CN103763045B - A kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation - Google Patents

Abstract

What the present invention relates to is a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation.Sound ray trace is converted into the function of shooting angle angle of pitch α and azimuthal angle beta by the method; Coordinate system (s, α, β) is introduced in sound ray adjacent domain; Set up ray center coordinate system (s, n ₁, n ₂) with coordinate system (s, α, β) between mapping relations; By wave equation at ray center coordinate system (s, n ₁, n ₂) under solution be converted to form under coordinate system (s, α, β).The present invention is used for three-dimensional underwater sound channel emulation, and intermediate link is few, and calculated amount is little, easy to use.

Description

A kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation

Technical field

What the present invention relates to is a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation.

Background technology

The lead time of underwater acoustic system is long, investment is large, experiment is complicated, in development process, utilize computing machine to emulate, estimate the impact of sound field environment on system performance, can shorten lead time, saving funds, raise the efficiency, be the important technical of underwater acoustic system development.Along with developing rapidly of computing machine science and technology, emulation technology obtains in underwater sound field and develops rapidly.

Ray acoustics is theoretical owing to having the plurality of advantages such as physical image is clear, computing velocity is fast, applied widely, has a wide range of applications in underwater acoustics.Along with deepening continuously of research, utilize ray acoustics method to perform the performance calculated and also improving constantly, its range of application also will be more extensive.

Become increasingly complex along with Sonar system becomes, three-dimensional modeling also seems more important.Three-dimensional ray acoustic method can meet underwater sound equipment distance, and constantly increase and New Methods of Signal Processing forecast requirement to remote sound field.Ray acoustics theory is adopted to emulate underwater acoustic channel, significant on engineer applied.

Gaussian beam method draws from seismic field, Gaussian beam is the high-frequency approximation solution of wave equation, wave equation and ray method combine by this method closely, avoid the impact of human factor on sound ray trace, have good effect to critical section, shadow region.

Summary of the invention

The object of the present invention is to provide a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation, to realize the computer sim-ulation utilizing this Gaussian beam method to three-dimensional underwater sound channel.

The object of the present invention is achieved like this:

(1) sound ray trace is converted into the function of shooting angle angle of pitch α and azimuthal angle beta;

(2) coordinate system (s, α, β) is introduced in sound ray adjacent domain;

(3) ray center coordinate system (s, n is set up ₁, n ₂) with coordinate system (s, α, β) between mapping relations;

(4) by wave equation at ray center coordinate system (s, n ₁, n ₂) under solution be converted to form under coordinate system (s, α, β);

(5) receiver or sampled point and acoustic line data point r is calculated ₀(s _n, α ₀, β ₀) at t (s), e ₁(s), e ₂distance t on (s) direction _rec=(δ s, n ₁, n ₂), and utilize ray center coordinate system (s, n ₁, n ₂) with coordinate system (s, α, β) between mapping relations, by receiver or sampled point at e ₁(s), e ₂distance n on (s) direction ₁with n ₂be rewritten as the angular difference on α (s) with β (s) direction and β;

(6) be used in α (s) and replace item relevant with (α, β) in Solution of Wave Equations with the window function on β (s) direction, simplification is carried out to the solution of wave equation and calculates.

Sound ray trace r ₀(s), r _ms (), two sound ray traces are adjacent one another are, e ₁(s), e ₂s () is perpendicular to sound ray r ₀liang Ge unit orthogonal vector in the plane of (s), t=dr ₀/ ds is the vector of unit length pointing to the sound ray direction of propagation, then unit orthogonal vector t (s) and e ₁(s), e ₂s () constitutes ray center coordinate system (s, n ₁, n ₂), s, n ₁, n ₂represent respectively and prolong t (s), e ₁(s), e ₂distance on (s) direction of principal axis.

Sound ray r _m(s): r _m=r ₀(s)+n ₁e ₁(s)+n ₂e ₂(s).

Wave equation is:

${\▿}^{2}u=\frac{1}{C^2}\frac{{\∂}^{2}u}{\∂t^2}$

$u(s,n_1,n_2,t)=\mathrm{\Ψ}\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}}\exp \{-i\mathrm{\ω}\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\]+\frac{i\mathrm{\ω}}{2}{n}^T\mathrm{\Γ}n\}$

Ψ is constant, c (s)=C (s, 0,0), n=[n ₁n ₂] ^t, Γ is a square Matrix, has Γ=PQ ^-1, square Matrix P and Q meets:

$\frac{dQ}{ds}=cP,\frac{dP}{ds}=-\frac{1}{c^2}CQ$

$C=\left[\begin{array}{cc}\frac{{\∂}^{2}C}{\∂n_1^2}& \frac{{\∂}^{2}C}{\∂n_1\∂n_2}\\ \frac{{\∂}^{2}C}{\∂n_1\∂n_2}& \frac{{\∂}^{2}C}{\∂n_2^2}\end{array}\right]$

$P\left(0\right)=\frac{1}{c\left(0\right)}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],Q\left(0\right)=0$

$Q=\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right]$

In formula, α and β is two parameters of sound ray emergence angle when representing under spherical coordinate system, has under cartesian coordinate system:

t(0)＝(sinβcosα cosβcosα sinα)。

$\left[\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right]=Q^{-1}\left[\begin{array}{c}{n}_1\\ n_2\end{array}\right],Q=\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right],u(s,\mathrm{\α},\mathrm{\β},t)=\mathrm{\Ψ}A\left(s\right)\mathrm{\φ}(s,\mathrm{\α},\mathrm{\β})\exp \[{\mathrm{i\ω\τ}}_0\left(s\right)\]$

In formula,

$A\left(s\right)=\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}},{\mathrm{\τ}}_0\left(s\right)=-\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\].$

Beneficial effect of the present invention is:

The present invention is used for three-dimensional underwater sound channel emulation, and intermediate link is few, and calculated amount is little, easy to use.

Accompanying drawing explanation

Fig. 1 is ray center coordinate system schematic diagram.

Fig. 2 is window function φ (s, α, β) schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further

1. sound ray trace is considered as the function with shooting angle (angle of pitch α and azimuthal angle beta);

2. introduce new coordinate system (s, α, β) in sound ray adjacent domain;

3. set up ray center coordinate system (s, n ₁, n ₂) with coordinate system (s, α, β) between mapping relations;

4. utilize acquired results in the 3rd step, by wave equation at ray center coordinate system (s, n ₁, n ₂) under solution be rewritten as form under coordinate system (s, α, β);

5. the method using window function to replace simplifies the item relevant with (α, β), the Solution of Wave Equations be finally simplified.

Principle of work of the present invention is:

R as shown in fig. 1 ₀(s), r _ms () is the sound ray of two vicinities, e ₁(s), e ₂s () is perpendicular to sound ray r ₀liang Ge unit orthogonal vector in the plane of (s), t=dr ₀/ ds is the vector of unit length pointing to the sound ray direction of propagation, then unit orthogonal vector t (s) and e ₁(s), e ₂s () constitutes ray center coordinate system (s, a n ₁, n ₂), s, n ₁, n ₂represent respectively and prolong t (s), e ₁(s), e ₂distance on (s) direction of principal axis.

Under ray center coordinate system, with sound ray r ₀s sound ray r that () is contiguous _ms () can be expressed as:

r _M＝r ₀(s)+n ₁e ₁(s)+n ₂e ₂(s) (1)

Solving wave equations under ray center coordinate system:

${\▿}^{2}u=\frac{1}{C^2}\frac{{\∂}^{2}u}{\∂t^2}$ Can obtain:

$u(s,n_1,n_2,t)=\mathrm{\Ψ}\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}}\exp \{-i\mathrm{\ω}\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\]+\frac{i\mathrm{\ω}}{2}{n}^T\mathrm{\Γ}n\}---\left(2\right)$

In formula, Ψ is a constant, c (s)=C (s, 0,0), n=[n ₁n ₂] ^t, Γ is a square Matrix, has Γ=PQ ^-1, square Matrix P and Q meets:

$\frac{dQ}{ds}=cP---\left(3a\right)$

$\frac{dP}{ds}=-\frac{1}{c^2}CQ---\left(3b\right)$

In formula, $C=\left[\begin{array}{cc}\frac{{\∂}^{2}C}{\∂n_1^2}& \frac{{\∂}^{2}C}{\∂n_1\∂n_2}\\ \frac{{\∂}^{2}C}{\∂n_1\∂n_2}& \frac{{\∂}^{2}C}{\∂n_2^2}\end{array}\right].$

The initial value of selection P and Q is:

$P\left(0\right)=\frac{1}{c\left(0\right)}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],Q\left(0\right)=0---\left(4\right)$

Then have:

$Q=\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right]---\left(5\right)$

In formula, α and β is two parameters of sound ray emergence angle when representing under spherical coordinate system, has under cartesian coordinate system:

t(0)＝(sinβcosα cosβcosα sinα)

Notice sound ray r ₀(s) and sound ray r _ms () can be expressed as: r ₀(s α ₀β ₀), r _m(s α _mβ _m), have:

α _M＝α ₀+α，(|α|≤δα)；β _M＝β ₀+β，(|β|≤δβ)

In formula, δ α and δ β represents the angle of two adjacent sound ray exit directions on α and β direction respectively.At this moment sound ray r _ms () can be expressed as:

r _M(s)＝r ₀(s)+αα(s)+ββ(s) (6)

Then according to formula (1) and formula (6), can obtain:

$\left[\begin{array}{cc}\mathrm{\α}& \mathrm{\β}\end{array}\right]\left[\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right]=\left[\begin{array}{cc}{e}_1& e_2\end{array}\right]\left[\begin{array}{c}{n}_1\\ n_2\end{array}\right]$

$\mathrm{\α}\left(s\right)=\frac{\∂n_1}{\∂\mathrm{\α}}{e}_1\left(s\right)+\frac{\∂n_2}{\∂\mathrm{\α}}{e}_2\left(s\right),\mathrm{\β}\left(s\right)=\frac{\∂n_1}{\∂\mathrm{\β}}{e}_1\left(s\right)+\frac{\∂n_2}{\∂\mathrm{\β}}{e}_2\left(s\right)$

That is:

$\left[\begin{array}{cc}\mathrm{\α}& \mathrm{\β}\end{array}\right]=\left[\begin{array}{cc}{e}_1& e_2\end{array}\right]\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}{e}_1& e_2\end{array}\right]Q---\left(7\right)$

Then α, β and n ₁, n ₂pass be:

$\left[\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right]=Q^{-1}\left[\begin{array}{c}{n}_1\\ n_2\end{array}\right]---\left(8\right)$

Therefore formula (2) can be written as following form:

u(s,α,β,t)＝ΨA(s)φ(s,α,β)exp[iωτ ₀(s)] (9)

In formula,

$A\left(s\right)=\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}},{\mathrm{\τ}}_0\left(s\right)=-\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\]$

Because have | α |≤δ α, | β |≤δ β, and φ (s, 0,0)=1, can be reduced to following form by φ (s, α, β):

Formula (9) and formula (10) together constitute the Gaussian beam computing method being applicable to three-dimensional underwater sound channel and emulating.

1. set up cartesian coordinate system (x, y, z), its x-axis direction represents the spacing distance on left and right directions, and y-axis direction represents the spacing distance on fore-and-aft direction, and z-axis direction represents the distance on above-below direction, i.e. the degree of depth.Sound ray trace r is tried to achieve in calculating ₀(s, α ₀, β ₀)=(x (s, α ₀, β ₀), y (s, α ₀, β ₀), z (s, α ₀, β ₀)), α ₀, β ₀angle of pitch when being respectively this sound ray outgoing and azimuth angle, set up ray center coordinate system (s, n ₁, n ₂) and calculate P (s, α according to formula (3) and (4) ₀, β ₀) and Q (s, α ₀, β ₀).

2. for being positioned at y (s _n, α ₀, β ₀) and y (s _n+1, α ₀, β ₀) between receiver or sampled point, its coordinate under cartesian coordinate system is expressed as r _rec=(x _rec, y _rec, z _rec), calculate itself and acoustic line data point r ₀(s _n, α ₀, β ₀) at t (s), e ₁(s), e ₂distance t on (s) direction _rec=(δ s, n ₁, n ₂), and utilize interpolation method to estimate Q (s _n+ δ s, α ₀, β ₀).

3. utilize in step 2 the Q (s calculating gained _n+ δ s, α ₀, β ₀), according to formula (8) by t _recat e ₁(s), e ₂s the distance on () direction is rewritten as angular difference on α (s) and β (s) direction and β.

4. the angular difference calculated in the 3rd step and β are substituted into formula (9), calculate finally by formula (10) and this sound ray r can be tried to achieve ₀(s, α ₀, β ₀) in the value of receiver or sample point u.

Claims (4)

1. be applicable to a Gaussian beam method for three-dimensional underwater sound channel emulation, it is characterized in that:

(1) sound ray trace is converted into the function of shooting angle angle of pitch α and azimuthal angle beta;

(2) coordinate system (s, α, β) is introduced in sound ray adjacent domain;

(3) ray center coordinate system (s, n is set up ₁, n ₂) with coordinate system (s, α, β) between mapping relations;

(4) by wave equation at ray center coordinate system (s, n ₁, n ₂) under solution be converted to form under coordinate system (s, α, β);

(5) receiver or sampled point and acoustic line data point r is calculated ₀(s _n, α ₀, β ₀) at t (s), e ₁(s), e ₂distance t on (s) direction _rec=(δ s, n ₁, n ₂), and utilize ray center coordinate system (s, n ₁, n ₂) with coordinate system (s, α, β) between mapping relations, by receiver or sampled point at e ₁(s), e ₂distance n on (s) direction ₁with n ₂be rewritten as the angular difference on α (s) with β (s) direction and β;

(6) be used in α (s) and replace item relevant with (α, β) in Solution of Wave Equations with the window function on β (s) direction, simplification is carried out to the solution of wave equation and calculates; Described sound ray trace r ₀(s), r _ms (), two sound ray traces are adjacent one another are, e ₁(s), e ₂s () is perpendicular to sound ray r ₀liang Ge unit orthogonal vector in the plane of (s), t=dr ₀/ ds is the vector of unit length pointing to the sound ray direction of propagation, then unit orthogonal vector t (s) and e ₁(s), e ₂s () constitutes ray center coordinate system (s, n ₁, n ₂), s, n ₁, n ₂represent respectively and prolong t (s), e ₁(s), e ₂distance on (s) direction of principal axis.

2. a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation according to claim 1, is characterized in that: described sound ray r _m(s): r _m=r ₀(s)+n ₁e ₁(s)+n ₂e ₂(s).

3. a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation according to claim 1 and 2, is characterized in that: described wave equation is:

${\▿}^{2}u=\frac{1}{C^2}\frac{{\∂}^{2}u}{\∂t^2}$

$u(s,n_1,n_2,t)=\mathrm{\Ψ}\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}}\exp \{-i\mathrm{\ω}\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\]+\frac{i\mathrm{\ω}}{2}{n}^T\mathrm{\Γ}n\}$

Ψ is constant, c (s)=C (s, 0,0), n=[n ₁n ₂] ^t, Γ is a square Matrix, has Γ=PQ ^-1, square Matrix P and Q meets:

$\frac{dQ}{ds}=cP,\frac{dP}{ds}=-\frac{1}{c^2}CQ$

$C=\left[\begin{array}{cc}\frac{{\∂}^{2}C}{\∂n_1^2}& \frac{{\∂}^{2}C}{\∂n_1\∂n_2}\\ \frac{{\∂}^{2}C}{\∂n_1\∂n_2}& \frac{{\∂}^{2}C}{\∂n_2^2}\end{array}\right]$

$P\left(0\right)=\frac{1}{c\left(0\right)}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],Q\left(0\right)=0$

$Q=\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right]$

In formula, α and β is two parameters of sound ray emergence angle when representing under spherical coordinate system, has under cartesian coordinate system:

t(0)＝(sinβcosα cosβcosα sinα)。

4. a kind of Gaussian beam method being applicable to three-dimensional underwater sound channel emulation according to claim 3, is characterized in that: $\left[\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right]=Q^{-1}\left[\begin{array}{c}{n}_1\\ n_2\end{array}\right],Q=\left[\begin{array}{cc}\frac{\∂n_1}{\∂\mathrm{\α}}& \frac{\∂n_1}{\∂\mathrm{\β}}\\ \frac{\∂n_2}{\∂\mathrm{\α}}& \frac{\∂n_2}{\∂\mathrm{\β}}\end{array}\right],$ u(s,α,β,t)＝ΨA(s)φ(s,α,β)exp[iωτ ₀(s)]

In formula,

$A\left(s\right)=\sqrt{\frac{c\left(s\right)}{\left|\right|Q\left|\right|}},{\mathrm{\τ}}_0\left(s\right)=-\[t-{\∫}_{s_0}^s\frac{ds}{c\left(s\right)}\];$