1. technology and computing
2. mp3 and midi

Acoustic bedload velocity estimates using a broadband pulse-pulse
time correlation technique
Don W. Sutton and Jules S. Jaffe
Scripps
Institution
ofOceanography,
MarinePhj•sical
Laboratory,
La Jolla,California92093
(Received10December1991;acceptedfor publication4 May 1992)
A novelnoninvasive
instrumentfor measuringbedloadvelocityhasbeendevelopedusinga
narrowbeam,high-frequency
underwatersonarsystem.Pulsedwidebandsignalscenteredat
2.2 MHz are usedto insonifya bedloadat a 30-deggrazingangle.Under theseconditionsthe
finestructureof thereturnedsignalsis dependent
on the inter-particlespatialrelationof the
bedloadparticleswithin theacousticbeam.A crosscorrelationof two consecutive
backscattered
waveformsis usedto obtainan estimateof the inter-pulsetranslationof the bed.
Thispermits
a maximum
likelihood
estimate
oftheve!ocity
ofthebed19ad.
Theresults
froma
seriesof staticexperimentsin whichagarembeddedsandwastranslateda precisedistance
showedan excellentcorrelationbetweenmeasured
andestimatedtranslations
usingthesignal
processing
method.In a setof dynamicexperiments,
the velocityof a jet-drivenbedloadwas
estimatedwith a standarddeviationin the estimatesof approximately5%. Thesewerefound
to be in goodagreementwith independentvideocameraestimates.
PACS numbers: 43.30.Pc, 43.30.Ma
INTRODUCTION
pling frequencies.Determination of particle velocities,
Existingmethodsusedto measurebedloadtransport
havenot adequatelymet the needsof thosestudyingthese
transport processes.Bottom sedimentedparticle, or bedload, transportdrivenby a fluid shearfield is an important
fundamentalissuein sedimentology,
hydrology,andcoastal
studies. Relevant bedload issues in these areas include alter-
ationsto river topologies(bottoms,courses,and mouths),
along with coastalerosion including beach erosion, and
blockageof harbormouths.Satisfactorybedloadtransport
measurementtechniqueswould allow for monitoringof
theseenvironments,
aswell as,providinga meansto fundamentallyresearchbedloadtransportby aidingin the developmentandsupportof mathematicalmodelsfor thesetransport processes.
Pastmeasurement
techniques
havereliedmainlyoncollectionsamplingand opticalincludingphotographic
techniques.Both methodsare handicappedby critical limitations. Collectionmethodsare invasive,tendingto alter the
transport
process
duringsampling.
,,2Opticalmethods
consistingof photographicor laserDoppler techniquesare difficult to setup andtime consumingto process.
They are also
both limited by the surroundinggeometryand fluid turbidity nearthebedloadregime.
3'4
An acousticsensingmethodhasa numberof desirable
characteristics
in regardto bedloadtransportmeasurement.
It can provide a noninvasivetechnique.The neededhardware is simplistic,and its useis not limited by the interferenceof smallsuspended
particles.Furthermore,signalprocessing methods can be developed to yield real-time
however, has not been addressed.
Thecurrentarticledescribes
a newlydeveloped
acoustic
bedloadvelocitymeter (ABVM), whichusespulsedbroadband waveformsand a temporalcorrelationtechniqueto
providean instantaneous
estimateof the bedloadvelocity.A
mathematicalmodel is presentedthat characterizesthe
transmittedandreturnedwaveformsignals,andoutlinesthe
methodsused to processthem. The resultsof laboratory
measurementsmade under static and dynamic bedloadconditions to test the model and determine the characteristics of
the ABVM are alsopresented.
I. SIGNAL
PROCESSING
Our processing
methodis basedon a cross-correlation
techniquethat utilizescoherentchangesin bedloadparticle
positionsbetweensuccessive
pulsesto yield a velocityestimate. Recently, similar techniqueshave been proposedto
measure
bloodflowvelocities,
7-9however,
toourknowledge
this techniquehas not been appliedto oceanography.
An
essentialrequirementof this techniqueis that the bedload
particlediametersareof thesameorderof magnitudein size
asthat of the transmittedwavelength.This resultsin a strong
scatter signal that has a fine structure unique to the inter-
particlespatialrelationof that portionof the bedloadsheet
that intersectsthe acousticbeam.By insonifingthe bedload
at a pulserepetitionratethat is rapidenoughto ensurethat
this inter-particlespatialrelationdoesnot changesignificantlybetweenpulses,yetallowsfor a significanttranslation
(i.e., sheet flow), similarities in the fine structure of succes-
clesviabackandsidescatter
returns.
5'6In thesestudies
par-
sivereturn signalscan be usedto yield a time shift correspondingto thistranslation.As demonstrated,
thistimeshift
canthenbeusedto provideanestimateof thevelocityof the
ticle sizesare detectedby analyzingreturnsat varioussam-
bedload.
information. Related acousticmethodshave focusedmainly
on sizeandconcentrationmeasurements
of suspended
parti-
1692
J. Acoust.Soc. Am. 92 (3), September1992
0001-4966/92/091692-07500.80
¸ 1992 AcousticalSocietyof America
1692
In general,bedloadparticlevelocitiesare not uniform
and the correlationmethodyieldsa maximum likelihood
estimateof spatiallyaveraged
particlesvelocities.
The lower
bound of the variance of this estimate is also discussed.
thebeam.Thiscanbemodeled
by a factorf(d•(t)). If z,ø.is
theith particleposition
at t = O,thentheparticleposition
at
timet isz•(t) = • + v•cos•t, where,o• is the inter-pulse
velocityfor particlei with positivevaluestakento be away
fromthe receiver.Ifg(t) is transmitted
at time t = r, then
thesignalwill bereceived
fromparticlei, 2z•(r + t')/c later,
where
z•
(r
+
t')
is
the
particle
positionwhenhit by sound
The geometryof the area consistingof the acoustic
leaving
the
transmitter
at
r
and
t'
isthetimeforthesoundto
hardwareand bedloadis shownin Fig. 1. The bedloadis
travel
from
the
transmitter
to
the
particle:
insonifiedusinga narrowbeamtransducersuspended
above
thebedloadat a grazingangle6. The receivingtransducer
is
zi(r + t') =z,Oq- (r + t')v• cos4•.
parallelto the transmittingtransducerand at an equaldisSincect' isequivalenttoz•(r + t' ), t' canbeexpressed
as
tancefrom thebedload.The particlesareassumed
to beuniz,ø.
cos
formlydistributedoverthebedloadwith the ith particleat a
distancezi from the receivingtransducer,and at a radial
c - " cos0 c - v,.cos
distancedi from the receivingbeamaxis.Comparedto the
Therefore,after somealgebra,the delay 2z•(7 q- t ')/c
beamwidthat the bedload,zi is assumedto be large. The
can be shownto be equalto
receivedscatteredsignalsareassumedto befrom singlescatA. Model for velocity estimates
ter eventsonly.
Assumingthatg(t) is the transmittedsignalfilteredby
theimpulseresponse
of thetransmitting
andreceiving
transducers,the analogfilters,and remainingelectronics,and
1o
ß (t,z,qb,a)the scatterfunctionfor a particleof radiusa,
then, the scatteredsignals(t) can be representedas g(t)
convolvedwith •(t,z,(b,a). In general,the receivedsignal
r(t) will dependontheradialpositionof theparticleswithin
2ziø
cos
+
c - vi cos
c-vcos
Thisimplies
thatforasingle
particle,
thereceived
signal
canbe representedas
(
Yi 7 q-
C-- Ui COS
•
)
{- AZi =f(di(7, t'))s(7).
where
AZ i --
c -- ui COS
• '
Now, considerthe completesignalas a sumof the receivedsignalsoverall particles.Then,the response
fromtwo
consecutive
pulsesignals,which havebeenspacedat time
period T apart, can be representedas
N
N
r,(t) = • r,(t)= • f(d,(7,t'))s(7),
i::-0
i=0
(1)
N+b
r2(t)= j-b• ri(t-- T(I
N
= • f(di(r-- T,t'))s(r-- T),
i ::= 0
(2)
where
(b)
2vi cos•
O•i --
C -- /3i COS•
and
t=7(1
+ai)
+AZ•.
Althoughexactlythe samenumberof particlesmay not
move into the beam as move out, here, the total number of
[]
FIG. 1. A schematicdiagramof the acoustichardwareand bedloadarea.
(a) is a side view, (b) is from above. Three transducersare used,transmitting 1, receiving2, and reference3. Both I and 2 arc at a grazing angle • and
3040 cm abovethe bedload.The referencetransduceroperatesat a delay
synchronized
to the transmittingtransducer.
A bedloadparticleis shown
with velocityvi at a distancezi from the receivingtransducer,and at a distancer• from its beamaxis.
1693
J. Acoust.Sec. Am.,Vol.92, No. 3, September1992
particlesNcontributingto a returnisassumed
to beconstant
forbothpulses.
The actualparticlescontributing
a returnfor
eachpulse,however,will changeslightlyas a resultof the
bedloadtransport.This hasbeenmodeledsuchthat for r2,
particlesindexed0 to b havemovedout of the beamat one
end,whileparticleN to N + b havemovedintothebeamat
the other end during the time T.
D.W. Suttonand J. S. Jaffe:Bedloadvelocityestimates
1693
A crosscorrelation of the two (finite duration) returns
is givenby
Q....
(7-)
=f rl(t)r2(t
d-•')dt.
(3)
If the pulserate is chosensuchthat the inter-pulsedistancetranslatedby thebedloadparticlesis smallcompared
to the beamwidth, then, the sameparticlesconstitutethe
majorityof thereturnfor thetwopulses,
i.e.,b•N. Furthermore,for thisconditionthe effectof the beamsensitivityfor
a particularparticlewill not changesignificantlyduring a
pulse period, i.e., fldi(r,t'))=fldi(r-T,t')).
Under
thesecircumstances,
r2(t), the signalreceivedfrom a sound
sentT seconds
later, canbe summedfrom j = 0 to N and
reduced to
M/2 is the noisespectraldensity,E is the energyof signal
r(t), andR (•o) theFouriertransformof r(t) forfrequencies
co.This equationcanbe reducedto a moreconvenientform
assuming
theautospectrum
istwosidedwithcenterfrequency•oo,bandwidthIF, anda signal-to-noise
ratioSN:13
o'>•....
1
I
1
1
/3•x/•Sx/g•COo
•
1
(10)
x/1d-W2/(12cog
)
In particular,theminimumvariance,or maximumreso-
lution,isproportional
to theinversesquarerootof thetimebandwidthproductandthe centerfrequency.
Thus,widebandsignals
havea smallerlowerbound.Furthermore,
fora
givenbandwildth
signals
witha highercenterfrequency
and
thusfewercycles
perpulsewidth
will performbetter.
N
r2(t)= j=o• r•(t-- T(I +atj)}.
(4)
II. EXPERIMENTS
Furthermore,if all particleswithinthebeamhavea constantand equalvelocity,then this can be expressed
more
simplyin termsof r• as
r2(t) •- r•(t-
T-
aT)
(5)
so that
Q....
(7-)
=;ri(t)r•(t
- T-aT+
7-)dt,
whichis the autocorrelation
functionof r• that hasbeen
shiftedby an amount T + a T or
Qr,r_,
(7-)-•-Q....(7-- T- aT).
(6)
Staticand dynamiclaboratoryexperiments
were performedto aidin thedevelopment
of theABVM andto assess
its performancecharacteristics.Statictests,wherea simulated bedload was translated in a controlled manner between
acousticpulses,wereusedto assess
the earlydevelopments
of thecorrelation
methods,
theeffectof thebeamsensitivity,
andthe decorrelation
of the returnsignalsasa functionof
translationdistance.Dynamictestswerecarriedout to demonstratethefeasibilityof thesignalprocessing
methodsand
overalltechnology,
and to characterize
the performance
of
the ABVM
in a more realistic environment.
This function has a maximum at 7-= T + Ta. In the
absence
of the Dopplereffect,the shiftwouldsimplybe T.
A. Methods
Thus the Doppler effectresultsin a time shift of the cross-
1. Systems hardware
correlated
signals
byanadditionalamountAt = T2v cos•/
A broadband
transmitted
signalwasgenerated
usinga
(c -- v cos•). This timediferentialcanbeusedto determine
waveform
generator
(Wavetek,
San
Diego,
CA),
which
conthebedloadvelocityby expanding
terms(assuming
v• cos•
sisted
of
2
cycles
at
2.2
MHz
and
pulsed
at
100-400/zs
at
10
,•c) and to a first-orderapproximation
canbe represented
V peak-to-peak.
The recieved
bedloadscattersignals
were
as
preamplified
(AnalogModulesInc.,Longwood,
FL), bandv = Atc/2Tcos q•.
(7)
passfiltered(600kHz-6 MHz), andsubsequently
digitized
Duarte,CA). Thesesignals
In processing
the signals,the cross-correlation
function at 40MHz, 8 bits(Markenrich,
for a consecutive
pair of returnsis normalizedby the maxi- weredirectlywritten to data fileson a PC (IBM PC/AT,
mum values of the autocorrelation functions of the two indi-
BocaRaton,FL) andlatertransferred
for processing
to a
vidual returns:
semi-mainframe(Sun Microsystems).All hardware was
Q....(•')=
triggered
usinga pulsegenerator(Hp, PaloAlto,CA). All
of thetransducers
usedhadcenterfrequencies
of 2.2 MHz
with 6-mmdiameters,
andproduced
narrowbeamswith a
Q....(7-)
x/max(Q
....(r) )x/max(Qr,
r,(7-))
If T is chosensuchthat a significant
peakresultsfrom
thenormalized
cross-correlation
(i.e.,b• N), thenEqs.(7)
and (8) can be used to obtain a maximum likelihood esti-
mate for the bedloadvelocity.
a smalloffsetnecessary
for thebeamsto intersectat the bed-
B. Minimum error analysis
A lowerboundfor the variance,•r, in the velocityestimateobtainedfrom Eqs. (7) and (8) canbeobtainedusing
theCramer-Raoinequalilty.
••'12
aa>
• YIR(co)12dco
/3 2E J'co2[R(co)[2
dco'
where/• = (2 T cosq)/c,
1694
J. Acoust.Sec. Am., Vol. 92, No. 3, September 1992
-- 3-dBattenuation
at 2 deg( Panametrics,
Waltham,MA).
The transmitting
andreceiving
transducers
werefixedin a
planethatintersected
thebedloadat a 30-deggrazingangle,
andat a distance
of 30to 40 cmabovethebedload(Fig. 1).
Theywerepositioned
nearlyparalleltoeachotherexcept
for
(9)
loadsurface.
A thirdtransducer,
placed15cmawayfrom,,
andaimedat, the receiving
transducer
generated
a signal
synchronized
with the transmitter.This provideda referencepoint on the receivedsignalsto be usedas a meansto
accuratelydeterminethe actualpulserate.Time shiftsbetweentheautocorrelated
andcross-correlation
signals
were
determined from this reference.
D. W. Suttonand d. S. Jaffe: Bedloadvelocityestimates
1694
2. Static tests
A testenvironmentwasassembled
that allowedfor precisestatictranslationsof the acousticsystemrelativeto the
bedload.
Thisapparatus
consisted
ofa 0.7-m3tankwitha 2D translatingstagesupportingthe acoustichardwarefixed
above the tank. Translations were made via a lead screw with
of0.01mmfor distances
translated
upto 9 mm,witha 4.9%
standarddeviation(Fig. 2).
The static results were also able to characterize the de-
correlationof the signalsas a functionof the translateddis-
tance(Fig. 3). It wasfoundthat peakheightsfor the normalized
cross correlations
had
values
near
0.90
for
translationsup to 1.5 mm, fallingto 0.5 near6 mm.
a 1.264-mm/revpitch.Threesimulated
bedloads
consisting
Returnsfrom controlsof sand-freeagar trayswereunof separatenarrowgradientsof sandsizes(0. l, 0.5, and 1
detectablefrom backgroundnoise,indicatinga negligible
mm diameter) fixedin traysof agar solutionwereusedas
scatterfrom the agar mediumand the bottomof the sand
acoustictargets.A seriesof translationswere madewith
trays, and no detectablecontributionfrom the transducer
acousticreturnsgeneratedat each translatedincrement. sidelobes.
Normalized
cross correlations were used to estimate the
translation distance ß by equating the expression
(cos•c) to the time shiftAt, the differencebetweenthe peak
locationsof cross-correlated
signals,and T, thepulseperiod.
Estimatesfor ß werethencomparedto actualtranslations.
3. Dynamic tests
A 5-mportionof a longchannel(30 m in length)witha
wettedcrosssectionof 60 by 60 cm anda bottomconsisting
of 1-mm-diamsilicasandwasusedasan experimental
bedload. A stationaryarrangementof the acoustichardware
similarto thatof thestaticexperiments
wassuspended
above
thebedload(Fig. 1). A fluidshearfieldprovidingtheenergy
At 2.2 MHz it wasnot known asto what bedloaddepth
particleswereableto contributea significantreturn.Experimentsusinga buriedreceivingtransducersensingtransmissionsfrom 30-deggrazingangle,showedthat the -- 3-dB
cutofffor soundpenetrationinto a stationarybedloadconsistingof l-mm-diamsandwaslessthan3 mm in depth.
As an exampleof typicalreturnsobtainedfrom the dynamicbedload,twoconsecutive
signalsobtainedfromthejet
drivenbedloadare shownin Fig. 4. Onsetof thesesignalsis
determinedby the return from the referencetransducer.
Some similar features in their fine structure between the two
signalscan be seen.Normalizedautocorrelatedand crosscorrelatedwaveformsof thesesignalsare shownin Fig. 5,
with thecorresponding
timeshiftAt betweentheautocorrepeaksshown. From this time
totransport
thebedload
wasgenerated
usinga high-pressure lated and cross-correlated
flowemanating
froma specially
fabricated
nozzleconsisting shift,an estimateof the velocityis arrivedat usingEq. (7),
of a 3-by 15-cmfacewith approximately100closelyspaced for this case a value of 67 cm/s.
holes (2 mm diameter). The nozzle was positioned5 cm
Our systemwassetup suchthat data signalsconsisting
abovethe bedloadat a 5-deggrazingangle.Acousticdata
of 32kpointswereobtained,eachcontainedapproximately5
weretakenduringshort5-sburstsof thejet witha resurfac- pulsereturns.TableI showsthe timeshiftsandcorrespond-
ingof thebedloadbetween
samples.
The samples
consisted
of 32 k datapointsandincluded4 to 8 pulsereturnswhen
pulsedat 100to 200/rs.In someexperiments
anunderwater
videocamerawasusedto simultaneously
recordthebedload
motion. Particles that could be uniquely identified on
successive
videoframeswereusedto obtainan independent
velocityestimate.
The onsetof returnsfrom individualpulseswithin the
10
-
1.0
mm
send
-
0.5
mm
send
/-
- 0.1 mm sand
32k datapointsamples
wereestablished
usingthereference
signalasa starting
point.Theseindividual
signals
werethen
digitallyfiltered,autocorrelated,
andcrosscorrelated
with
nearestneighbors.
The shiftsfromcenter,or autocorrelated
peaklocation,for thecross-correlated
peaks,labeledasAt,
werethenusedfollowingEq. (7) to estimatethe velocity.A
resolutionbelowthe40-MHz (0.025-/•s) samplingrate was
obtainedviaa quadraticcurvefittingto establish
timescorresponding
to peak locations.Heuristically,consistent
resultsindicatethat by thismethoda 0.005-/•sresolutionwas
possible.
B. Results
2
lation. Estimatesusingthe correlationtechniqueshoweda
linearresponse
to actualtranslations
for all threesandsizes.
For the 1-mm sand,the correlationmethodhad a resolution
1695
J. Acoust.Sac. Am.. Vol. 92. No. 3. September1992
•
•
6
8
Act,soltranslateddistonce(ram)
Resultsfrom the staticexperiments
indicatethat the
time eorelationtechniqueusingacousticbroadbandsignal
returnsis an accuratemeansof estimatingthe bedloadtrans-
•
4
FIG. 2. Actual translateddistancesplotted againstestimatesusingthe
cross-correlation
technique[Eqs.(7) and(9) ] fromthestaticexperiments.
The data are obtainedfrom three sandsizesof separatenarrow gradients
(0.1, 0.5, and 1.0 ram) set in an agar. The standard deviation from the
dashed 11ineis 4.9%.
D.W. Suttonand J. S. Jaffa: Redloadvelocityestimates
1695
1.0
•.o•
(a)
0.8
[]
[]
El
-1-0
1-0
0.0
0
•
•
•
•
•
2
4
6
8
10
Translateddistance (ram)
FIG. 3. Valuesfor the normalizedcorrelationplottedagainstthedistance
translatedby the bedload.Data are obtainedfrom the staticexperiments
usingthe 1.0-mmsand.
(a)
-1-0
t (izsec)
FIG. 5. Magnified
viewsofthenormalized
autocorrelation
of thesignalin
Fig.4(a), (a), andthenormalized
cross
correlation
ofthesignals
inFig.4,
(b). For thisexample,
thetimeshiftbetween
thetwopeaks,At, is0.155ps
(or aboutsixsamplingunits,at 40 MHz) corresponding
to a 67-cm/sbedload velocity.
I
I
I
I
(b)
ing velocitiesfrom nearestneighborcorrelationsfor 4 setsof
these32k length signals.Useful comparisonscan only be
madewithineach32 k lengthsample,sincefor our laboratory setupthe bedloadbecomes
deformedby thejet beforethe
systemis readyto accepta subsequent
32k file. A resolution
of 5 ns (one fifth of the 40-MHz samplinginterval) was
obtainedfor establishingcorrelationand triggerreference
peak locationsby useof the quadraticcurve fitting scheme.
The pulseperiodbetweensignalsvariedby about0.3 sampling intervalunits (7.5 ns at 40 MHz), however,this error
waseliminatedby matchingexactpulseperiodsto their correspondingcorrelationestimte.As outlinedin Table I, the
standarddeviationsfor the velocity estimatesare around
5%.
I
o
I
5o
1 oo
t (Izsec)
FIG. 4. Examplesof twoconsecutive
returnsobtainedat a pulserepetition
rateof 200/•s fromthejet shearfieldexperiments.
Signal(b) follows(a).
The triggerreferences
are at the far left.
1696
J. Acoust.Sec.Am.,Vol.92, No.3, September1992
The estimatesfrom the video analysiswere consistent
with thoseobtainedusingtheABVM. Averagevelocityvaluesfor 5 returnswithin a 32k signalwerewithin 15% of the
videoframeanalysisestimate.This 15% discrepancy
iscomparable to the error found when usingthe video method,
whichis handicapped
by the videolimitationof 30 sampling
framesper second.
D.W. SuttonandJ. S. Jaffe:Bedloadvelocityestimates
1696
TABLE I. Velocityestimates
obtained
fromfoursignals
consisting
of 32 k datapoints,eachwithfivepulsereturns.
Measurements
aremadebetween
autocorrelation
andnearest-neighbor
cross-correlation
peaks,
withthetimeshifts
reported
insampling
interval
unitsat40MHz (0.025#s). Pulse
periods
for
thesignals
ranged
between
130to 200/•s.
Sample1
Sample2
Velocity
Time shift
cm/s
Time shift
4.20
69.8
4.78
79.4
4.46
4.89
74.1
81.2
76.1 + 4.5
Sample3
Velocity
Sample4
Velocity
cm/s
Time shift
4.83
76.8
4.68
74.4
5.01
5.23
79.7
83.2
Velocity
cm/s
Time shift
cm/s
3.28
52.2
5.69
65.2
3.59
57.1
5.81
66.6
3.39
2.95
53.9
46.9
5.18
5.31
59.3
60.8
78.5 + 3.3
52.5 _+3.7
63.0 + 3.0
III. DISCUSSION
ticles and the transmission attenuation are relevant consid-
Analysisof Doppler-shiftedsignalscan be a useful
meansof determining
targetvelocityprovidedthefractional
changesin timeor frequencyare significant.Bedloadvelocitiesare ableto produceonly slightshiftsin the carrierfrequencyof signalsat MHz frequencies.
CarrierDopplershifts
resultingfrom transportof suspended
particleshave been
determinedby averagingindividualestimtesover long per-
erations in choosing this frequency. The scattering
coefficient
from a rigid sphereis, in general,dependent
on
iods.,4.•sAsanalternate
means
thecarriercanbepulsed.
By
1-mm sand.
pulsingthesignal,thelowerfrequencyof thepulseratewill
havea moresignificantDopplershift.This scheme,known
ascoherentor pulse-pulsecoherentDoppler,hasbeenproposedandcarriedout in a numberof oceanographic
applica-
Success
of the overallmethoddependson the ability to
obtaina strongcrosscorrelationbetweensuccessive
pulse
returns.The digitizationscheme,and the geometricoutlay
of theoverallsystem,are importantissues
that playa rolein
determiningthe decorrelation
of the signalsasa functionof
tions.•6'17
The majorityof thesefavora narrow-band
approachand usea frequencydomainaveragingtechniqueto
estimatethe velocityby meansof a phaseshift of the envelopeof the returnedsignal.
Our approachhas two distinct advantagesover this
method.By utilizinga time domainprocessing
technique
ambiguitiesin phasealiasingare eliminated.Secondly,the
traditionallyusednarrow-bandedsignalresultsin a higher
valuefor the lower boundof the variance[Eq. (10)]. A
narrow-bandedsignalwill havea wideautocorrelationfunction and henceits peak,whichis usedto detectthe velocity
estimate,will havea greateruncertaintyin position.In past
coherentDopplermethodsan averagingtechniquehasbeen
carriedout to compromise
this.Usinga broadbandsignal,a
narrowerestimateof the velocitycanbe madefrom a single
correlation,reducingthe needto average.Also, for widebandsignalsvariancesin the estimateswill more likely refleettheactualdistributionof theparticlevelocities.
Results
from the staticexperimentsshowedthat the width of the
crosscorrelationsremainedconstantthroughoutthe range
of translations(Fig. 3), indicatingthat any spreadseenin
the dynamicestimatewill likely reflectthe velocitydistribution. The higherresolutionand fasterestimationcapability
obtainedfrom broadbandsignalswill allow the systemto
detecthigherfrequencyoscillationsin particlemotions,a
featurethat is especiallyimportantin coastalstudyapplications.Broadbandschemes
haverecentlybeenproposedfor
acoustic
currentprofllers.'8
An importantdesignparameterof thesystemisthecarrier frequency.The scatteringcoefficient
of thebedloadpar1697
J. Acoust.$oc. Am_.Vol. 92. No. 3. September 1992
trigonometric
functions
of oddpowers
of ka.•oHighvalues
of the wavenumberk, however,needto becompromised
by
other factorsinfluencedby k includingbeamwidth,overall
beamfield,and signalattenuationin water.Considerations
of these issues led to our choise ofa 2.2-MHz
carrier for the
the translated distance of the bedload. Characterization
of
theseeffectswasthe primary concernof the statictests.Results of these tests indicate that a decorrelation of 10% oc-
cursfor translationsup to 1.5 mm (Fig. 3). This is mainly
dueto the 40 MHz digitizationrateof the 2.2-MHz carrier,
resultingin a 5.5% uncertaintyof thephase,whichleadsto
the 10% reductionof the normalizedcross-correlated
peak
height.Beyond1.5-mmtranslations,
furtherreductionsin
the peakheightcanbeattributedto an increasein the number of incoherentreturnsfrom new particlesenteringthe
beambetweenpulses.For our system,decorrelationresulted
in peak heightsthat matchedthe backgroundnoiselevelat
about 9-ram translations. Thus, for translations within this
limit velocityestimatescan be obtainedusingEqs. (7) and
(8) provideda puresheetflowof the bedloadismaintained.
Using the relationderivedfrom the Cramer-Rao inequality[Eq. (10) ], wecanpredictthe lowerboundof the
resolutionof our system.The relevantparametersare a 2.2MHz centerfrequency,a signal-to-noise
ratio of about30, a
bandwildthof I MHz, anda pulsewidth of 50/rs.Theseyield
a lower bound of approximately7 mm/s for the velocity
variance.Paststudieson Doppler systemshaveshownthat
actualvariancesalthoughcloseto their respectiveCramerRao lower bound do in fact exceed them. 17To achieve this
resolutionwith the 40-MHz samplingrate and quadratic
curvefittinga pulserate greaterthan 600/•s wouldhaveto
be used.For our jet-driven bedloadwith a velocityof about
70 cm/s, consecutive
return signalswoulddecorrelateto the
levelof backgroundnoiseat abouta 200-/zspulserate.
D.W. Suttonand J. S. Jaffe: Bedloadvelocityestimates
1697
Selectionof the optimalpulserate is dependent
on the
bedloadvelocityandthesamplingcapabilities
of thesystem.
The upperlimit of 9 mm for inter-pulsetranslationsin the
statictestsis feasiblefor dynamicsituationsonly if incoherentvariationslateralto thebeamaxisaresmallcomparedto
the particlesize.Ideally, the pulserate shouldbe selected
just long enoughto allow for a significanttime shift in the
peaklocationof the normalizedcorrelation,yetslowenough
to maintaina highpeakvalue.If Tis too small,a smallshift
will be detected,yieldinga poorresolutionin the estimate.
On the other hand, largevaluesfor Twill resultin a significantdecorrelation
of the signals.
This occursat our 200-/zs
limit for thejet flow. Factorssuchas the carrierfrequency
anddigitizationrate arealsoof consequence
in selectingT.
The resolutionof the systemismostdependenton the digitizationrate.Usinga quadraticcurvefittingtechniqueon the
40-MHz digitizationwe wereableto achievea 0.0075-mm
resolution.Our dynamic testswith the jet-driven bedload
resultedin inter-pulsetranslations
of 0.07-0.4 mm for pulse
repetitionratesof 10-5 kHz. At thesevaluesthe signal-tonoiseratiowasabout40. Decorrelationto the pointof backgroundnoisewasseenat about1.5-mmtranslations.
The bedloadparticlevelocitydistributionas a function
of depthis currentlynot addressed
by our ABVM. At 2.2
MHz we foundthat thesignalattenuationwithin thestationary bedloadto be -- 3 dB at a 3-ramdepth.Thusthe majority of the powerof the bedloadreturn is generatedfrom a
shallowdepth.The estimatefrom our correlationmethod
canbethoughtof asa spatialaverageof mainlysurfaceparti-
directionof a uniformfluidshearfieldactingon thebedload.
In general,the directionof shearmay not beknown,or perhapsbe variable.In order to assess
the transportin these
situations,a pairof orthogonaldevicessimilarto ourABVM
will be needed.Further developments
may alsoincludearraysof thesedevicesto givea spatialcharacterization
of the
transportwhich is importantfor the studyof bedloadsdriven by oscillatoryor other complexshearfields.
ACKNOWLEDGMENTS
This work wassupportedby the Army Corpsof Engineers under contract number DACW39-89-K-0023.
Fund-
ingwasfrom thecoastalengineering
researchprogramproject STILE (Sediment Transport Instrumentationfor the
Littoral Environment)directedby ThomasE. White. The
authorswouldlike to thankItzhackLevyfor hisengineering
assistance,
Edith Gallagherfor her laboratoryhelp,and Richard Seymourfor his adviceon the project.
•M. J. Crickmore,
andR. F. Aked,"Pump•amplerfor measuring
sand
transport
in tidalwaves,"Conference
onInstrumentating
Oceanography,
Proc.No. 32, Bangor,England(1975).
2A.P.Salkield,
G. P. LeGood,
andR. A. Soulsby,
"Amimpact
sensor
for
measuringsuspended
sandconcentration,"in Proceedings
of the ConferenceonOceanTechnology
(IERE, London,England,1981), pp. 37-47.
•I'. G. Drake,R. L. Shreve,
W. E.Dietrich,
P. L Whiting,
andL. B.Leopoid,"Bedloadtransportof finegravelobserved
by motionpicturephotography,"J. Fluid Mech. 192, 193-217 (1988).
cle velocities over the area of the intersection of acoustic
4R.L. Soulsby,
A. P.Salkield,
R. A. Haine,andB.Wainwright,
"Observa-
beamat thebedload,for our experimentsan areaofapprosil-
tionsof the turbulentfluxesof suspended
sandnearthe sea-bed,"Euromech,192,Munich, Germany(1985).
mately50 cm2.
•M. J.Crickmore,
I.E. Shepherd,
andP.M. Dore,"A fieldinstrument
for
andsizeof finesandsuspensions,"
Int. Conf.
Resultsfrom theseexperiments
indicatethat estimates measuringtheconcentration
MeasuringTechniques
of HydraulicPhenomena
in Offshore,Coastal,and
from singlepulsepairsare an accurateassessment
of the
InlandWaters,London,England(1986), pp.425-442.
velocityasseenby the low deviationin successive
estimates t,•. H. Flammer,
"Ultrasonic
measurements
ofsuspended
sediment,"
U.S.
(Table I). Thus theneedto time averageiseliminatedallow-
ingfor aninstantaneous
estimateof thevelocityandtheability to observedynamiceventsoccurringat higherfrequencies such as those due to wave motion and turbulence.
Geol. SurveyBull., 1141-A (1962).
?K.W. FerraraandV. R. Algazi,"A wideband
spreadtargetmaximum
likelihoodestimatorfor bloodvelocityestimation--partI: Theory,"IEEE
Trans.Ultrason.Ferroelec.Freq. Control•8, 1-16 (1990).
sO.Bonnefous
andP. Pesque,
"Timedomainformulation
of a Doppler
Our experiments
haveonlyaddressed
the performance ultrasoundandbloodvelocityestimationby crosscorrelation,"Ultrason.
of the systemin a laboratoryenvironment.In considering Imag. 8, 75-85 (1986).
•S.C[.Foster,
P.M. Embree,
andW. D. O'Brien,"Flowvelocity
profilevia
the ability of the deviceto measurebedloadtransportin a
time-domaincorrelation:erroranalysisandcomputersimulation,"IEEE
more realistic environment, such as the surf zone, several
issuedneedto beaddressed.
It isclearfromour experiments
that if an incoherentlateral translationof the inter-pulse
particletransportapproaches
that of the wavelength
of the
carrier,thenthesignalsfrom that particlewill not correlate.
Thus findingthe idealpulserate may not be trivial in complexfluidshearfields.In manybedloadregimesthetopology
of thebottomisconstantlychanging.This affectsthe geometry surroundingthe acoustics,
and hencethe return times
and strengthof the signals.The systemwill thus haveto
Trans.Ultrason.Fcrroelee.Freq.Control37, 164-175 (1990).
lop.M. MorseandK. U. Ingard,Theoretical
Acoustics
(Princeton
U.P.,
Princeton,NJ, 1996), Chap. 8.2.
•H. L. VanTrees,Detection,
Estimation,
andModulationTheory,
Part1
(Wiley, New York, 1968}.
•P. M. Woodward,
Probability
andInformation
Theory,
With•4pplications
to Radar (Pergamon,New York, 1953).
'SA.H. Quazi,"An overview
onthetimedelayestimate
in activeandpassivesystems
for targetlocalization,"IEEE Trans.Acoust.SpeechSignal
Process.29, 527-533 (1981).
•4J.L. Christensen,
"A newacoustic
Dopplercurrentprofiler,"SeaTechnol. 24, 10-13 (1983).
•ZR.Pinkel,"Observations
on nonlinear
motionin theopenseausinga
adaptto suchchanges.
Also,thepossibility
of interference range-gatedDopplersonar,"]. Phys.Ocean.9, 675-680 ( 1979}.
fromsuspended
particles
will havetobeaddressed
including •R. Lhcrmitte
andR. Serafin,
"Pulsetopulsecoherent
Dopplersonarsigits role in determiningan idealcarrierfrequency.
Our ABVM wasdeveloped
to demonstrate
thefeasibility of themethodandthereforeconsisted
of onlyonedirectionaldegreeformeasuring
bedloadvelocities.
For laboratory environments
thiscanbeusedbyaligningthedeviceto the
1698
J. Acoust.Sec.Am.,Vol.92, No.3, September1992
nal proceasing
techniques,"
J. Atmos.OceanicTech. 1, 293-308 (1984).
'7R.Pinkel,"OntheuseofDoppler
sonarforinternal
wavemeasurement,"
Deep-SeaRes. 28A, 269-289 ( 1981).
'aB.H. Brumley,K. G. Cabrera,K. L. Denies,andE. A. Terray,"Performanceof a broad-bandacousticDopplercurrentprofiler,"IEEE J. Ocean
Eng. 16, 402-407 (1991).
D.W. SuttonandJ. S. Jaffe:Bedloadvelocityestimates
1698