An introduction to the parabolic equation for acoustic propagation

1984 ◽  
Vol 76 (4) ◽  
pp. 1268-1268
Author(s):  
Alan B. Coppens
Keyword(s):  
Parabolic Equation ◽  
Acoustic Propagation

MULTIPLICATIVE PADÉ PE FORMULATION APPLIED TO SWAM'99 TEST CASES

2001 ◽  
Vol 09 (01) ◽  
pp. 227-241 ◽  
Author(s):  
WOOJAE SEONG ◽  
BYUNGHO CHOI
Keyword(s):  
Parabolic Equation ◽  
Shallow Water ◽  
Environmental Changes ◽  
Near Field ◽  
Acoustic Propagation ◽  
Acoustic Modeling ◽  
Test Cases ◽  
Underwater Sound ◽  
Depth Direction ◽  
National University

Accurate forward modeling of acoustic propagation is crucial in underwater sound applications that rely on coherent field predictions, such as source localization and geoacoustic inversion based on matched field processing concepts. As acoustic propagation in shallow water environments becomes important in recent years, range-dependent modeling due to environmental changes has to be considered of which parabolic equation (PE) method has received widespread use because they are accurate and relatively fast. In this paper, Seoul National University parabolic equation (SNUPE) employing a multiplicative Padé formulation is developed. Linearization of the depth direction operator is achieved via expansion into a multiplication form of Padé approximation. To approximate the depth directional equation, Galerkin's method is used with partial collocation to achieve computational efficiency. To approximate the range directional equation, Crank–Nicolson's method is used. Finally, numerical self-starter has been used to initiate the near-field solution. The Shallow Water Acoustic Modeling (SWAM'99) Workshop provides an opportunity to test SNUPE's accuracy and compare its results with others for a variety of synthetic environments. In this paper, the numerical implementation and accuracy of SNUPE is tested by comparing with RAM12 results for the SWAM'99 test cases. Numerical experiments for SWAM'99 test cases give satisfactory results in accuracy for SNUPE and show the importance of the bottom information in the shallow water acoustic modeling.

Wide-Angle Parabolic Equation Solution of Ocean Acoustic Propagation with Lossy Penetrable Bottom

1999 ◽  
Vol 38 (Part 1, No. 5B) ◽  
pp. 3361-3365 ◽  
Author(s):  
Masuya Hada ◽  
Taro Fujii ◽  
Takenobu Tsuchiya ◽  
Tetsuo Anada ◽  
Nobuyuki Endoh
Keyword(s):  
Parabolic Equation ◽  
Acoustic Propagation ◽  
Wide Angle ◽  
Equation Solution

Analysis of measured broadband acoustic propagation using a parabolic equation approach

2003 ◽  
Vol 114 (4) ◽  
pp. 2429-2429
Author(s):  
Mason Gray ◽  
D. P. Knobles ◽  
Robert Koch
Keyword(s):  
Parabolic Equation ◽  
Acoustic Propagation ◽  
Equation Approach

PARABOLIC EQUATION DEVELOPMENT IN RECENT DECADE

1995 ◽  
Vol 03 (02) ◽  
pp. 95-173 ◽  
Author(s):  
DING LEE ◽  
ALLAN D. PIERCE
Keyword(s):  
Parabolic Equation ◽  
Underwater Acoustics ◽  
Low Frequency ◽  
Recent Decade ◽  
Acoustic Propagation ◽  
Early Years ◽  
Future Research ◽  
Research Development ◽  
Scientific Fields ◽  
Made In

Numerous contributions have been made in the enhancement of the Parabolic Equation (PE) approximation method, which has been shown to be a useful tool for solving realistic problems in many different scientific fields. Evidence of its usefulness is the application of PE to solve ocean acoustic propagation problems. In early years, when the PE was introduced to the field of underwater acoustics, its main purpose was to predict long-range, low-frequency acoustic propagations in range-dependent environments; thus, there were certain limitations. In the recent decade, these limitations have been relaxed a great deal due to many useful contributions. The time has come to survey and report these important contributions and to discuss how these contributions enhance the capability of the PE method. This paper gives a brief review of what had been done before 1984 and highlights some important PE developments from 1984 to 1994. Also, some applications of the PE to predict ocean acoustic propagation problems will be presented. We shall call attention to a few important issues related to the PE developments and applications. Looking ahead we will discuss what more a PE can do in order to stimulate future research, development, as well as applications.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers

2016 ◽  
Vol 139 (5) ◽  
pp. 2672-2682 ◽  
Author(s):  
Jon M. Collis ◽  
Scott D. Frank ◽  
Adam M. Metzler ◽  
Kimberly S. Preston
Keyword(s):  
Parabolic Equation ◽  
Normal Mode ◽  
Acoustic Propagation
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