Underwater noise from impact pile driving is studied through measurements using a vertical line array (VLA) placed at range 120 m from the pile source (water depth 7.5 m) over which bathymetry varied gradually increasing to depth 12.5 m at the VLA. The data were modeled assuming the pile impact produces a radial expansion that acts as sound source and propagates along the pile at supersonic speed. This leads to the conceptualization of the pile as a discrete, vertical line source for which frequency- and source-depth-dependent complex phasing is applied. Dominant features of the pressure time series versus measurement depth are reproduced in modeled counterparts that are linearly related. These observations include precursor arrivals for which arrival timing depends on hydrophone depth and influence of a sediment sound speed gradient on precursor amplitude. Spatial gradients of model results are taken to obtain estimates of acoustic particle velocity and vector intensity for which active intensity is studied in the time domain. Evaluation of energy streamlines based on time-integrated active intensity, and energy path lines based on instantaneous (or very-short-time integrated) active intensity reveal interesting structure in the acoustic field, including an inference as to the source depth of the precursor.

1.
P. G.
Reinhall
and
P. H.
Dahl
, “
Underwater Mach wave radiation from impact pile driving: Theory and observation
,”
J. Acoust. Soc. Am.
130
(
3
),
1209
1216
(
2011
).
2.
M.
Zampolli
,
M. J. J.
Nijhof
,
C. A. F.
de Jong
,
M. A.
Ainslie
,
E. H. W.
Jansen
, and
B. A. J.
Quesson
, “
Validation of finite element computations for the quantitative prediction of underwater noise from impact pile driving
,”
J. Acoust. Soc. Am.
133
(
1
),
72
81
(
2013
).
3.
T.
Lippert
and
O.
von Estorff
, “
On a hybrid model for the prediction of pile driving noise from offshore wind farms
,”
Acta Acustica United with Acustica
100
(
2
),
244
253
(
2014
).
4.
S.
Schecklman
,
N.
Laws
,
L. M.
Zurk
, and
M.
Siderius
, “
A computational method to predict and study underwater noise due to pile driving
,”
J. Acoust. Soc. Am.
138
,
258
266
(
2015
).
5.
M. V.
Hall
, “
An analytical model for the pressure from underwater sound pressure waveforms radiated when an offshore pile is driven
,”
J. Acoust. Soc. Am.
138
(
2
),
795
806
(
2015
).
6.
P. H.
Dahl
and
P. G.
Reinhall
, “
Beam forming of the underwater sound field from impact pile driving
,”
J. Acoust. Soc. Am.
134
(
1
),
EL1
EL6
(
2013
).
7.
Preliminary Geotechnical Report, SR-160 MP 7.48, Vashon Ferry Terminal Timber Trestle Replacement
,” Washington State Department of Transportation (
2011
).
8.
M. D.
Collins
, “
A split-step Pade solution for the parabolic equation method
,”
J. Acoust. Soc. Am.
93
,
1736
1742
(
1993
).
9.
W.
Munk
,
P.
Worcester
, and
C.
Wunsch
,
Ocean Acoustic Tomography
(
Cambridge University Press
,
New York
,
1995
), pp.
67
68
.
10.
L.
Brekhovskikh
,
Waves in Layered Media
(
Academic
,
New York
,
1960
), pp.
394
395
.
11.
F. B.
Jensen
,
W. A.
Kuperman
,
M. B.
Porter
, and
H.
Schmidt
,
Computational Acoustics
(
Springer
,
New York
,
2011
), p.
442
.
12.
C. T.
Tindle
,
H.
Hobaek
, and
T. G.
Muir
, “
Downslope propagation of normal modes in a shallow water wedge
,”
J. Acoust. Soc. Am.
81
,
275
286
(
1987
).
13.
J. W.
Choi
and
P. H.
Dahl
, “
First-order and zeroth-order head waves, their sequence, and implications for geoacoustic inversion
,”
J. Acoust. Soc. Am.
119
(
6
),
3660
3668
(
2006
).
14.
G. V.
Frisk
,
J. F.
Lynch
, and
S. R.
Rajan
, “
Determination of compressional wave speed profiles using model inverse techniques in a range-dependent environment in Nantucket Sound
,”
J. Acoust. Soc. Am.
86
(
5
),
1928
1938
(
1989
).
15.
N. R.
Chapman
and
L.
Jaschke
, “
Freeze bath inversion for estimation of geoacoustic parameters
,” in
Inverse Problems in Underwater Acoustics
, edited by
M. I.
Taroudakis
and
G. N.
Makrakis
(
Springer
,
New York
,
2001
), pp.
15
34
.
16.
J. W.
Choi
and
P. H.
Dahl
, “
Spectral properties of the interference head wave
,”
J. Acoust. Soc. Am.
122
(
1
),
146
150
(
2007
).
17.
B. S.
Chekin
, “
The effect on a head wave of small inhomogeneities in a refracting medium
,”
Izv. Acad. Sci. USSR, Earth Phys. Ser.
3
,
143
147
(
1965
).
18.
D. D.
Ellis
and
D. M. F.
Chapman
, “
A simple shallow water propagation model including shear wave effects
,”
J. Acoust. Soc. Am.
78
,
2087
2095
(
1985
).
19.
Z. Y.
Zang
and
C.
Tindle
, “
Improved equivalent fluid approximations for low shear speed ocean bottom
,”
J. Acoust. Soc. Am.
98
(
6
),
3391
3396
(
1995
).
20.
M. B.
Porter
and
E. L.
Reiss
, “
A numerical method for ocean acoustic normal modes
,”
J. Acoust. Soc. Am.
76
,
244
252
(
1984
).
21.
P. H.
Dahl
,
D. R.
Dall'Osto
, and
J.
Laughlin
, “
Measurements of pile driving noise from control piles and noise-reduced piles at the Vashon Island ferry dock
,” Washington State Transportation Center (TRAC) WA-RD 861.2 (
2017
).
22.
P. H.
Dahl
,
P. G.
Reinhall
, and
D. M.
Farrell
, “
Transmission loss and range, depth scales associated with impact pile driving
,” in
Proceedings of the 11th European Conference on Underwater Acoustics
(
2012
), pp.
1860
1867
.
23.
M. A.
Ainslie
,
P. H.
Dahl
,
C. A. F.
de Jong
, and
R. M.
Laws
, “
Practical spreading laws: The snakes and ladders of shallow water acoustics
,” in
Proceedings of UA2014-2nd International Conference and Exhibition on Underwater Acoustics
(
2014
), pp.
879
886
.
24.
R. V.
Waterhouse
,
T. W.
Yates
,
D.
Feit
, and
Y. N.
Liu
, “
Energy streamlines of a sound source
,”
J. Acoust. Soc. Am.
78
,
758
762
(
1985
).
25.
J. A.
Mann
 III
,
J.
Tichy
, and
A.
Romano
, “
Instantaneous and time-averaged energy transfer in acoustic fields
,”
J. Acoust. Soc. Am.
82
,
17
30
(
1987
).
26.
C. J.
Chapman
, “
Energy paths in edge waves
,”
J. Fluid Mech.
426
,
135
154
(
2001
).
27.
D. M. F.
Chapman
, “
Using streamlines to visualize acoustic energy flow across boundaries
,”
J. Acoust. Soc. Am.
124
,
48
56
(
2008
).
28.
O. A.
Godin
, “
Wave refraction at an interface: Snell's law versus Chapman's Law
,”
J. Acoust. Soc. Am.
125
,
EL117
EL122
(
2009
).
29.
V.
Shchurov
,
Vector Acoustic of the Ocean
(
Vladivostok
,
Dalnauka, Russia
,
2006
), p.
16
.
30.
R. T.
Heyser
, “
Instantaneous intensity
,” in
Proceedings of the 81st Convention of the Audio Engineering Society
, preprint 2399 (
1986
).
31.
D. R.
Dall'Osto
,
J. W.
Choi
, and
P. H.
Dahl
, “
Properties of the acoustic intensity vector field in a shallow water waveguide
,”
J. Acoust. Soc. Am.
131
,
2023
2035
(
2012
).
32.
F. J.
Fahey
,
Sound Intensity
, 2nd ed. (
Chapman and Hall
,
London
,
1995
), p.
105
.
33.
P. T.
Madsen
,
M.
Johnson
,
P. J. O.
Miller
,
N. A.
Sato
,
J.
Lynch
, and
P.
Tyak
, “
Quantitative measures of air-gun pulses recorded on sperm whales (Physeter macrocephalus) using acoustic tags during controlled exposure measurements
,”
J. Acoust. Soc. Am.
120
,
2366
2379
(
2006
).
You do not currently have access to this content.