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COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 10 Computational Ocean Acoustics • Ray Tracing • Wavenumber Integration • Normal Modes • Parabolic Equation

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Page 1: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Computational Ocean Acoustics

• Ray Tracing• Wavenumber Integration• Normal Modes• Parabolic Equation

Page 2: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Wavenumber Integration• Range-independent – Integral Transform solution• Exact depth-dependent solution

– Global Matrix Approach– Propagator Matrix Approach– Invariant Embedding

• Numerical Integration– Fast-Field Program (FFP)– Fast Hankel Transform

• Numerical issues:– Numerical stability of depth solution– Aliasing and wrap-around

• Numerical Examples

Page 3: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

kr

km*

kmax

-km

* C1

C2

C3

kmin

Poles

Branch cut for kz = km2 - kr

2

Page 4: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

kr

km

*

kmax

-km

*C1

C2

C3

kmin

Poles

Branch cut for kz = km2 - kr

2

Page 5: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 9

See Fig 4.7 in Jensen, Kuperman, Porter and Schmidt. Computational Ocean Acoustics. New York: Springer-Verlag, 2000.

Example: Pekeris waveguide with pressure-release surface and penetrable fluid bottom

Page 6: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 7: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 8: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 9: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

kr

km*

kmax

-km* C1

C2

C3

kmin

Poles

Branch cut for kz = km2 - kr

2

Page 10: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 11: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 12: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Page 13: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Adaptive Integration

k1 k2

(b)(a)

k1 k2

Page 14: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Numerical ExamplesPekeris Waveguide with Elastic Bottom

Page 15: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow WaterWaveguidewith Fast Shear Bottom

[See Jensen, Fig 4.9]

C = 600 m/ss

Page 16: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Stratified Elastic BottomScholte wave – Fast Sand Seabed

C = 600 m/ss

Page 17: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

s

Scholte Waves in Shallow Water

Reproduced by permission from Rauch, Dieter, "Experimental and Theoretical Studies of Seismic Interface Waves in Coastal Waters." In Bottom-Interacting Ocean Acoustics: NATO Conference Series, Marine Sciences. Edited by William A. Kuperman & Finn B. Jensen. New York: Plenum Press, 1980.

Page 18: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Scholte Waves InversionFor Seabed Shear Properties

[See Jensen, Figs 8.9, 8.10, 8.11]

Page 19: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Seabed Shear Propertiesfrom Scholte Wave Inversions

Reproduced by permission from Jensen, Finn B. and Henrick Schmidt."Shear Properties of Ocean Sediments Determined from Numerical Modelling of Scholte Wave Data." In Ocean Seismo-acoustics: Low Frequency Underwater Acoustics (NATO Conference Series, Marine Sciences). Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press, 1986.

Page 20: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow WaterWaveguidewith Slow Shear Bottom

[See Jensen, Fig 4.10]

C = 300 m/ss

Page 21: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Stratified Elastic BottomScholte wave – Silt Seabed

C = 600 m/ss

Page 22: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow WaterWaveguidewith Porous, Unconsolidated Sand Bottom

Porous Sand – Permeability k = 10 -10

Page 23: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow WaterWaveguidewith Porous, Unconsolidated Sand Bottom

Porous Sand – Permeability k = 10 -10

Page 24: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Seabed DispersionSand Seabed - Elba

See Maguer, Pouliquen, Bovio, Fox, and Schmidt. “Comparison between subcritical penetration models and in situ data.”Journal of the Acoustical Society of America 103, no. 5 (May 1998): 2901.

Page 25: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow WaterWaveguideTransversely Isotropic Bottom

p<C > = 1800 m/s

<C > = 300 m/ss

Silt 1600/200Sand 2000/400

PSV

SH

Page 26: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Stratified Elastic BottomEvanescent Tunneling Regime

C = 600 m/ss

Page 27: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Evanescent Wave Tunneling

See Fig. 4.14 in Jensen, Kuperman, Porter and Schmidt. Computational Ocean Acoustics. New York: Springer-Verlag, 2000.

Page 28: Computational Ocean Acoustics - MIT OpenCourseWare · 13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 10 ... Edited by Tuncay Akal and Jonathan M. Berkson. New York: Plenum Press,

COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 10

Shallow Water Seismo-Acoustics

• Bottom-limited Waveguide Propagation– Critical angles 15-25 degrees – Normal mode propagation characteristics for longer ranges– Branch line integral contribution significant for ranges < 5-10 H– Evanescent penetration and scattering dominant - tunneling– Wavenumber integration modeling ‘exact’ and decomposes into physically

interpretable components • Elasticity

– Very low shear speeds -<10-100 m/s – makes shear a perturbative effect– Scholte waves dominating propagation mechanism below 10 Hz

• Porosity of sandy sediments– Strong dispersion in 1-10 kHz regime

• Transverse Isotropy– Seasonal sedimentation creates significant anisotropy (P: 10%, S: 30%)


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