The influence of gas bubbles on sediment acoustic properties: in situ, laboratory, and theoretical results from Eckernförde Bay, Baltic sea

Transcription

1 Continental Shelf Research 18 (1998) The influence of gas bubbles on sediment acoustic properties: in situ, laboratory, and theoretical results from Eckernförde Bay, Baltic sea R.H. Wilkens *, M.D. Richardson Hawaii Institute of Geophysics and Planetology, University of HI at Manoa, Honolulu, HI 96822, USA Marine Geosciences Division, Naval Research Laboratory, Stennis Space Center, MS , USA Abstract Acoustic turbidity caused by the presence of gas bubbles in seafloor sediments is a common occurrence worldwide, but is as yet poorly understood. The Coastal Benthic Boundary Layer experiment in the Baltic off northern Germany was planned to better characterize the acoustic response of a bubbly sediment horizon. In this context, in situ measurements of compressional wave speed and attenuation were made over the frequency range of khz in gassy sediments of Eckernförde Bay. Dispersion of compressional speed data was used to determine the upper limit of the frequency of methane bubble resonance at between 20 and 25 khz. These data, combined with bubble size distributions determined from CT scans of sediments in cores retained at ambient pressure, yield estimates of effective bubble sizes of mm equivalent radius. The highly variable spatial distribution of bubble volume and bubble size distribution is used to reconcile the otherwise contradictory frequency-dependent speed and attenuation data with theory. At acoustic frequencies above resonance ('25 khz) compressional speed is unaffected by bubbles and scattering from bubbles dominates attenuation. At frequencies below resonance ((1 khz) compressibility effects dominate, speed is much lower (250 m s ) than bubble-free sediments, and attenuation is dominated by scattering from impedance contrasts. Between 1.5 and 25 khz bubble resonance greatly affects speed and attenuation. Compressional speed in gassy sediments ( m s ) determined at 5 15 khz is variable and higher than predicted by theory ((250 m s ). These higher measured speeds result from two factors: speeds are an average of lower speeds in gassy sediments and higher speeds in bubble-free sediments; and the volume of smaller-sized bubbles which contribute to the lower observed speeds is much lower than total gas volume. The frequency-dependent acoustic propagation is further complicated as the mixture of bubble sizes selectively strips energy near bubble resonance frequencies (very high attenuation) allowing lower and higher frequency energy to propagate. It was also demonstrated that acoustic characterization of gassy sediments can be used to define bubble size distribution and fractional volume Elsevier Science Ltd. All rights reserved. * Corresponding author /98/$ See front matter 1998 Elsevier Science Ltd. All rights reserved PII: S (98)

2 1860 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Introduction Gas bubbles are a common occurrence in organic-rich, muddy sediments of coastal waters and shallow adjacent seas (Judd and Hovland, 1992). Depths and horizontal distributions of these gas-charged sediments are usually determined from seismic profiling. The presence of gas bubbles often impedes acoustic characterization of sediments below the gas horizon and terms such as acoustic masking or blanking, acoustic turbidity, bright spots, wipeouts, and pulldowns are used to characterize gas-charged sediments. In this paper, in situ and laboratory measured values of sediment structural, physical and geoacoustic properties are used to calculate bubble size limits and to validate acoustic propagation and scattering models for the gas-rich sediments of Eckernförde Bay. In spite of the acoustic evidence for gassy sediments, direct measurements confirming the existence of in situ gas bubbles are rare. Measurements of bubble size, shape, distribution, relationships of bubbles to sediment and pore fluid matrix, and the bubble volume concentration required for modeling acoustic response of gassy sediments are almost non-existent and those measurements that are reported were often made after sediments were retrieved from the seafloor. Decompression of gaseous sediments, retrieved from the seafloor by coring, can form bubbles where none exist in situ or change the size, shape, and distribution of in situ bubbles. Most surficial gas originates from the generation of methane as a by-product of metabolism by methanogenic bacteria methane (Floodgate and Judd, 1992). In mud with high organic content, aerobic respiration is restricted to the upper few centimeters. Below this brown oxic zone, sulfur bacteria produce black, smelly sediment rich in hydrogen sulfide. After all of the sulfate is used as a terminal electron acceptor, methanogenic bacteria further reduce simple organic compounds producing methane. Pore water methane concentrations increase until they exceed saturation levels and free methane bubbles form in sediment. Martens et al. (this issue) have modeled the complex biochemical interaction of bacterial methane production, methane consumption at the base of the hydrogen sulfide reduced horizon, advective and diffusive transport processes, organic supply, and sedimentation rates for Eckernförde Bay sediments. Methane saturation concentrations are controlled by temperature, salinity, and pressure and are modeled for Eckernförde sediments by Wever and Fiedler (1995) and Abegg and Anderson (1997). Both models predict a free methane gas horizon m below the seafloor. Models of sediment acoustic behavior depend on the relationship between particle and bubble size. If the bubbles are small relative to particle size, they remain within the pore fluid and behave as bubbles in water. In this instance, acoustic propagation is primarily affected by changes in the fluid water compressibility (Wheeler, 1988). If, on the other hand, bubbles are large relative to particle size (such as in Eckernförde Bay) the structure of the sediment frame interacts with the bubbles and changes both bubble compressibility and resonance. More complicated conditions exist if sediment particles are trapped inside the bubble (Wheeler, 1988). Anderson et al. (this issue) refer to these bubble matrix relationships as interstitial bubbles (small bubbles within

3 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) the sediment matrix), sediment displacing bubbles (bubbles large compared to particle size), and gas reservoirs (sediment particles within the bubbles). Reverberation mechanisms are controlled by bubble size, bubble resonance frequency, and the acoustic frequency. The greatest reverberation occurs when the acoustic frequency matches the resonance frequency of the bubbles. Resonance frequency is controlled by effective bubble radius, the ratio of specific heats of the gas, ambient hydrostatic pressure, the real component of the sediment complex shear modulus, sediment density and the polytropic coefficient (Lyons et al., 1996). For acoustic frequencies well below bubble resonance (wavelengths much larger than bubble size) reverberation is controlled by the bulk modulus (compressibility) of the gas water mixture and decreases rapidly with decreasing frequency. At frequencies well above bubble resonance (wavelengths much smaller than bubble size), reverberation is the result of geometric scattering controlled by bubble cross-sectional area and bubbles can be modeled as single-point or multiple-point scatterers. Reverberation above resonance is much higher than for bubble-free sediment. For acoustic propagation at frequencies well above the resonance frequency of bubbles, compressional wave speed is the same as bubble-free sediment; whereas, well below the resonance frequency of bubbles, compressional wave speed is much lower than in bubble-free sediment (Anderson and Hampton, 1980a, b). Compressional speed at frequencies slightly greater than the resonance frequency of bubbles is predicted to be higher than the speed in bubble-free sediments. Attenuation is highest at the bubble resonance frequency decreasing rapidly at frequencies above and below bubble resonance. Most gaseous sediments contain a mixture of bubble sizes and the frequency-dependent compressional wave speed and attenuation as well as acoustic reverberation are a summation of the combined effects of various bubble sizes in the population. Frequency-dependent acoustic wave speed and attenuation as well as scattering strengths can theoretically be used to estimate the bubble size density function in sediments (Anderson and Hampton, 1980a; Gardner, 1988; Boyle and Chotiros, 1995). Similar acoustic techniques are used for determining the air bubble distribution in seawater (Clay and Medwin, 1977; Koller et al., 1992), although the mechanisms governing bubble formation and stability favor larger-sized bubbles in sediments compared to water (Boyle and Chotiros, 1995). Acoustic wave speed and attenuation as well as scattering strengths are used to determine over which frequency ranges bubble resonance dominates and over which frequencies the sediment acts as a highly compressible medium (below resonance effects) and where bubble scattering dominates (above resonance effects). For a dispersed collection of bubbles covering a variety of size ranges, the largest bubbles control below resonance acoustic behavior and above resonance behavior is controlled by the smallest bubbles. In this study, in situ measurements of compressional and shear wave speed in gassy sediments are summarized and then used to predict the limits of bubble sizes for sediments in Eckernförde Bay. Normal incidence acoustic profiles were collected with an acoustic sediment classification system. Buried hydrophones were used to determine vertical changes in the speed and attenuation of acoustic energy penetrating into the sediments. In situ vertical interval acoustic speed was measured using transducers

4 1862 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) attached to a sediment core barrel, whereas horizontal speeds were measured with probes inserted by divers. High-frequency laboratory compressional speed and attenuation measurements were also made on sediments that were maintained at ambient pressures using pressure containers. The frequency range of reverberation and bulk geoacoustic properties ranged between 5 and 400 khz. Analyses of these acoustic data coupled with the extensive environmental data are used to determine bubble size distribution and validate acoustic propagation and scattering models for gassy sediments (Anderson and Hampton, 1980a, b; Wheeler and Gardner, 1989). 2. Environmental setting Eckernförde Bay, a semi-enclosed, fjord-like bay located in the southwestern Baltic Sea, has long been characterized by acoustic turbidity, masking deeper sediments from acoustic characterization (Schüler, 1952; Edgerton et al., 1966; Whiticar, 1982; Wever et al., this issue). During the recent Coastal Benthic Boundary Layer (CBBL) experiments in Eckernförde Bay, this acoustically turbid zone was evident in acoustic records covering the frequency range of khz (Lambert et al., 1995; Haynes and Davis, 1995; Schock et al., 1995; Wever et al., this issue). Acoustic turbidity is restricted to sediments lying in deeper waters (22 24 m) of the Bay and is spatially and temporally variable (Wever and Fiedler, 1995). The uppermost acoustic horizon ranges from 50 to 200 cm bsf (below seafloor) and migrates vertically in response to temperature, nearer the sediment water interface when sediments are warmest. As early as the studies of Schüler (1952), acoustic turbidity at this site was attributed to the presence of free gas in the sediments. The free gas is methane produced in situ by methanogenic bacteria (Whiticar, 1978; Martens et al., this issue). X-ray computed tomography (CT) scans of cored sediments, which were retained at in situ pressures, reveal discontinuous zones of methane bubbles in Eckernförde sediments (Abegg and Anderson, 1997). The bubbles resolvable by CT scans range from 0.5 to 5 mm in equivalent radius with 0 2% (mean 0.1%) percent gas by volume. Small gas bubbles are spherical but larger bubbles appear coin -shaped with the longer axis vertical. Considerable horizontal variability was found in methane bubble concentrations (by volume, number of bubbles, and size distribution) in cores collected 2 20 m apart (Anderson et al., this issue). This is in agreement with the meter-scale variability in acoustic reverberation noted in acoustic profiling records. In general, methane bubble distribution corresponds to the uppermost depth of the acoustic turbidity horizon. Central Eckernförde Bay is a depositional environment with bottom currents normally too slow ((10 cm s ) to erode surficial sediments (Friedrichs and Wright, 1995). High sedimentation rates (3 10 cm yr ) and high water column productivity result in near-surface anoxic conditions restricting benthic biological activities to the upper few centimeters of sediment (Nittrouer et al., this issue). Sediment organic carbon content averages 5% dry weight. The resultant surficial sediments (0 30 cm bsf) are silty-clay sized with very low values of shear strength ( kpa), bulk

5 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) density ( kg m ), compressibility (virgin compression index ), and permeability (10 10 ms ), and with high water contents ( %) (Briggs and Richardson, 1996; Silva et al., 1996; Brandes et al., 1996). Illite, kaolinite, smectite and minor amounts of quartz, plagioclase and potassium feldspar dominate the silty clay sediments. Low values of surficial sediment compressional wave speed ( m s ) and attenuation ( db m at 58 khz) and shear wave speed (7 9ms ) reflect the easily compressed and low rigidity nature of these sediments (Richardson and Briggs, 1996). Sediment porosity (84%), bulk density ( kg m ) and grain size (11 ) vary little over a depth range of cms bsf (Richardson and Briggs, 1996). Shear wave speed increases from 7 to 9 m s in surficial sediments and 15 to 20 m s at 2 3 m depth (Richardson and Briggs, 1996; Stoll and Bautista, this issue, Davis et al., 1996). Sediment permeability decreases from 10 ms at 10 cm bsf to 3 to 4 10 ms at 300 cm bsf, and compressibility decreases with depth in the sediment (Silva et al., 1996). The high organic content of the sediment provides an ample energy source to drive biochemical reactions in surface sediments. Oxic metabolism of organic matter is restricted to the upper 1 2 cm of sediment. Sulfur bacteria metabolize organic matter producing the characteristic H S gas smell to depths of cm. Below that depth, methanogenic bacteria dominate and produce considerable quantities of methane (Martens et al., this issue). Once the methane exceeds saturation levels free methane bubbles form in the sediment creating the acoustic scattering that dominates acoustic records from this site (Abegg and Anderson, 1997). 3. Methods and results In the presentation of results of acoustic measurements from Eckernförde Bay, aspects of both propagation speed and attenuation of compressional waves in gassy sediments at different frequencies will be examined. These data cover frequencies (5 400 khz) well above, at, and slightly below the resonant frequencies of the spectrum of bubble sizes measured in the Eckernförde sediments (Anderson et al., this issue). Each set of acoustic measurements will be presented in turn and discussed in relation to frequency-dependent predictions of compressional wave speed, attenuation, and scattering for gas-charged sediments. These data result from several different experiments but all measurements were made within the CBBL test site in Eckernförde Bay between 28 June and 7 July 1994 (Fig. 1, Table 1). Data collected at normal incidence by the Acoustic Sediment Classification System (ASCS) shows that the depth to the acoustic scattering layer of gas bubbles at the site varies over very short distances. The 30 khz data displayed in Fig. 2 were collected while the ship swung at anchor and represents about 8.5 min of recording during which the ship may have moved only several 10s of meters. The depth below seafloor to the reflecting gas horizon varies over this area by about 50 cm, from 0.7 to 1.2 mbsf. Bottom variability is further illustrated by a display of individual ASCS waveforms in Fig. 3. While the ship moved only a short distance during the time these data were

6 1864 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 1. Eckernförde Bay is located in the western Baltic Sea along the coast of northern Germany. The CBBL test site, located in approximately 24 m water depth, is the locus of experiments used in this study. Table 1 Characteristics of the acoustic systems discussed in this study Name Type of measurement Frequency ASCS Reflection profiling 15, 30 khz Acoustic Lance In situ vertical sound speed and attenuation 5 20 khz Neptune In situ horizontal sound speed and attenuation 38, 58 khz ISSAMS In situ horizontal sound speed and attenuation 58 khz ISSAMS In situ shear wave speed Hz Pressure cores Lab sound speed and attenuation under pressure 400 khz Buried hydrophones Insertion loss 15, 21, 25, 30, 35 khz recorded, a change in intensity of 100% can be seen in the first seafloor reflection, as well as changes both in intensity and depth of the sub-seafloor gas horizon reflection. These variations are typical for the experimental area and represent spatial variability in sediment characteristics. Transducer motion was minimal as the seas were calm

7 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 2. Acoustic Sediment Classification System (ASCS) data recorded during Acoustic Lance deployment at CBBL test site. Horizontal axis is elapsed time, as the WFS PLANET was anchored while these data were collected. Horizontal grid represents meters depth based on a sound speed of 1500 m s. The yellow vertical line depicts the location of deployment of the Acoustic Lance and represents an approximately 90 s gap in the geophysical record. Notice how the gas horizon reflection changes in intensity and depth while the ship swung on its anchor over short distances.

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9 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 3. ASCS seismic waveforms were recorded once per second before and after deployment of the Acoustic Lance. The approximately 90 s gap in the recorded ASCS signals (marked by L) eliminated possible acoustic interference from ASCS transmissions with recorded Lance signals. The ASCS waveforms are the same as those that produced that portion of the seismic record shown immediately about the Lance deployment line in Fig. 2. Note the variability in both the intensity of the seafloor return and the intensity and depth below seafloor of the primary gas horizon reflection (G). and the transducer was firmly mounted in the moonpool of the 80-m-long WFS PLANET. The Acoustic Lance consists of an array of hydrophones attached as outriggers along the barrel of the gravity corer deployed from WFS PLANET. An acoustic source is attached to the weightstand of the corer. When the source is fired the receivers (8 in this case) record the acoustic waveform as it passes (Fu et al., 1996). Examples of Lance waveforms collected in water and in gassy sediments at the CBBL test site are shown in Fig. 4. Picks of the first arrivals yield interval compressional wave speeds. Intervals between receivers were 60 cm for all but the first pair used in this experiment. The uppermost pair was separated by 47 cm. The usable frequency range of the Acoustic Lance is between 5 and 20 khz, as demonstrated by a power spectrum of Lance data collected in water (Fig. 4). Greatly increased attenuation within the gassy sediments is evident in the comparison of the water and gassy sediment waveform records in Fig. 4. Data collected from the CBBL test site are displayed with variable amplification in Fig. 5. After only short

10 1868 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 4. Waveforms recorded by the Acoustic Lance suspended in water (left) and in sediments containing gas bubbles (right). Signal strength in water falls off roughly as the square of the distance from the source, which is mounted 1.4 m above the first receiver. In the sediments (right), signal strength suffers high attenuation after encountering the gas horizon at about 1 m below the top receiver. Attenuation within the sediments above the gas layer is very low, almost the same as in water. A power spectrum is inserted for the Lance signals transmitted through water. distances, signals propagating through the gassy sediments are reduced to levels near the noise and first arrivals are difficult or impossible to pick. An interesting observation not well illustrated in Fig. 5, but present in signals from some of the other sites, is a tendency for the spectral content of signals within the gassy zone to show a relative increase in power at higher frequencies. This behavior is not consistent with the normal increase of attenuation coefficient with frequency that is commonly measured for seafloor sediments. In most of the Lance data there is a noticeable slowing of compressional wave speed within the gassy sediments. Slowing of the signal at 15 khz was also demonstrated during recording of the ASCS signal by the Lance array. This waveform, a narrowband 15 khz signal, is illustrated in Fig. 6. Lines have been drawn on the data illustrating signal moveout for speeds of 1430 m s (the speed of non-gassy sediments) and for 1100 m s. Clearly, at 15 khz, sediment compressional wave speeds are significantly slower than in non-gassy sediments nearby. Compressional wave speeds from the Acoustic Lance and other experiments are plotted in a composite in Fig. 7. Because of the variability in depth to the gassy

11 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 5. Self-normalized Lance records (all signals divided by their own maximum) collected from CBBL test site. Signal-to-noise ratio greatly decreases by the third receiver (1.07 m), and the signal totally disappears into the noise by the sixth (2.87 m) receiver as a result of high attenuation. Picking first arrivals in the low amplitude signals is less accurate than picking first arrivals in the signals above the gassy layer. horizon illustrated in Fig. 2, and some question as to the exact depth of penetration of the Lance receivers, all of the speed profiles have been adjusted so that the decrease in speed occurs at 1 mbsf. This meant shifts of up to 1 m from depths estimated by observation of the position of mud on the outside of the core barrel, and while not satisfying, it at least lends coherence to the data. Speeds above the gassy horizon average around 1430 m s although several of the profiles suggest speeds somewhat higher immediately above the speed slowdown. Speed differences of less than 40 m s between Lance and other measurements are not significant as they represent a difference of compressional wave arrival time of a single digitization point at the spacing of Lance receivers used in Eckernförde Bay. Speeds drop off sharply in all profiles, save one, to values between 1100 and 1200 m s. The only profile with enough energy to transmit more than 3 m deep was one of the ASCS source records. It suggests that speeds may in fact increase below the bubble horizon, entering a region without bubbles once again. Interestingly, the approximately 1.5-m-thick zone of reduced speed indicated by the Lance results corresponds to the interval of methane bubble stability described in Wever et al. (this issue) based on temperature and pressure

12 1870 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 6. Waveforms transmitted using the hull-mounted ASCS transducer (15 khz) were recorded by the Acoustic Lance receiver array. The uppermost receiver was probably embedded at or near the top of the gassy sediment horizon. Lines on the figure indicate moveout of first arrival times given sediment sound speeds of 1430 m s (mud without gas) and 1100 m s. conditions at the test site. Beneath the postulated bubble stability zone, methane may remain in solution. Additional speed data including measurements using in situ probes and measurements of speed on sediment cores maintained at in situ pressure are also shown in Fig. 7. These data represent speeds measured at distinct horizontal depth levels, as opposed to the vertical interval speeds of Lance. The in situ measurements of Neptune (38 and 58 khz) and the in situ Acoustic Measurement System (ISSAMS) (58 khz) are both made over cm path lengths using pulse techniques (time-of-flight and amplitude) described by Barbagelata et al. (1991) and Richardson et al. (1991). Both sets of data are in agreement, showing sediment speeds at around 1430 m s from the surface to approximately 1.5 mbsf (Richardson and Briggs, 1996). Compressional wave speed was also measured from diver cores that were sealed in pressure-tight containers at the seafloor (Abegg and Anderson, 1997). Cores were opened, and speed measured using pulse transmission techniques, in a hyperbaric chamber so that the sediment did not decompress after collection (Richardson and Briggs, 1996). The 400 khz measurements, with a small correction to in situ temperatures, are in excellent agreement with lower frequency in situ data measure using ISSAMS and Neptune. While speeds of sediments measured at the higher frequencies discussed above do not indicate the presence of gas through reduced speed, acoustic waveforms from

13 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 7. Composite plot of compressional wave speeds measured in this study. Solid lines represent interval speeds from the Acoustic Lance. Symbols are discrete point measurements made either in situ (ISSAMS, Neptune) or in the laboratory on cores maintained at in situ pressure. All laboratory values were corrected to in situ temperature. Error for Lance speeds is about $20 m s (one digitization point); whereas ISSAMS, Neptune, and laboratory core measurements have errors of less than $5ms. Neptune and the pressure cores do reveal the presence of gas bubbles through increased attenuation. Waveforms collected by Neptune at the CBBL test site are displayed in Fig. 8. Note that the waveforms in this figure propagated over identical 50-cm horizontal paths, unlike the vertical travel paths of the Lance waveforms of Fig. 5. The waveforms show little decrease in amplitude until a depth of 1.3 mbsf, where attenuation is strong (40 50 db m ). Below this depth, however, signal strength returns, and attenuation is similar to gas-free sediment. Since there is little difference in arrival times of the attenuated or strong signals, the measurement frequencies are interpreted to be well above the resonance frequency of bubbles present in this depth interval.

14 1872 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 8. In situ waveforms measured using Neptune (38 khz). Note that arrivals below 0.5 mbsf are fairly uniform (speeds about 1430 m s ). Attenuation of the signal increases with depth to 1.3 mbsf, which is below the gassy horizon. At 1.5 mbsf signal amplitude is nearly equivalent that in non-gassy sediments above the gas horizon. Time includes delays from a variety of sources in addition to transit time in the sediments. Speed is calculated from the difference between arrival time between transducers at fixed distances in seawater and in sediments. Greatly enhanced attenuation is seen in the pressure core records in the same manner, at about 1.2 mbsf (Fig. 9). The zones of high attenuation correspond to intervals of large concentrations of bubbles in CT-scans of these same cores (Anderson, personal communication). Neptune and pressure core data suggest that gas is present in the sediments, but does not diminish speeds of compressional waves with frequency in excess of 40 khz. Furthermore, the fact that in each case only a single waveform exhibited extreme damping, is evidence of the discreet nature of gas bubbles, e.g. they may reside in concentrated layers within the sediments, or even perhaps pockets (Abegg and Anderson, 1997). As part of an experiment to measure acoustic insertion loss across the sediment seawater interface as well as loss within the gassy horizon, six hydrophones were pushed into the bottom by divers. The hydrophones were used to record waveforms generated by the ASCS transducer at discrete frequencies of 15, 21, 25, 30 and 35 khz. Signals were demodulated to 5 khz and sampled at 50 μs intervals.

15 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 9. Laboratory compressional wave measurements (400 khz) made for sediments in a core (P3) retained at in situ pressure. Signals recorded for sediment at 1.3 mbsf were more highly attenuated than for sediments at depths above and below. Attenuation calculated as 20 log of the ratio of signal amplitudes received through sediment and a reference standard (distilled water). Another hydrophone was set on the seafloor above the buried phones to act as a timing reference, since the ship drifted at anchor over the course of the experiment and total travel times depended on the location of the ship relative to the arrays. Two waveforms from the uppermost buried hydrophone (C2) and two from the deepest hydrophone (C7) are displayed in Fig. 10. At a calculated depth of 14 cm (see below), arrival times at the hydrophones well above the gassy horizon are identical for both 15 and 35 khz. However, at a depth of 1.36 m there is a noticeable difference. The high frequency signal arrives earlier than the lower frequency. This observation reflects differences between the higher speeds of Neptune and ISSAMS and the slower interval speeds of Lance seen in Fig. 7. Using a sediment speed of 1430 m s from the 38 khz Neptune measurements, depths to the buried hydrophones were calculated based on arrival times from the 35 khz experiment. (Note that the 50 μs sampling rate is not high enough to obtain interval speeds over the spacing involved in the hydrophone burial.) Profiles of the waveforms at both frequencies are displayed in

16 1874 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 10. Signal waveforms recorded with buried hydrophones using the ASCS as a source. Data have been demodulated to 5 khz and sampled at 50 μs. Upper signals were recorded from a hydrophone buried approximately 0.14 mbsf using the ASCS as a 15 and 35 khz source. Lower pair of signals were recorded from a hydrophone buried at approximately 1.36 mbsf. Note that the 35 khz signal arrives earlier than the 15 khz signal at the deeper hydrophone; whereas, signals arrive at the same time at the shallower depth. Fig. 11. Differences between the 15 and 35 khz arrival times at the same receivers below approximately 60 cm depth are evident. The difference in arrival times from the hydrophone at approximately 98 cm suggests that the hydrophones were deployed in an area where the gassy horizon was shallower than 1 mbsf. Upward traveling energy (to the right of the arrow in Fig. 11) appears to be reflected from a depth a little below 0.5 mbsf.

17 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 11. Self-normalized (all signals divided by their own maximum) waveforms recorded with buried hydrophones using the ASCS as a source. Depths were determined using travel times from 35 khz waveforms and 1430 m s sediment speed. Note the substantial arrival delays at hydrophones near and below 1 m for 15 khz compared to 35 khz signals. Travel times of the first arrivals at all frequencies recorded during the buried hydrophone experiment are plotted versus approximate depth in Fig. 12. Above the level of the gas layer reflection, seen in the full waveforms (0.5 m), arrivals at all frequencies are at the same time. Dispersion, in the form of later arrivals by the 21 and 15 khz signals, begins to show up in the signals recorded by the deeper hydrophones. The 15 khz signals exhibit the greatest increase in travel time relative to the 35 khz

18 1876 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 12. Traveltime versus depth for signals recorded by buried hydrophones using the ASCS as a source of five discrete frequencies. The lower frequencies generally arrive later than the higher frequencies at depths greater than 0.5 mbsf. Also, note that the biggest difference in arrival time was not recorded at the deepest hydrophone. arrivals. This would appear to reflect the fact that, given a distribution of bubble sizes, the longer wavelengths of the 15 khz signals include a greater volume of gas bubbles which are below bubble resonance frequency and which contribute to lower compressibility than the higher frequency (shorter wavelength) signals. The 21 khz signals experience some slowing, although not to the extent of the 15 khz signals, whereas the other, higher-frequency acoustic waves do not appear to experience significant slowing. This observation will make it possible, later, to examine bubble size limits within the sediments penetrated by the buried hydrophones. The greatest difference in arrival times between high- and low-frequency signals is not seen at the deepest receiver, but rather occurs at approximately 90 cm below the seafloor. This observation can be explained either by low-frequency (15 khz) speeds between 90 cm and 1.3 m being greater than those at 35 khz (not likely) or by a locally heterogeneous horizontal gas bubble distribution in the area. The lower speeds would suggest more gas above the receiver buried to 90 cm than above those buried deeper. In addition, some unknown effect of the insertion process that mimics the dispersion characteristics of the gassy sediments cannot be entirely ruled out.

19 4. Discussion R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Before proceeding with a discussion of the data it is useful to summarize what the various experiments reveal about the behavior of the gassy sediments of Eckernförde Bay. Compressional wave speed shows strong frequency dependence. Low interval speeds are measured within the gassy sediments using the Acoustic Lance over the frequency range of 5 20 khz. Reduced speed begins at approximately the same depth as the appearance of acoustic turbidity seen in 15 and 30 khz acoustic reflection records. Higher-frequency measurement systems (ISSAMS, Neptune - 38 and 58 khz) do not record lower speed in the same gassy sediments, but do exhibit enhanced attenuation at discrete levels below the depth of onset of acoustic turbidity. Acoustic Lance signals also exhibit high attenuation so much so that first arrivals are below noise levels at depths greater than 3 m. Furthermore in some, but not all, signals identifiable within the gassy zone there is less attenuation of high frequencies versus low frequencies. Lower frequencies must suffer greater damping due to some combination of gas bubble size and volume distribution. Compressional speed measured using buried hydrophones at frequencies of 21 khz and below are similar to those measured using the Acoustic Lance. Interestingly, the deepest hydrophone did not show the largest delay between high and low frequency signals, strongly hinting that there is heterogeneity of bubble concentration on a very local scale in the Eckernförde Bay mud. These observations along with measured sediment physical and geoacoustic properties will be used to predict frequency dependent effects of bubbles on shear and compressional wave propagation in Eckernförde gassy sediments Effects of gas bubbles on shear wave speed (shear modulus) In situ shear wave speed of Eckernförde Bay sediments was measured with probes using a pulse technique (Richardson and Briggs, 1996). Near surface speeds ranged from 7 9, increasing to m s in gassy layers at 2 mbsf (Fig. 13). Relative shear wave attenuation did not vary with depth. Based on near surface gas-free measurements and an expected gradient with depth (D, m)of» "»s(@1.0m) D (1) where»s(@1.0m) is the shear wave speed at 1.0 mbsf, predicted shear wave speed ranges from 12 to 16 m s at 2 mbsf and 14 to 18 m s at 3 mbsf. Near-surface gradients of shear wave speed can also be predicted by an empirical relationship to sediment void ratio (e) based on in situ measurements made in a variety of sediment types in La Spezia Bay, Italy (Richardson et al., 1991)» "(85/e)D (2) Given an average void ratio of 5.5, predicted shear wave speed increases from 11 m s at 0.3 mbsf, 15 m s (1.0 mbsf), 19 m s (2.0 mbsf), to 21 m s at 3.0 mbsf. The similarity between shear wave speed empirical predictions for bubble-free sediments and in situ measurements of the gassy sediments of Eckernförde Bay, suggest that low concentrations of bubbles ((2.0% by volume) have little affect on shear wave

20 1878 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 13. Shear wave speed as a function of depth. Shear wave speed was measured using probes deployed by divers at approximately the same time and location as the compressional wave measurements plotted in Fig. 8. speed or attenuation. The Eckernförde Bay results are in agreement with continuum model predictions of Wheeler and Gardner (1989) for large bubbles within a saturated medium and the laboratory measurements of Gardner (1988) and Duffy et al. (1994) on muddy sediment containing large bubbles. The less than 2% decrease in shear modulus ((1% for shear wave speed) predicted for gassy sediments with 1% gas by volume using the Wheeler and Gardner model are within the variability of the in situ measurements. It is therefore concluded that shear wave speed or shear modulus is essentially unaffected by the volume of bubbles found in Eckernförde Bay sediments. Sediment dynamic shear modulus is an important sediment characteristic controlling bubble resonance and gas bubble frame or frictional damping (Anderson and Hampton, 1980b). Bubble resonance and gas bubble damping, in turn, are important components in determination of compressional wave attenuation and scattering. Higher values of sediment shear modulus yield higher bubble resonance frequencies, especially when compared to seawater, higher attenuation, especially at frequencies

21 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) near or above bubble resonance, and changes in the frequency dependent speed and scattering. Sediment dynamic shear modulus (G) for an elastic solid is G"» ρ (3) where» is the shear wave speed and ρ is the sediment density. For sediments in Eckernförde Bay, shear modulus is kpa at 0.3 mbsf and kpa at 2 mbsf Gas bubble resonance in sediments Gas bubbles in sediments are capable of vibratory motion with a sharply peaked resonance at the fundamental pulsation frequency. Resonance in sediments occurs at a higher frequency than in water because the sediment provides elasticity and mass to the bubble wall increasing the restoring force of the vibratory motion. Resonance frequency is therefore controlled by resonance of the bubble in water modified by the elastic properties of the solid (the sediment). Fundamental pulsation (resonance) frequency ( f ) of a bubble in sediments is f "(3γP /Aρ #4G/ρ ) /(2πr ) (4) where γ is the ratio of specific heats of the bubble gas, P is the ambient hydrostatic pressure, ρ is the bulk density of the sediment, G is the real part of the complex sediment dynamic shear modulus, r is the bubble radius, and A is the polytropic coefficient (Anderson and Hampton, 1980b). The expression used to calculate the polytropic coefficient is given in the appendix. Adiabatic dynamics applies at resonance for the range of bubble sizes considered here, therefore A was set to 1 for calculation of bubble resonance frequency. Resonance frequency calculated for bubbles found 2 meters below the sediment water interface (Fig. 14) is based on values of parameters presented in Table 2. The ratio of specific heats for methane can be found in most chemical handbooks. Sediment bulk density was determined from sediment water content and grain specific gravity (Richardson and Briggs, 1996); shear modulus was calculated from shear wave speed (this study); and the ambient hydrostatic pressure was corrected for 24 m water depth and 2 m of sediment cover. Bubble resonance frequencies for Eckernförde sediments are about 37% greater than for bubbles of the same radius in seawater at the same depth and temperature. For comparison bubble resonance is calculated for typical coastal sand and mud sediments based on the data from Richardson et al. (1991). Shear wave speed (40 m s for mud and 100 m s for sand) and sediment bulk density (1.61E 10 kg m for mud and kg m for sand) were the only parameters changed. The increase in bubble resonance with increasing shear modulus is easily seen Limits of bubble size distribution in Eckernfo rde Bay sediments Bubble size distributions for sediment collected at the experimental site were measured using X-ray computed tomography (CT) of sediment cores transported

22 1880 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 14. Bubble resonance frequency as a function of gas bubble radius for Eckernfo rde Bay sediments, seawater, and typical shallow-water mud and sand sediment. The shear modulus of sediments is important in determining bubble resonance frequency and is largely responsible for separation of the data. from seafloor to laboratory in pressure tight aluminum chambers (Abegg and Anderson, 1997; Anderson et al., this issue). Bubble sizes ranged from a resolution limit of about mm equivalent diameters (diameter of a sphere with volume equal to the actual volume of the bubble). Bubble size distribution and the gas volume were estimated from CT-scan imagery. Compressional wave speed and attenuation measurements made in the hyperbaric chamber were from those same CT-scanned cores. Gas volume ranged from 0 to 2% with a mean of 0.1% for sediments collected at the experimental site. By contrast, gas volumes as high as 8% were measured in cores collected from a nearby pockmark (Lyons et al., 1996). The depth of the free-gas horizon corresponded with that of initiation of acoustic turbidity. Bubbles were not evenly distributed throughout the length of the gassy zone but occurred in discrete layers or horizons interspersed with bubble-free layers (Abegg and Anderson, in press). For an accurate prediction of the effects of bubbles on acoustic scattering and propagation the full spectrum of bubble size distribution must be known. Based on the speed data collected with buried hydrophones, the transition to below resonance effects, where bubbles dominate sediment compressibility, first begins

23 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Table 2 Values of parameters used to calculate bubble resonance and compressional wave speed and attenuation for gassy sediments in Eckernfo rde Bay Water depth 24 m Sediment depth 2 m Sediment temperature C at surface; C at 180 cm Sediment salinity 20 ppt at surface; ppt at depth Bubble radius (r ) m Bubble fractional volume (n ) (mean 0.001) Ratio of specific heats of gas (γ) 1.31 at 15 C Thermal conductivity of gas (C ) Js m C Specific heat at constant pressure (s ) 2.19 J kg C Gas density at 1 atm (ρ ) kg m Hydrostatic ambient kpa pressure (P ) at 1 atm Fractional porosity (n) 0.85 Seawater density (ρ ) kg m Sediment bulk density (ρ ) kg m Sediment grain density (ρ ) kg m Shear modulus of sediment (G) kpa at 2 mbsf Bulk modulus of grains (K ) kpa Bulk modulus of pore kpa water (K ) Permeability 3 10 ms between 21 and 25 khz. These data suggest that the smallest effective bubble radius in Eckernförde gassy sediments is between 0.3 and 0.4 mm. Combined with the CT-scan data discussed above, the effective bubble sizes in Eckernförde sediment are therefore between 0.3 and 5.0 mm radii. The bubble size distribution, bubble resonance frequency, and shear modulus determined in the last three sections will now be used to predict frequency-dependent speed and attenuation of the gassy sediments of Eckernförde Bay Effects of gas bubbles on compressional wave speed At acoustic frequencies well below the resonance frequency of the largest bubbles, and for small bubbles within the interstices of grains, compressibility (β ) of a bubbly fluid (pore water) is the volume-weighted sum of fluid and gas compressibility β "S β #(1!S )β (5) where S is the degree of saturation, β is the compressibility of the pore fluid, and β is the compressibility of the methane gas (Stoll and Bautista, this issue). Density is also the volume-weighted sum of the fluid and gas densities. Using these values (compressibility in a fluid medium) as inputs to the Biot model (essentially reduced to

24 1882 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) the Gassmann equation because of the high permeability), Stoll and Bautista predict compressional wave speeds that quickly reduce to 250 m s at saturation less than (at 0.42% bubbles by volume). Theoretical predictions of compressional wave speed based on the combined elastic behavior of gas and sediments (Wheeler and Gardner, 1989), where bubbles are large relative to particle size, also indicate speeds of less than 250 m s at volume fractions less than 2%, for sediments with low shear modulus, such as in Eckernförde Bay. The low speeds are dependent upon the shear modulus of the sediment as well as the void fraction of bubbles. Bulk modulus is dependent on the shear modulus of the sediment because compression of the bubble cavities is controlled by deformation of the surrounding matrix. Anderson and Hampton (1980b) calculate compressional wave speed of gassy sediments, at acoustic frequencies much less than the fundamental resonance frequency of bubbles, from the bulk and shear moduli of gassy sediments and the sediment density (see the appendix). Sediment shear modulus and density were measured as part of this study (Table 2) and the bulk modulus is the composite bulk modulus of mineral grains, the frame, and of pore fluid modified by gas. Using the Anderson and Hampton model, compressional wave speed is predicted to decrease rapidly with increasing gas content at acoustic frequencies much lower than the resonance of bubbles found in sediments from Eckernförde Bay (Fig. 15). For sound speeds at or above bubble resonance frequency, the effects of bubble resonance and damping must be considered. Anderson and Hampton (1980b) modified the Fig. 15. Compressional wave speed as a function of free gas content. Speed calculations are based on the Anderson and Hampton model (Eq. (A.9) in the appendix) for frequencies much lower than the resonance frequency of the bubbles. Average sediment and water properties are found in Table 2. Very small concentrations of gas reduce compressional wave speed substantially.

25 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) mathematical expressions for sound speed in a uniform distribution of gas bubbles in water to include the addition of shear modulus and the effects of shear modulus on bubble resonance and damping to calculate the sound speed ratio (c /c) (see the appendix). Sound speed ratios are calculated for Eckernförde gassy sediments using values of sediment, water and gas properties presented in Table 2. As the acoustic frequency increases to near bubble resonance, predicted compressional speed first decreases then increases to values greater than for bubble free sediment for all bubble sizes ( mm radius) and gas volumes (1, 0.1 and 0.01%) considered (Fig. 16). At frequencies much greater than the resonance frequency of bubbles, predicted compressional speed approximates that of gas-free sediments. The importance of bubble resonance in prediction of compressional speeds in gassy sediments is easily seen by a comparison of Fig. 16 with the relationship between bubble resonance frequency and bubble size (Fig. 14). Actual speeds measured in gassy layers at frequencies below the lower resonance limit (Lance, 5 15 khz and buried hydrophone data 15 khz) were higher ( m s ) than predicted by the models of Stoll and Bautista (this issue) and Wheeler and Gardner (1989). Compressional speeds measured in gassy sediments at frequencies above resonance including Neptune (38 and 58 khz), pressure cores (400 khz), and hydrophones ('21 khz) were all near that of bubble-free sediments. These data do not show the higher speeds near resonance predicted by calculations (Fig. 16) based on the Anderson and Hampton (1980b) model. Bubble size distribution and the spatial variability in bubble distribution may, in part, explain the higher than predicted speeds measured at acoustic frequencies below bubble resonance. The effects of bubble distribution and attenuation on compressional speed above resonance will be discussed in the next section. Abegg and Anderson (1997) and Anderson et al. (this issue) describe bubble distributions which are variable on vertical scales of centimeters (thin layers a few centimeters thick) and on horizontal scales of meters (from cores collected 2 20 m apart). The centimeter and meter scale spatial variations in methane bubble concentrations are supported by the pore water methane concentrations which alternate above and below saturation downcore (Abegg and Anderson, 1997) and vary between cores collected in the experimental site. The limited Neptune (38 and 58 khz) data demonstrate layers of low attenuation typical of bubble-free sediments interspersed between layers of higher attenuation typical of bubble scattering. All of these data suggest a highly variable spatial distribution of bubble concentrations which, depending on acoustic frequency, produce alternate layers (or lenses) of low speed (below resonance) and high speed (bubble-free sediments), variable attenuation due to bubble scattering above resonance, resonance scattering over the range of 1 30 khz, and volume scattering (below resonance) from lower impedance layers, lenses, or patches of lower speed. In order to obtain compressional wave speeds of m s in such a variable low (250 m s ) and high (1430 m s ) speed medium, the distance traveled in low speed gassy sediments must range between 2.1% (for 1300 m s ) and 9.1% (for 1000 m s ) of the total propagation path. Based on CT-scans of Eckernförde sediments these percentages are unrealistically low and additional explanations must be invoked to account for the observed wave speeds.

26 1884 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Gas bubble volume is dominated by the distribution of large-sized bubbles (Anderson et al., this issue). The volume of smaller-sized bubbles which contribute to the lower observed speeds (between 5 and 25 khz) is much lower than total gas volume and at frequencies ranging from 5 to 25 khz the smaller bubbles contribute much less than the 0.1% volume used for compressional wave speed calculations in Fig. 16. At bubble volumes of 0.01%, calculated compressional wave speed ranges from 1000 to 1200 m s, over the frequency range of 5 25 khz, with little contribution from bubbles with radii larger than 1.5 mm. These calculations suggest a volume fraction of near 0.01% for bubbles with radii less than 1.5 mm in Eckernförde Bay gassy sediment. At lower frequencies, such as the 500 Hz measurements of Gehrmann (1985), all bubble sizes contribute to reduced compressional speeds (300 m s ) and calculations based on bubble volumes of 0.1% (Fig. 16) best account for this longer wavelength, compressional wave propagation Attenuation in gassy sediments Attenuation in gassy sediments includes scattering from bubbles, frame frictional absorption, and internal absorption due to bubblewall motion (damping losses) (Anderson and Hampton, 1980a). Average measured values of attenuation for gas-free saturated Eckernförde sediments are 4 db m at 58 khz and 80 db m at 400 khz (Richardson and Briggs, 1996). These values can be used to approximate frame frictional losses for gassy sediments. Compressional wave attenuation measured in gassy sediments over the frequency range of khz, was much higher than can be accounted for by these frame frictional losses and must therefore be the result of bubble damping losses or scattering. Damping due to bubble motion is a function of thermal, radiational, and frame or viscous damping (Anderson and Hampton 1980a, b). Attenuation due to bubble motion is calculated for Eckernförde gassy sediments using values of compressional wave speed in gassy and saturated sediments, gas and saturated bulk moduli, and bubble resonance frequency determined from sediment, water and gas properties presented in Table 2 (see the appendix). Highest predicted attenuation occurs at the resonance frequency with values in excess of 2000 db m for small bubbles at a fractional volume of 1% (Fig. 16). Attenuation increases rapidly with higher bubble fraction and smaller bubble size. Predicted attenuation due to bubble motion decreases rapidly with acoustic frequency below bubble resonance but remains high above bubble resonance for all bubble sizes ( mm radius) and gas volumes (1, 0.1 and 0.01%) considered (Fig. 16). High attenuation of compressional waves at frequencies at or slightly greater than bubble resonance may explain why the predicted high wave speeds were not observed. At 400 khz, the combined attenuation due to frame frictional absorption (80 db m ) and bubble damping ((10 db m as determined from Fig. 16) does not fully account for the high attenuation indicated by measurements of pressurized cores (see Fig. 9). These data suggest that scattering from bubbles must dominate attenuation measured at these high frequencies. Attenuation measured at 400 khz on diver-collected cores that are allowed to depressurize at the surface often exceeds

27 R.H. Wilkens, M.D. Richardson/Continental Shelf Research 18 (1998) Fig. 16. Sound speed ratio (color scaled) and attenuation (contours in db m ) as a function of bubble size and acoustic frequency for bubble volume concentrations of 1% (a), 0.1% (b), and 0.01% (c). Sound speed and attenuation calculations based Anderson and Hampton (1980b) model (Eqs. (A.9) (A.13) of the appendix) and values of sediment, water, and gas properties presented in Table 2.