m, off Oregon

V5 V geophone 6/13/90 concrete slab in air

buried, soft bottom buried, sandy bottom buried sandy bottom, test l buried sandy bottom, test 2 on sandy bottom, test 2 buried sandy bottom, test 1 buried sandy bottom, test 2 buried, soft bottom, response changed to velocity for plot 3-point tripod under package

H9 H geophone 7/11/91 620 m, off Oregon

HI0 H geophone 7/11/91 620 m, off Oregon

Hll H geophone 7/11/91 620 m, off Oregon

HI2 H geophone 7/11/91 620 m, off Oregon

HI3 (2 curves) H geophones 12/90 5 m, off Oahu H14 (2 curves) H geophones 6/13/90 5 m, off Oahu H15 (2 curves) H geophones 6/t3/90 concrete slab in air

on soft bottom in sled l, sensitive across length on soft bottom in sled 2, sensitive across lei3gth on soft bottom in sled 1, sensitive along length on soft bottom in sled 2, sensitive along length on sandy bottom on sandy bottom 3-point tripod under package

sponse times s) to steps of acceleration using the above formulations are shown in Figure 8 for several cases for the ONR OBS. Comparison of the synthetic signals in Figure 8 with the horizontal transients recorded at the Lopez Island Experiment (Sutton eta[. , 1980) indicate that most of the OBSs tested at Lopez Island are sensitive to, and their signals can be distorted by, horizontal motion of the water, since the equation of motion for transient tests and for water motion are the same except for the characteristics of the driving force and buoyancy. The Lopez results also indicate that a considerable amount of horizontal ground mo- tion is detected by the vertical sensors in some instru- ments. This is observed in the transient test results and in the response to explosive sources, where the signal recorded on some vertical components has character- istics of the signal seen on the horizontal components (Lewis and Tuthill, 1981). The signals observed on the vertical and horizontal buried sensors at Lopez were visually independent of each other. Transient tests were performed on the ONR OBS by Trehu and Sutton (1994). They observed considerable cross coupling with some vertical signals from horizontal transients that were larger than equivalent vertical signals from vertical transients. They also noted large signals on the deployed sensor package that had radiated from the large support package about 1 meter from the sensor package. The results from these experiments

and those displayed in Figure 7 indicate that the rela- tively simple model presented here may not be suffi- cient in some cases to predict the complex response expected from experimental situations.

Current Response. Determination of the response of OBSs to bottom currents requires that the torque on the package generated by a bottom current be consid- ered in detail. The drag can be ignored at seismic particle velocities, but drag force becomes

(sYw)2 2 F~ = CO,,, ~ ~r~, (42)

at the relatively high velocities of ocean currents, where C = 0.4 is an estimate of the drag coefiScient for a sphere for Reynolds numbers above 100 (Webb, 1988), which can occur at current velocities above about 0.005 m/s for a sphere radius of 0.15 m (Binder, 1955, p. 180). We can estimate the current velocity spectrum using the estimate from the HEBBLE current spectrum (Gross et al., 1986), and Webb's (1988) (corrected) estimate of the spectrum:

sy~ = Uo 0.0003(s/2~0 -15 (43)

where U0 is the current velocity 1 meter above the bottom (0.18 m/s for the HEBBLE data). Including the drag force defined by equations (42) and (43) in equations (5) and (24) leads to an estimate of' hori-

Page 16: Fidelity of ocean bottom seismic observations

550 F. K. DUENNEBIER AND G. H. SUTTON

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-100

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Horizontal pull at plate on lower horizontal

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Horizontal pull at plate on vertical

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0

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Fig. 8. Theoretical response to transient pulls on the O N R OBS sensor package. A step of force is applied to a point on the package by releasing a buoyant float. The pull from the sphere results in a net tilt or acceleration generating a slope of - 12 dB/oct at low frequencies. The pull at the base and the vertical pull generate a net displacement, but not a net tilt or velocity, thus their velocity spectra are flat at low

frequencies,

Page 17: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 551

zontal noise levels that are expected from bottom cur- rent forces on the OBS. However, the wavelength of current eddies may be roughly the size of the ONR sensor package sphere even at frequencies below 1 Hz. When eddy sizes are considerably less than the size of the sphere, they are expected to have little effect on noise level. We use equation (40) to calculate this effect, assuming that the relationship among wavelength, speed, and frequency is the same as for seismic waves. The expected noise level on the ONR OBS for currents of 0.01 and 0.1 m/s are shown in Figure 9 together with a low-noise model for continental stations (Rogers, 1992), and a "typical" quiet noise level for seismic noise in the ocean compiled by the authors. The theory predicts that bot tom currents with speeds of less than 0.01 m/s will contribute to horizontal noise levels at long periods, and current speeds greater than 0.1 m/s will contribute strongly to noise levels above 2 Hz. Sutton et al. (1988) observed strong correlation between tidal bot tom currents and ULF horizontal component noise at the Columbia-Point Arena ocean bot tom seismic station. A large broad-band variation in noise level was observed reaching a maximum of 20 dB above background level near 0.04 Hz with max- imum currents less than 0.08 rn/s. Trehu (1985b) also observed current generated noise consistent with these predictions above 2 Hz at 850 m depth on the Blake Plateau. Current noise has also been observed as nar- row band noise believed to result from shedding of vortices from parts of the OBS structure (Duennebier et al., 1981).

8. Sensor Package Burial

The theory presented above predicts that ocean bottom seismic sensors placed on soft sediments are likely to respond to ocean bot tom currents. This interaction should be decreased by reducing the cross section in the water. A test using a prototype tilt sensor package (approximately 0.15 m in diameter and 0.2 m tall) in shallow water (5 m) off Oahu showed that the noise level on the sensors was more than 20 dB higher below 0.4 Hz when the package was placed on the ocean floor than when buried. In a second test, the package was "buried" by placing it inside a "dirt bag" about 1 m in diameter and 0.2 m high with a density near that of the bottom. A package such as this might be appropriate in areas where true burial is difficult, such as on hard bottoms. The horizontal noise levels in the dirt bag were reduced by more than 10 dB compared to levels observed on the bottom, but were still nearly a factor of four higher in amplitude than when the

package was buried (Duennebier and Harris, 1989). Above 0.4 Hz, the noise level of the buried package was about 12 dB lower than the package on the bottom, and 6 dB lower than the package in the dirt bag.

Tests to check the decrease in noise levels at long periods obtained by burial were accomplished in 1990 in approximately 5 m of water on a sandy bot~om off Oahu. The ULF/VLF Experiment sensor package, a right circular cylinder 0.38 m tall and 0.31 m in dia- meter with a mass of 55 kg was placed on the bottom on its flat base, and was also buried until the top of the package was covered. Data from broad-band (GURALP CMG-3) sensors in the package show that noise levels on the vertical sensor were decreased by approximately 5 dB between 0.02 Hz and 10 Hz, while horizontal noise levels were decreased by approxi- mately 10 dB above 1 Hz and more than 20 dB below 0.4 Hz when the package was buried compared to when set on the bottom (Figure 10). As the package was moved no more than a meter between recording on the surface and when buried, and the data were taken within hours of each other, the observed decrease must be the result of burial, rather than from changes in ambient conditions. These results again strongly imply that burial of sensor packages below the ocean floor can greatly decrease noise problems caused by currents.

9. Discussion

Symptoms of poor coupling are relatively easy to spot in OBS data; these include resonant signals and noise, horizontal noise levels considerably higher than ver- tical noise levels, the appearance of large shear wave signals on vertical sensors, nonsense vector particle motion, resonant response to natural and applied tran- sients, and poor coherence between nearby collinear sensors. These problems are very common in OBS data, implying that considerable effort should be put into design and testing of OBS systems if the goals of seismology on the ocean floor are to be achieved. OBSs are intended to detect motion of the ocean floor, not the motion of the water or package tilt relative to the bottom. While it is possible that the tilt of the ocean floor itself could be significant in some situations (Webb, 1988), it is much more likely that measured tilt is the result of package inertia and interactions with the water. A certain way to test whether package rota- tions are significant is to place identical sensors (sensi- tive in the same direction) at opposite sides of a package (vertical sensors placed in different horizontal locations, and horizontal sensors placed in different

Page 18: Fidelity of ocean bottom seismic observations

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Page 19: Fidelity of ocean bottom seismic observations

FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 553

>

-10

-30

-50

-70

/

\ "% . ~ . ~ ' ~ ' " ~ " " %

0.01

,"~ I X.. _. -/ ~]

i

I

f , r

.I., ~ J ,.

I ?

0.10

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1.00

Frequency, Hz

Fig. 10. The effect of sensor package burial on noise level observed on horizontal sensors. A horizontal broad-band seismometer n a right circular cylinder resting on the bo t tom displays noise levels shown by the dark curve. When the package is buried to the top of the cylinder, the noise level is observed to decrease to the levels shown in the light curve. This decrease is approximately 10 dB above 1 Hz, and more

than 20 dB below 0.4 Hz.

vertical locations); if identical collinear sensors do not produce the same signals, then the package is re- sponding to ground motion by rotation or other distor- tions rather than by rectilinear motion. These effects are minimized as the footprint of the sensor package base is increased relative to the package height, al- though sensitivity to high frequency shear and inter- lace waves decreases as package size approaches a significant fraction of the wavelength. The necessity of removing the sensors from packages that contain buoyant parts and that have an appreciable cross sec- tion in the water is apparent, particularly when the bottom is soft. If tilt of a package is a factor in its response to motion, then horizontal sensors placed at any level, and vertical sensors not placed on the vertical axis through the center of mass (more generally, in the same vertical plane as the axis of rocking motion) will detect motion of the package caused by changes in tilt (Barash eta/., 1994). Horizontal sensor response will depend strongly on vertical offset from the axis of rotation and will be particularly sensitive to tilt at long periods. Cross coupling on the vertical sensor caused by horizontal input can be even larger than the signal generated by a vertical input of the same magnitude.

Comparison of response curves generated by the theory presented in this paper with existing data shows that signals recorded by horizontal seismic sensors placed on the ocean floor are likely to be severely

distorted by relative motion between the sensor pack- age and the bottom. Determination of the transfer function of the system to obtain true particle motion would be difficult at best because of the large number of variables, even with the knowledge obtained from an internal calibration device. It appears that the most reliable method for recovering true horizontal particle motion of the ocean floor is to bury the sensors below the ocean bottom.

When the seismic package is buried, and when it has a density similar to that of its surroundings, it must move with the ocean floor in response to seismic wave input up to frequencies where the wavelength of the seismic waves approach four times the bearing radius (Sutton and Duennebier, 1987). When the den- sity of the package and the material it is buried in are equal, the response to seismic waves is not affected by the elastic properties of the material, although a buried package can display a resonant response to a shaker or point source input (Sutton and Duennebier, 1987). Thus, the advantages of OBS burial over placement on the bottom, particularly in regions covered by soft sediments, are apparent.

Placement of sensors on hard bottoms presents other problems. In the examples presented in this paper we used a sediment shear velocity appropriate for a relatively soft ocean bottom. The equations predict excellent coupling to frequencies above 100 Hz for the

Page 20: Fidelity of ocean bottom seismic observations

554 F. K. DUENNEBIER AND G. H. SUTTON

ONR OBS if we use parameters appropriate for a basaltic bottom (v,= 1000 m/s, p=2100 kg/m3). On uncompliant bottoms where burial is difficult, such as at spreading centers, the package base mass can be increased to ensure that the gravitational coupling forces are much larger than the forces exerted by the water, and that the center of mass is kept as low as possible. An ONR OBS with a 200 kg base still couples well at frequencies above 100 Hz on a basaltic bottom. The amount of the package base in contact with the bottom will vary greatly on hard bottoms, however, and unstable, poorly coupled packages could be com- mon. This problem could be alleviated by embedding the sensors in a heavy particulate 'bag' for use on hard bottoms. Making the base heavy decreases the tendency to move with the water, and making it partic- ulate increases the surface area in contact with the bottom.

Burial of sensors a short distance below the bottom should solve a large number of the problems encoun- tered in coupling to soft bottoms. At broad-band seis- mic stations on land, noise levels can be significantly reduced by burial several tens of meters below the earth's surface, but it should not be necessary to deeply bury sensors in the ocean to reduce noise levels. On land, most noise sources and temperature variations are strongest at the surface, but nearly all noise ob- served at the deep ocean floor has its source at the ocean surface several kilometers away, not at the ocean floor, and the temperature at the ocean floor is nearly constant. Burial at several tens of meters below the ocean floor will not appreciably increase the distance to the source of the noise. Deeper burial will reduce the amplitude of any low phase velocity boundary waves scattered into the bottom by bottom irregulari- ties, and burial within basement would take advantage of the impedance increase relative to the sediment and water above, although coupling of instruments to bore- holes in the ocean is not an easy task (Stephen et al., 1994; Duennebier et al., 1987). It remains to be seen whether the cost and complications of deep burial are justified by increased signal-to-noise ratios.

This paper suggests that most modern OBSs in use today suffer because their design can prevent them from collecting high fidelity data in many situations. As a test of this allegation, an experiment is suggested where OBSs in use today are deployed together in a region with a uniformly flat bottom together with at least two buried packages, and possibly with a borehole instrument. The output of all sensors sensitive in the same direction should be nearly identical if they are detecting true ground motion. Experiments such as those planned near the OSN 1 site should be ideal.

The major equations in this paper have been coded in MATHEMATICA TM script to produce many of the figures. These text scripts can be obtained by anony- mous FTP from elepaio.soest.hawaii.edu, login: anonymous; password: your email address; cd pub/ fred; get filename. Please address problems and com- ments to [email protected].

Acknowledgements

The authors would like to express their appreciation for work contributed by others for this paper, including C. Bradley, Diane Henderson, and to our wives and families for putting up with us. The experiments de- scribed in this paper were funded by the U.S. Navy; analyses and preparation of this paper were unfunded. School of Ocean and Earth Science and Technology contribution number 4006.

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Barstow, N., Sutton, G. H., and Carter, J. A., 1989, Particle Motion and Pressure Relationships of Ocean Bottom Noise; 3900 m Depth; 0.003 to 5 Hz, Geophys. Res. Lets. 6, 1185-1188.

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FIDELITY OF OCEAN BOTTOM SEISMIC OBSERVATIONS 555

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