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Home , Challenger Deep, Don Walsh, HMS Challenger (K07), Mariana Trench, Victor Vescovo

REGULAR ISSUE FEATURE

IMPLOSION IN THE WITH THE SHOCK WAVE

By Scott Loranger, David Barclay, and Michael Buckingham

Deployment of autonomous, free-falling acoustic platform Deep Sound Mk. II over the Challenger Deep. Deep Sound Mk. II recorded the implosion of its sister platform, Deep Sound Mk. III, when both platforms were below 8,000 m depth. Mk. II recorded multiple reflections of the implosion from the seafloor and surface. The reflections of the implosion made it possible to compute an estimate of the depth of the Challenger Deep: 10,983 ± 6 m.

Oceanography4 | June 2021| Vol .Early34, No Online.2 Release ABSTRACT. Since HMS Challenger made the first sounding in the Since the 1951 Challenger II expe- in 1875, scientists and explorers have been seeking to establish the exact location and dition, a wide range of estimates of depth of the deepest part of the . The scientific consensus is that the deepest the depth of the Challenger Deep have depth is situated in the Challenger Deep, an abyss in the Mariana Trench with depths been reported in the peer-reviewed lit- greater than 10,000 m. Since1952, when HMS Challenger II, following its namesake, erature, mainstream periodicals, and returned to the Mariana Trench, 20 estimates (including the one from this study) of the cruise reports. In Figure 1, the published depth of the Challenger Deep have been made. The location and depth estimates are as results are summarized while unpub- diverse as the methods used to obtain them; they range from early measurements with lished results are neglected for the sake explosives and stopwatches, to single- and multibeam , to , both of clarity. The published results are rep- crewed and remotely operated. In December 2014, we participated in an expedition resentative of the unpublished results, to the Challenger Deep onboard Schmidt Ocean Institute’s R/V Falkor and deployed most of which come from cruise reports. two free-falling, passive-acoustic instrument platforms, each with a glass-sphere pres- The methods used to measure such sure housing containing system electronics. At a nominal depth of 9,000 m, one of extreme ocean depths, besides tradi- these housings imploded, creating a highly energetic shock wave that, as recorded by tional sounding with a weighted rope or the other instrument, reflected multiple times from the sea surface and seafloor. From cable, have included explosives and stop- the arrival times of these multi-path pulses at the surviving instrument, in conjunction watches (Carruthers and Lawford, 1952; with a concurrent measurement of the sound speed profile in the , we Gaskell et al., 1953), single-beam obtained a highly constrained acoustic estimate of the Challenger Deep: 10,983 ± 6 m. (Hanson et al., 1959; Mantyla and Reid, 1978; Taira et al., 2004, 2005; Nakanishi INTRODUCTION time, money, and intellectual energy and Hashimoto, 2011), multibeam sonar is often defined by its extremes: the have been invested in the development (Hydrographic Department and Japan tallest mountain, the driest desert, the of techniques for measuring the deepest Marine Safety Agency, 1984; Fujioka et al., deepest ocean. In March 1875, during depth in the ocean (Gardner et al., 2014; 2002; Nakanishi and Hashimoto, 2011; the first major expedition devoted pri- Stewart and Jamieson, 2019), includ- Gardner et al., 2014; van Haren et al., marily to the fledgling science of ocean- ing the development of crewed sub- 2017), side-scan sonar (Fryer et al., 2003), ography, the three-masted sailing cor- mersibles capable of making the round and sensors (Piccard and Dietz, vette HMS Challenger of the trip to the bottom of the Challenger 1967; Todo et al., 2005; Bowen et al., 2009; discovered a deep depression in the sea- Deep. The first such descent was made 2012 dive; Dziak et al., bed in the western —while on January 23, 1960, by the oceanog- 2017; Fitzherbert, 2019). Gardner et al. en route to , the ship had been rapher and US Navy (2014) and Stewart and Jamieson (2019) blown off course to the west and ser- Lt. in the both provide a review of previous inves- endipitously tracked over the southern (Piccard and Dietz, 1967; Walsh, 2009), tigations of the deepest part of the ocean. end of the Mariana Trench. Traditional whose onboard instruments indicated a The seafloor in the Challenger Deep depth soundings were taken by the crew depth of 11,521 m, although it was sub- has been further divided into three dis- at regular intervals, the deepest of which sequently revised downward to 10,916 m. tinct depressions, clearly evident from the indicated a depth of 8,140 m. Some Over five decades later, on March 26, clustering of measurements in Figure 1: 76 years later, during a three-year circum- 2012, filmmaker and explorer James the western, central, and eastern basins, navigation of Earth, HMS Challenger II, Cameron made the second crewed dive each of which contend for the location of following its namesake, returned to the to the bottom of the Challenger Deep, a the greatest depth (see Figure 6 in Stewart Mariana Trench, where its echo sounder solo descent in his DeepSea and Jamieson, 2019, and Figure 3 in recorded a depth of 10,863 m. To com- Challenger, and recorded a depth of Gardner et al., 2014). Only one estimate memorate the discovery of the deep- 10,908 m (http://www.deepseachallenge. of the corrected depth in the Challenger est trench in the world ocean by the two com/​the-expedition/). More recently, on Deep exceeds 11,000 m. During the Soviet British ships, the deep depression in the April 28, 2019, piloted his expeditions in 1957 and 1958 aboard southwestern Mariana Trench was named DSV Limiting Factor to a world record R/V Vityaz, the vessel made several Challenger Deep. depth of 10,925 ± 4 m, and then made a transects across the trench while oper- While it is generally accepted that second trip on May 1, 2019, becoming the ating a 10 kHz echo sounder (Hanson the deepest abyss in the ocean is indeed first person to have descended to the bot- et al., 1959). Water-sampling bottles and the Challenger Deep, the exact location tom of the Challenger Deep twice (Cassie thermometers were deployed to a depth and the depth of the very deepest spot Bongiovanni, Caladan Oceanic, pers. of 10,200 m, acquiring and are still topics of interest to the ocean- comm., September 24, 2020; Stokstad, salinity data from which a mean vertical ographic research community. Much 2018; Fitzherbert, 2019; Taub, 2019;). sound speed profile was computed with

Oceanography | https://doi.org/10.5670/oceanog.2021.201 the aid of an empirical equation (Hanson lower value of 10,983 ± 50 m is obtained, well-​constrained measurements of the et al., 1959). The resultant estimate of the closer to the results of the numerous throughout the water col- deepest depth was 11,034 ± 50 m. Taira other investigators. umn. In the past, before reliable deep-​ et al. (2005), however, found that, when Time-of-flight measurements of im- water-rated instruments were readily using the integrated sound speed profile pulsive acoustic signals from explosive available, the sound speed profile over as opposed to a water column average, a shots and echo sounders require very the full depth of the Challenger Deep was

VESSEL NAME: YEAR A...... HMS Challenger II: 1952 a B...... R/V Vityaz: 1957 C...... R/V Stranger: 1959 D...... DSV Trieste: 1960 E...... R/V Spencer Baird: 1962 F..... R/V Thomas Washington: 1976 G...... S/V Takuyo: 1984 H...... R/V Hakuho Maru: 1992 I...... R/V Hakuho Maru : 1992 J...... ROV Kaiko: 1995 K...... R/V Moana Wave: 1997 L...... R/V Kairei: 1998 M...... R/V Kairei: 2002 N...... ROV Nereus: 2009 O...... USNS Sumner: 2010 P.... DSV : 2012 Q ...... This Study: 2014 R...... USCGC Sequoia: 2015 S...... R/V Sonne: 2016 T...... DSV Limiting Factor: 2019 U...... DSV Limiting Factor: 2019 10.70 10.75 10.80 10.85 10.90 10.95 11.00 11.05 11.10 Depth (km)

b Challenger Deep, Mariana Trench

Central Basin East Basin 1 0 , 0

0

0 West Basin m K I H 1,260 Q G M B L T Lorem ipsum R U N F P dolor sit amet, S ,000 m A 10 1,250 J O C D 1,260 Northings (km) c 1,240 600 610 620 630 640 Mk.660 III 670670 680680 690 700 710 Eastings (km) Implosion Mk. II Recovery

1,255

Mk. III Mk. II Northings (km) Deployment Deployment

1,250 655 660 665 Eastings (km)

FIGURE 1. (a) Depth estimates in the West Basin (red), Central Basin (black), and East Basin (blue) of the Challenger Deep, Mariana Trench, and their uncertainties (if reported) taken from the peer-reviewed and popular literature, accompanied by (b) the respective positions of each measurement. The solid gray region is bounded by the 10,000 m depth contour and the area in the dashed outline is shown in (c)—the close-up of the Deep Sound Mk. II deployment and recovery positions, and the Deep Sound Mk. III deployment and approximate implosion positions. References: A = Carruthers and Lawford, 1952; Gaskell et al., 1953; Fisher, 1954. B = Hanson et al., 1959. C = Fisher and Hess, 1963. D = Piccard and Dietz, 1967; Nakanishi and Hashimoto, 2011. E = Fisher and Hess, 1963 (not shown); Fisher, 2009. F = Mantyla and Reid, 1978. G = Hydrographic Department and Japan Marine Safety Agency, 1984. H and I = Taira et al., 2005. J = Todo et al., 2005. K = Fryer et al., 2003. L = Fujioka et al., 2002. M = Nakanishi and Hashimoto, 2011. N = Bowen et al., 2009. O = Gardner et al., 2014. P = 2012 James Cameron dive. R = Dziak et al., 2017. S = van Haren et al., 2017. T and U = Cassie Bongiovanni, Caladan Oceanic, pers. comm., Sept. 24, 2020. (Note that the estimate in K was made using a combination of data from R/V Moana Wave in 1997 and R/V Melville in 2001. The position of E [R/V Spencer Baird, not shown] was made by a celestial fix, which can have errors of up to 2.2 km [Karl, 2007]; however, it was stated in Fisher and Hess [1963] that the measurement was in the western basin.)

Oceanography | June 2021 Early Online Release obtained from Matthew’s tables of sound tral and eastern basins of the Challenger an elapsed time, or a minimum bat- speed (Matthews, 1939; Carruthers and Deep with varying scientific objectives, tery charge, at which point an iron drop Lawford, 1952; Mantyla and Reid, 1978; including water sampling and CTD pro- is released, allowing the system Zheng, 2015), comprising a compilation filing throughout the water column, col- to ascend to the surface under buoy- of historical measurements of water col- lection and video recording of hadal ancy, with a speed of 0.56 m s–1 in both umn chemistry by latitude and longi- amphipods, and recording the broadband directions. At the time of the R/V Falkor tude. In modern times, direct measure- (5 Hz to 30 kHz) ambient sound over the cruise in December 2014, the first of the ments of the sound speed profile over the full ocean depth on vertically and hor- Deep Sound systems, Mk. I, had been Challenger Deep have been made with izontally aligned pairs of . retired from service, but the remain- conductivity, temperature, depth (CTD) Some of the findings from the expedition ing two, Mk. II and Mk. III, were both sensors mounted on either deep sub- have been previously reported in the pop- operational. The Vitrovex glass sphere mersibles or free-falling vehicles (Piccard ular (Nestor, 2014) and scientific (Barclay installed on Mk. II was pressure rated to and Dietz, 1967; Bowen et al., 2009; Taira et al., 2017; Lan et al., 2017) literature. 9,000 m and that on Mk. III was specified et al., 2004; Barclay et al., 2017; Dziak On December 17, 2014, we deployed to 11,000 m. Both systems had previously et al., 2017; van Haren et al., 2017) and two free-falling instrument platforms, made successful descents to a depth of with expendable bathythermographs designated Deep Sound Mk. II and Deep about 9,000 m (Barclay and Buckingham, (XBTs; Fujioka et al., 2002; Gardner et al., Sound Mk. III, into the Challenger Deep 2014). In all three Deep Sound plat- 2014). Ideally, for depth estimation, such within about 25 minutes of one another. determinations of the sound speed pro- Each had a CTD profiler and multiple LED strobe file should be concurrent with the acqui- hydrophones on board, with system elec- RF sition of the time-of-flight data; other- tronics contained in a 38 cm Vitrovex GPS

wise, significant errors can arise in the glass sphere pressure housing (Barclay HDPE 〰 acoustic estimate of the ocean depth and Buckingham, 2009). At a nominal “hard hat” (Beaudoin et al., 2009). depth of 9,000 m, during its descent to 1 TB SS memory Here, we discuss how an imploding the bottom, the spherical pressure hous- Deep Sound III DAQ CPU INS instrument enabled one of the deepest and ing on Deep Sound Mk. III imploded, Vitrovex glass sphere most constrained estimates of the depth creating a highly energetic shock wave Li-ion Ch 1 of the Challenger Deep. First, we discuss that reflected multiple times from the sea Ch 2 the expedition and the instruments used. surface and the seafloor. The direct-path Ch 3 Ch 4 We then outline the instrument deploy- shock wave and several of the multi-path ment and implosion, followed by a dis- reflections were detected by the surviv- CTD/SVX cussion of the paths traveled by the shock ing instrument, Deep Sound Mk. II. The Burn wire wave generated by the implosion and the shock wave itself saturated the receivers acoustic signal processing used to deter- on Deep Sound Mk. II and, consequen- mine the time of arrival of multiple reflec- tially, was unusable as a timing reference, tions of the shock wave. We then deter- but the arrivals of the multiply reflected Drop weight mine the depth of the Challenger Deep impulses, which were much less ener- and the uncertainty in that depth esti- getic, provided accurate time-of-flight mate. Finally, we discuss how this estimate data for the full water column. When FIGURE 2. Schematic of Deep Sound Mk. III fits with other estimates of the Challenger combined with the sound speed profile, showing four channels (not in oper- ational configuration), three recovery antennas Deep and the sources of uncertainty that obtained concurrently from the CTD on (LED, RF, GPS), and the CTD/SVX module. can partially explain the discrepancies Deep Sound Mk. II, the multiple reflec- Ch X = Hydrophone channel number X between different depth estimates. tions provided the information necessary CPU = Central processing unit for estimating the depth of the Challenger CTD/SVX = CTD/sound velocity meter THE EXPEDITION Deep at the measurement site. GPS = Global Positioning System In December 2014, a multidisciplinary HDPE = High-density polyethylene expedition to the Mariana Trench DEEP SOUND MK. II AND MK. III DAQ = Data acquisition unit INS = Inertial navigation system on board Schmidt Ocean Institute’s The Deep Sound instrument platforms LED = Light emitting diode Figure 2 R/V Falkor was led by Douglas Bartlett ( ) are deep-diving, autonomous Li-ion = Lithium-ion batteries of Scripps Institution of Oceanography. profilers designed to descend under RF = Radio frequency transponder Several autonomous, deep-diving instru- gravity until a pre-programmed condi- SS = Solid state ment platforms were deployed in the cen- tion is met, for instance, a pre-set depth, TB = Terabyte

Oceanography | https://doi.org/10.5670/oceanog.2021.201 forms, the control and data acquisition lecting water-property data, which at least in respect to this study, occurred electronics, a bank of lithium-ion batter- allowed computing of the sound speed during what was intended to be simulta- ies, and the power management system profile throughout the water column neous passive acoustic measurements of are contained within the Vitrovex glass from a standard algorithm (see Sound the ambient noise field by both Mk. II sphere, and a skeletal frame of titanium Speed section below). Mk. III was carry- and Mk. III. Mk. II was programmed to and high-density polyethylene (HDPE) ing an integrated CTD and a sing-around descend to 8,890 m before returning to provides an external structure on which sound velocity meter (Valeport MIDAS the sea surface. Mk. III was to go deeper, various sensors, including hydrophones, SVX2). The SVX2, in addition to the to the , recording ambient noise could be mounted. water properties from the CTD, provided and water column data until the battery During the deployment over the a direct measure of the local sound speed. was nearly exhausted, and then ascend to Challenger Deep, both platforms were Both Mk. II and Mk. III carried surface the surface. carrying four HTI-99-DY (High Tech activated satellite, radio frequency, and Circumstances intervened, however. Inc.) hydrophones configured as an high-intensity strobe-light beacons to The Mk. III platform catastrophically “L”-shaped array mounted outside the facilitate recovery. On a previous expe- failed during the descent at a nomi- motion-induced turbulence of the main dition, both instruments had descended nal depth of 8,600 m, when the glass instrument package. Two of the sen- to the bottom of the to a sphere pressure housing imploded, cre- sors were aligned in the horizontal and depth in excess of 8,500 m and returned ating a shock wave with multiple echoes three in the vertical (one was common intact. More detail on their design and from the seafloor and the sea surface, the to the two configurations). The acous- hardware specifications can be found in sequence of which was recorded by the tic bandwidth of the sensors is 5 Hz to Barclay and Buckingham (2009, 2014). surviving instrument. 30 kHz. The hydrophones were connected No precise underwater positioning through bulkheads in the spheres to the DEPLOYMENT AND IMPLOSION data are available during the deploy- data acquisition system, which recorded Mk. III was deployed first, at 11°21.26'N, ment, but it is assumed that the gener- continuous pressure time series simulta- 142°27.24'E, followed by Mk. II 24 min- ation and reception of the implosion neously on the four channels at a sam- utes and 50 seconds later at 11°21.60'N, occurred within the area bounded by the pling rate of 204.8 kHz per channel and 142°27.25'E, corresponding to a lateral deployment and recovery positions of the a dynamic range of 24 bits and a sea state separation of the two deployments of probes, shown in Figure 1. The hypotheti- zero sensitivity of –157 dB re: 1V/ µ Pa. 626 m. Mk. II was recovered eight hours cal recovery position for Mk. III was pro- Mk. II had an externally mounted after it entered the water at 11°21.67'N, jected by assuming a uniform flow regime CTD (FSI Standard 2'' MCTD) for col- 142°26.46'E (Figure 1). A fortuitous event, in the region and an identical drift pat- tern for both instruments. Figure 3 shows a schematic of the experiment geometry at the time of the A B implosion. The two instruments were separated by a horizontal distance r, and 1 2 the imploding source was at height z (Z – z ) z 1 1 2 above the seafloor, while the receiver was

at depth z2. The depth of the Challenger a b b c Deep at the experiment site, which is to r be determined, was Z. Z Z

Receiver THE PATHS TRAVELED BY ~ 834 m Source Source Receiver THE IMPLOSION ECHOES The implosion generated a very high amplitude, long pulse length, broadband pulse that was detectable even after mul- z1 (Z – z2) tiple reflections from the seafloor and the surface (Figure 4a). The paths traveled by the implo-

sion pulse were: the direct path, pd, fol- FIGURE 3. (A) The diagram of the paths taken by sound during the implosion and the variables lowed by the first bottom reflected path, describing those paths used in Equations 1–7, and (B) the diagram paths ps (solid line) and psbs (dashed line) accounting for the incident angle of the sound. pb, the first surface reflected path,p s, the

Oceanography | June 2021 Early Online Release bottom-​surface reflected path, pbs, the surface-​bottom reflected pbsb = z1 + Z + Z + (Z – z2) – w∆tbsb–d (6) path, psb, the bottom-​surface-​bottom reflected path, pbsb, and psbs = (Z – z1) + Z + Z + z2 + w∆tsbs–d, (7) finally the surface-​bottom-surface​ reflected path,p sbs. The paths are described by the following equations: where Z is the unknown depth and w is the sinking rate of the receiver, 0.56 m s–1 with a standard deviation of 3 × 10–5 m s–1 2 2 over the time period of the recorded echoes. ∆t is the differ- pd = r + (Z – z2 – z1) (1) sbs–d ence in time between the arrival from path psbs and path pd. pb = z1 + (Z – z2) + w∆tb–d (2)

ps = (Z – z1) + z2 + w∆ts–d (3) SOUND SPEED PROFILE The pressure, salinity, and temperature were recorded by Mk. II p = z + Z + z + w∆t (4) bs 1 2 bs–d with a sampling rate of 1.83 Hz, corresponding to an aver-

psb = (Z – z1) + Z + (Z – z2) – w∆tsb–d (5) age spatial resolution of 1.02 m, from the surface to its maxi- mum deployment depth of 8,894 m. The sound speed was com- puted using both the Del Grosso equation (Del Grosso, 1974)

0.05 and the TEOS-10 equation (IOC, SCOR, and IAPSO, 2010) for sound speed. The depth estimate resulting from the Del Grosso equation was 1 m shallower than that from the TEOS-10 equa- tion, and therefore the more conservative estimate from the 0.00 Del Grosso equation was chosen (Figure 5). More direct mea- surements of sound speed are needed at greater depths in trenches in order to evaluate the most appropriate model. CTD Normalized Amplitude

–0.05 and sound velocity data collected during an earlier deployment –5 0 5 10 15 20 25 30 35 in the Tonga Trench were used to compute the effective lags of Time (s) each sensor on the CTD, either due to the mounting geometry of 120 the probes with respect to the direction of motion or the charac- teristics of the probes themselves. The measurement uncertainty 100 /Hz

2 for each probe was reported by the manufacturer as 0.002°C for –1 80 temperature, 0.0002 S m for conductivity, and 0.02% for pres- sure. To predict the travel time for depths below 8,894 m, the

dB ref 1µPa 60 sound speed profile was extended using a least-squares fit. Below 2,000 m, the sound speed profile is dominated by the increasing 40 10–2 10–1 100 101 102 pressure and the relationship between depth and sound speed Frequency (kHz) is well characterized. The sound speed profile from 2,000 m to 2 1.0 8,894 m was fitted with a second order polynomial (r > 0.9999, C Direct Surface-re ected p < 0.0001), extending the profile to 12,000 m. 0.8 arrival (clipped) 0.6 Bottom- re ected a b 0.4 FIGURE 5. (a) The sound Bottom-surface 2 speed determined from 0.2 Surface-bottom-surface measurements of tempera- Normalized Correlation ture, salinity, and pressure 0.0 –5 0 5 10 15 20 25 30 35 4 from Deep Sound Mk. II and Time (s) the Del Grosso (1974) equa- tion, and (b) the uncertainty FIGURE 4. (a) The pressure time series recorded on Deep Sound Mk. II in the sound speed incorpo- with the unfiltered raw signal (gray) and the band pass filtered signal rating propagated measure- e (m) (black), where the pseudo-transmit signal used in matched filter pro- ment uncertainty and uncer- cessing is highlighted (red). (b) The power spectra of the raw (gray) and 8 tainty in the Del Grosso band pass filtered pseudo-transmit signal (red), showing a pronounced equation (0.05 m s–1). peak and null structure in the pass band of the filtered signal. (c) The 1 output of matched filter processing where the peaks in the correlation between the time series and the pseudo-transmit signal correspond to the arrival times of the shock wave as labeled. The mechanical satura- 12 tion of the hydrophone and clipping during the digitization of the acous- 1 3 tic signal cause the direct arrival to appear as a group of three peaks in 14 1 1 cerai the matched filter output. Sou See (m –1) (m –1)

Oceanography | https://doi.org/10.5670/oceanog.2021.201 ACOUSTIC SIGNAL PROCESSING (transmit) signal in the matched filter the time of arrival of the direct path at the Matched filter signal processing is a processing. The time series and matched receiver, and assuming the horizontal dis- method used in radar and sonar sys- filter segment were filtered using a sixth tance between the source and the receiver tems to determine the time of arrival of order Butterworth filter with a pass band was 626 m, the same as the distance an echo (see Turin, 1960; Lavery et al., from 3 kHz to 24 kHz, highlighting the between their deployment locations. 2010). A replica of the transmitted sig- peak and null structure in the spectrum. Approximating the time of arrival nal is correlated with the recorded time for each echo revealed that the peaks in series, and maxima in the correlation are IDENTIFYING THE ECHOES Figure 4c were the first bottom reflected used to determine the arrival times of the IN THE TIME SERIES echo, pb, the first surface reflected echo, reflected signal. Compared with the raw The output of the matched filter shows ps, the bottom-surface reflected echo, pbs, signal arrivals, the matched filter tech- four discernible peaks, which, as shown and the surface-bottom-surface reflected nique provides improved timing preci- in Figure 4c, may be identified as echo, psbs. The surface-bottom reflected sion and higher processing gain. These multipath arrivals. Preceding the first of echo, psb, and the bottom-surface-bottom performance metrics of matched filter these echoes, the three peaks labeled as reflected echo, pbsb, were not detected. processing improve with greater transmit “clipped” are associated with the direct- The signal from pbs masked the signal signal bandwidth and frequency modula- path arrival of the shock wave. As men- from psb, which was estimated to arrive tion (Chu and Stanton, 1998; Stanton and tioned earlier, the distortion in this initial 0.27 s afterwards, while the pbs arrival was

Chu, 2008; Lavery et al., 2010; Stanton arrival renders it unsuitable as a precision still active. However, pbs arrived first and et al., 2010). The distinct pattern gener- timing tool, although it is adequate for was easily discerned from the ambient ated by varying the instantaneous fre- providing a rough estimate of the travel noise. The pbsb signal was the only pulse in quency is a poor match for Gaussian times of the echoes. the series that would have reflected off the noise and deterministic signals with To determine the likely path related to seafloor twice and, assuming that the sea- unrelated frequency content. In the case each peak, the travel time along each path floor was a weaker scatterer than the sea of this experiment, the implosion gen- was estimated and the arrival times were surface, pbsb was likely to be masked by erated a highly energetic shock wave, determined by computing tk, the dis- either psbs or the ambient noise. The fact which, although not frequency modu- cretely integrated time of flight that the surface return from ps at about lated, had a broad bandwidth spanning K 11 s in Figure 4a had a much higher ∆ zi the entire frequency response band of the tk = , (8) amplitude than the other paths that ci hydrophones. However, a distinct pattern i = I reflect from the seafloor lends credence of peaks and nulls in the frequency con- where ∆zi is the width of the depth bin to the assumption that the seafloor was tent of the implosion (Figure 4b) was suf- and ci is measured sound speed at zi, I is a weaker scatterer of sound compared to ficiently robust to permit the detection of the starting depth of integration, and K the surface. echoes that traveled as far as the surface-​ is the end depth. The depth bin size was bottom-​surface reflected path, psbs. The constrained by vertical resolution of the THE DEPTH OF THE direct-path arrival of the very high ampli- measured sound speed profile, which was CHALLENGER DEEP tude shock wave was clipped before sat- set by the sampling frequency of the CTD Without knowledge of the exact time of urating the hydrophones completely aboard Mk. II, as well as the instrument’s the implosion (t0) or exact a priori knowl-

(Figure 4a time, t = 0–1 second), thereby descent rate. edge of the length of pd, it is impossible to precluding it as an effective timing ref- Using a nominal depth, Z, of 10,984 m, determine the absolute arrival time of any erence. Accordingly, only the echoes along with estimates of z1 and z2, it was individual path. Therefore, analysis was from the surface and bottom bound- possible to identify the four peaks in restricted to evaluating the differences in aries were included in the matched-​ Figure 4c. The depth of the receiver,z 2, arrival times among the four peaks. The filter correlations. was estimated to be 8,259 m at the time of only echoes necessary for determining Eleven seconds after the direct arrival, the implosion, based on the CTD data and Z were the surface-bottom-surface echo, the surface-reflected echo arrived sep- the pressure sensor on Mk. II using the psbs, and the first surface echo ps, arated in time from the preceding and Gibbs Sea Water package (IOC, SCOR, p – p = 2Z + w∆t . (9) following echoes (Figure 4a). Showing and IAPSO, 2010). Using the known sbs s sbs–b a distinct peak and null structure in the descent rate of the source, 0.56 m s–1, and To determine the depth Z, Equation 8 was frequency band from 3 kHz to 24 kHz the time of the implosion, the depth of computed from the surface (i = 0) to the (Figure 4b) and isolated in time from the source was estimated to be 9,093 m, bottom (K = Z) while iteratively increas- other arrivals, this segment of the time (Z – z1). The time of the implosion was ing K until tk was equal to the difference series was suitable for use as the template approximated by visually determining in the arrival times between psbs and ps,

Oceanography | June 2021 Early Online Release accounting for the distance traveled by While the potential error for the slant For the peak picking methodology, the receiver array, w∆tsbs–b. Four estimates range correction for Z was only about the uncertainty is assumed to be fully of Z were made by this method (one 1 m, potential errors for reflections from described by the standard deviation of from the time series recorded on each of the seafloor (z1 and Z – z2 in Figure 3A) the estimates of the travel times from the the four hydrophones), and it was found due to uncertainties about the depth and, four hydrophones. The standard devi- that Z = 10,980 m with a standard devia- more importantly, the distance between ation between the estimates of the dif- tion of 5.0 m. the probes, were potentially more pro- ference in arrival times between psbs and

nounced than for the first surface and ps was 3.1 ms, which gives a difference ACCOUNTING FOR later reflections. For these reflections, in Z of 5.0 m. ASSUMPTIONS the ratio of horizontal distance between The uncertainties in the peak pick- Figure 3A and Equations 1–7 are sim- instruments to the range from the instru- ing methodology, the slant range calcula- plifications of the paths traveled by the ments to the seafloor was much larger, tion, and the modeled travel were com- sound generated by the implosion. It was and the uncertainty in the horizon- bined to determine the total propagated assumed that the ratio of the horizontal tal distance made estimates of z1 and z2 uncertainty in the depth estimate. The distance between Mk. II and Mk. III to obtained from paths pb and pbs uncertain. total propagated uncertainty amounts the depth of Mk. II and Mk. III was suf- to 3.5 ms, which corresponds to a depth ficiently small to allow the paths to be UNCERTAINTY ANALYSIS uncertainty of ± 6 m (see online supple- approximated as being perpendicular The uncertainty of the estimate of the mentary materials). Therefore, the esti- to the sea surface and the seafloor. The depth of the Challenger Deep in this mate of the depth of Challenger Deep actual paths traveled by the shock wave study came from two main sources: the is 10,983 ± 6 m. would each be the shortest path cor- uncertainty in measured arrival times responding to a refracted ray at some from the hydrophone time series and the DISCUSSION AND CONCLUSION angle determined by the sound speed uncertainty in the modeled travel time. The estimate of the depth of the profile gradient, the depths of Mk. II The modeled travel times rely on the Challenger Deep derived in this study, and Mk. III, and the horizontal distance empirical equation of state for seawater 10,983 ± 6 m, is among the deepest esti- between the probes. Figure 3B outlines (IOC, SCOR, and IAPSO, 2010) and the mated depths (Figure 1a). The three other a more realistic view of the paths trav- Del Grosso equation (Del Grosso, 1974), deepest measurements are by R/V Vityaz eled by the implosion pulse. In deter- from which the depth and sound speed in 1957 (11,034 ± 50 m, revised to 10,983 mining Z, it was assumed that differ- can be computed from measurements ± 50 m by Taira et al., 2005), R/V Hakuho ences between paths a and 1 and paths c made by the pressure, salinity, and tem- Maru in 1992 (10,965 ± 49 m), and the and 2 were negligible. It was also assumed perature sensors, each of which has some USNS Sumner in 2010 (10,984 ± 25 m). that the difference between Z and path b associated uncertainty. Among those measurements, this esti- was negligible. It is possible to test these The sound speed profile was modeled mate is the most tightly constrained, with assumptions using nominal values for according to Del Grosso (1974) using val- an uncertainty of ± 6 m. Factors that con- the depths of Mk. II and Mk. III and ues measured by the pressure, salinity, and tributed to its low uncertainty include the the distance between them. The differ- temperature probes. Del Grosso’s empiri- concurrent and co-located CTD mea- ence between the slant range, line b in cally derived relationship relies on regres- surement of the sound speed profile Figure 3B, and water depth Z was deter- sion fits to a library of previously collected made with modern temperature, salin- mined using nominal values for the data sets and describes their uncertainty ity, and pressure probes with relatively depths of Mk. II and Mk. III (8,259 m and as 0.05 m s–1. The depths of the sound low measurement uncertainties; pre- 9,093 m, respectively) and for the water speed profile measurements were deter- cise measurement of reflected path arriv- depth (10,984 m). Using these nominal mined using the TEOS-10 pressure-to- als, as permitted by the broad bandwidth values and assuming that the source and depth conversion equation that accounts of the implosion and multiple receivers; receiver maintained a horizontal sepa- for the dynamic height anomaly and the and low acoustic noise floor at the receiv- ration of 626 m, the difference between geopotential at zero pressure and has an ers. As Figure 1 shows, the estimate of the slant range path and the vertical path error of less than 0.1 m (IOC, SCOR, the deepest part of the ocean has varied (where r = 0) translates to a depth esti- and IAPSO, 2010). The uncertainties in over time. Part of this variability can be mate difference of 3 m (see online sup- the two models were combined with the accounted for by the differences in the plementary materials). The estimate ofZ instrument uncertainty to determine the positions of the estimates. The West Basin in this study was accordingly increased complete propagated uncertainty in the and East Basin are separated by approx- by 3 m to 10,983 m to account for this modeled travel time (see online supple- imately 50 km, over which the depth of potential path length difference. mentary materials). the seafloor is likely to change.

Oceanography | https://doi.org/10.5670/oceanog.2021.201 A significant portion of the differences floor is perpendicular to the path of the depth. Similar results could be obtained in depths can also be attributed to the sound wave, are higher in amplitude than by a broadband, frequency-modulated variability in the methods used to make reflections from terrain at other angles. echo sounder deployed on a free-falling these estimates—not only the meth- The peak of the matched filtered signal instrument. This instrument could ping ods for generating the soundings (explo- represents the highest amplitude return as it descends through the water column sives, single- and multibeam sonars, pres- from the surface-bottom-surface reflec- while making simultaneous direct mea- sure sensors, imploding instruments) tion. The peak of the surface-bottom-​ ​ surements of the sound speed. Sound but also the methods used to determine surface reflection was less pronounced speed equations and the equation-of- water column properties and the tempo- and introduced significant uncertainty. In state of seawater are limited by a paucity ral lag between the water column prop- fact, the peak picking uncertainty is larger of deepwater measurements for verifica- erty measurements and the soundings. (3.1 ms) than the propagated uncertainty tion. Such an instrument would generate Precise measures of sound speed and for the modeled time of flight, includ- a large data set of many measurements of density throughout the water column ing the instrument uncertainty from the depth in a single dive, as well as provide are necessary for accurate soundings and CTD measurements and model uncer- much needed direct measurements of the for converting pressure measurements to tainties (2.0 ms). sound speed in the ocean at great depths. depth. These differences in methods cer- For acoustic measurements of depth, Such an instrument could be deployed at tainly explain some of the variability in the uncertainty must account not only for Challenger Deep sites that have been indi- the depth estimates. While the uncer- the uncertainty in the time-of-flight mea- cated to be the deepest in order to more tainty in an individual measurement has surement but also for both the uncertainty robustly estimate the depth and poten- improved, the uncertainty when compar- in the determination of the sound speed tially settle the questions: how deep and ing across measurements still raises ques- profile and any uncertainty due to differ- where is the deepest part of the ocean? tions as to the true depth of the deepest ences in time between when the sound- part of the ocean. ing is made and when the water column is SUPPLEMENTARY MATERIALS The supplementary materials are available online at The accuracy of this estimate is limited profiled (Beaudoin et al., 2009). The con- https://doi.org/10.5670/oceanog.2021.201. by uncertainty in the time of arrival; the measurements of water column REFERENCES measurement uncertainty for the conduc- properties and time-of-flight made by the Barclay, D.R., and M.J. Buckingham. 2009. Deep tivity, temperature, and pressure probes; Deep Sound platform do not suffer from Sound: A free-falling sensor platform for depth-​ profiling ambient noise in the ocean. Marine and the inexact underwater positioning such uncertainty. Technology Society Journal 43(5):144–150, information for the source and receiver. Because depth computed directly https://doi.org/​10.4031/MTSJ.43.5.19. Barclay, D.R., and M.J. Buckingham. 2014. On the Additionally, the empirical equations from a is deter- spatial properties of ambient noise in the Tonga used to compute the bulk properties of mined by integrating the water column Trench, including effects of bathymetric shad- owing. 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Oceanography | https://doi.org/10.5670/oceanog.2021.201