JPH0129430B2 - - Google Patents

Description

Detailed Description of the Invention (Technical Field) The present invention relates to a sound wave propagation simulation method for analyzing underwater sound wave propagation characteristics, and in particular, to a sound wave propagation simulation method for analyzing sound wave propagation characteristics in water. Regarding the simulation method for determining the received wave output when a wave receiver is placed and receives sound waves, especially when the sound source and receiver are directional,
The present invention provides a simulation method that can accurately represent the directivity effect.

(Background Art) The performance of marine acoustic equipment such as sonar varies greatly depending on the marine environment at the site of its operation. Therefore,
For effective operation of equipment, it is important to understand the characteristics of sound wave propagation in the ocean, and various sound wave propagation models have been developed.

Normal mode theory is a method for providing exact solutions to wave equations. According to this, sound waves emitted from a sound source are expressed as a superposition of cylindrical traveling waves (this is called a normal mode wave) that forms a standing wave in the vertical direction.

This situation will be explained using the cylindrical coordinate system shown in FIG. A sound field in a stratified medium from a point sound source of unit intensity that vibrates harmonically at frequency f is expressed by the following Helmholtz equation.

▽ ² φ(r→)+k ² (r→)φ(r→)=−4πδ(r→
−r→ _S ) (1) where ▽ ² is the Laplace operator, r→ is the coordinate of the receiving point, r→ _S is the coordinate of the sound source, φ(r→)exp(−i2πft) is the sound pressure, k( r→)=2πf/C(r) is the wave number of the sound wave in the medium, and δ is the Dirac delta function. Hereinafter, for the sake of simplicity, φ(r→), which is the complex amplitude of sound pressure, will be simply referred to as sound pressure.

Here, assuming that k(r→) is a function of depth only, k(Z _R ), the solution to equation (1) becomes symmetrical with respect to the Z axis.
Therefore, from now on, we will consider on the plane of θ = 0,
The notation of θ is omitted. The solution to equation (1) is as a superposition of sound waves spreading in all directions, φ (r, Z) = 2∫ ^∞ ₀ G (Z, Z _S ; k) J ₀ (k _r ) kdk(2) expressed. Here, J ₀ is a zero-order Betzel function. In addition, G is a Green's function, and the following equation (3) for Z and the boundary condition (sound pressure and vertical particle velocity are continuous at the interface between the sea surface and the zero sound pressure layer at infinite depth) be satisfied. Further, k is a complex number on the complex plane.

d ² G／dZ ² + [k ² (Z)−k ² ]G=−δ(Z−Z _S ) (3) The normal mode solution is obtained by applying the residue theorem to equation (2), and the normal mode It is expressed by the cumulative sum of waves and some branch line integrals as follows.

φ (r, Z) = πi 〓 ⁿ H ₀ ⁽¹⁾ (k _o r) U _o (Z) U _o (Z _S ) +∫ _BL G (Z・Z _S ;k) H ₀ ⁽¹⁾ (kr ) kdk (4) where n is the mode number and H ₀ ⁽¹⁾ represents the zero-order Hankel function of the first kind. Further, k _o is an eigenvalue of the n-th mode, and is a singular point on the complex plane of the Green's function G. U _o (Z) is the normal mode eigenfunction in the normalized depth direction, and the homogeneous equation d ² U _o (Z) / dZ ² + [K ² (Z) − K ² _o ] U _o (Z)=0 (5) and the boundary conditions are satisfied. Also, the following orthogonality condition is satisfied∫ ^∞ ₀ [P(Z)/P(Z _S )]U _o (Z)U _n (Z)dZ=δ _o
n
(6) Here, P(Z) is the density of the medium, and δ _on represents the Kronecka delta function.

The second term on the right side of equation (4) represents the integral along the branch line of G on the complex plane of complex number k. A branch line occurs when G becomes a multivalued function with respect to k and has a branch point in a half plane where the real part of k is positive. Therefore, we divide the ocean, including the ocean floor, into arbitrary layers, and express the square of the refractive index of the sound wave within each layer as a linear function with respect to depth (approximate the sound speed profile with a polygonal line).
Then, G becomes a single-valued function with respect to k, the integral term in equation (4) disappears, and a complete sound field is represented only by the discrete normal mode waves of equation (7) below.

P (r, Z _R , Z _S ; f) = iπ _∞ 〓 ⁿ⁼¹ U _o (Z _S ) U _o (Z _R ) H ₀ ⁽¹⁾ (k _o r) (7) If the sound source or receiver For directional cases,
Conventionally, this effect was introduced in the form of the following equation.

P(r, Z _R , Z _S ; f)=iπ _∞ 〓 〓 ⁿ⁼¹ D _S (θ _oS )D _R (θ _oR )U _o (Z _S )U _o (Z _R )H ₀ ⁽¹⁾ ( k _o r
)(8) Here, D _S (θ) and D _R (θ) are the vertical directivity coefficients of the sound source and the receiver, respectively, and θ is the angle of depression with the downward direction being positive with respect to the horizontal direction. θ _oS and θ _oR represent depression angles at the sound source and receiving point depths of an equivalent sound ray for the n-th mode normal mode wave (a sound ray having the same turning point depth as the n-th mode normal mode wave). That is, if the wave number in the medium is expressed as k(Z) as a function of depth Z, θ _oS = cos ^-1 [k _o /k(Z _S )], θ _oR = cos ^-1 [k _o
/k(Z _R )](9).

In other words, what Equation (8) means is that when each normal mode wave is radiated from a sound source, the sound source directivity coefficient D _S (θ _oS ) corresponding to the depression angle θ _oS at the sound source depth of the equivalent sound ray is radiates with weight,
Receiving directivity D _R (θ _oR ) corresponding to the depression angle θ _oR at the receiving depth of the equivalent sound ray when the wave is received at the receiving point.
This means that it is weighted and output.
This method is based on the assumption that each normal mode wave is radiated in a direction along the equivalent sound line and arrives at the receiving point from the direction along the equivalent sound line.

However, this method has the following problems.

(a) As is clear from equation (7), each normal mode wave has an amplitude distribution of U _o (Z) in the vertical direction and propagates in the horizontal direction (θ = 0), as shown in Figure 3. It does not propagate in the direction along the equivalent sound line as shown in . The propagation of energy in the direction of the equivalent sound ray is caused by mutual interference of several normal mode waves. Therefore, the above assumption does not hold.

(b) In order for a sound source or receiver to have directivity, it must have a finite size, and directivity is defined when a thing of that finite size is placed in a homogeneous medium. However, in the actual ocean,
Since the medium is inhomogeneous, the above-mentioned directivity cannot be strictly achieved and will have errors. Conventional methods cannot evaluate this error.

(c) There are two equivalent sound rays of the normal mode wave radiated from the sound source: one radiated from the sound source in the +θ _oS direction and one radiated in the −θ _oS direction. Therefore, in order to express the effect of sound source directivity using equation (8), D _S (θ) must be symmetrical with respect to θ=0. The same can be said about the received wave directivity D _R (θ). Therefore, in the conventional method, it is not possible to evaluate the effect of directivity that is asymmetric with respect to θ=0, such as when the main axis of the directivity pattern has an angle of depression.

(Problem to be solved by the invention) In order to eliminate these drawbacks, the present invention provides a vertical linear array sound source and a vertical linear array receiver having vertical directivity equivalent to the directional sound source and the directional receiver, respectively. The sound field due to the directional sound source is calculated as a superposition of the sound field due to each element of the vertically arrayed sound source, and the received wave output of the directional receiver is calculated as a superposition of the sound field due to each element of the vertically arrayed sound source. This is calculated as the sum of the received wave outputs of the elements, and will be explained in detail below.

(Structure and operation of the invention) First, the concept of the invention will be explained. directionality of sound source
Assume that D _S (θ) is defined in a homogeneous infinite medium with the speed of sound C ₀ . Consider a Cartesian coordinate system x-ζ with the sound source position as the origin and the ζ axis pointing vertically downward. If the weight distribution of a vertical linear sound source with vertical directivity equivalent to the directional sound source is W _S (ζ), then D _S
The following relationship holds true between (θ) and W _S (ζ).

D _S (θ)＝∫ ^∞ _-∞ W _S (ζ)exp(i2πf／C ₀ ζsinθ)
αζ(10) Here, by replacing η=f/C ₀ sinθ (11), equation (10) becomes an inverse Fourier transform, and W _S (ζ) is given by the following Fourier transform.

W _S (ζ)＝∫ ^∞ _-∞ D[θ(η)]exp(−i2πηζ)α
η(12) θ(η)=sin ^-1 (C ₀ η/f) (13) Approximating equation (12) by discrete Fourier transform, we get
A weight distribution of a vertically arranged sound source having vertical directivity equivalent to that of the directional sound source is obtained, and is expressed by the following equation.

W _Sl =1/N _S exp(-i2πη _S0 ζ _Sl ) _NS-1 〓 〓 ^m=0 E _Sn exp(-i2πlm/N _S ), l=0, 1, 2,..., N _S
−1(14) where E _Sn exp(−i2πmζ _S0 Δη _S ), D _Sn =D _S [θ(η _S
n ) ] (15) ζ _Sl =ζ _S0 +lΔζ _S , η _Sn =η _S0 +mΔη _S , Δζ
_S・Δη _S = 1/N _S (16) where ζ _Sl and η _Sn are the sample values of ζ and η, respectively.
Δζ _S and Δη _S represent sampling intervals of ζ and η, and N _S represents the number of sample points.

Since the depth of the center of the sound source underwater is Z _S , the depth N _Sl of each element of the vertically arranged sound source is N _Sl =Z _S +ζ _Sl =Z _S +ζ _S0 +lΔζ _S (17).

Regarding the equivalent linear array receiver for the directional receiver, the position and weight (receiving sensitivity) of each receiving element can be determined in a similar manner. N _Rp for each,
W _Rp , p=0, 1, ..., N _R -1, (15)
Sample data of received wave directivity corresponding to E _Sn and D _Sn in the equation are E _Rq , D _Rq , q=0, 1,..., N _R −
Set to 1.

Next, the sound field and receiver output when the equivalent linear array sound source and the equivalent linear array receiver are placed in the actual ocean will be explained. Point (0, 0,
Z _Sl ) by an omnidirectional point source with a weight of 1,
Let the sound pressure at the point (r, 0, Z _Rp ) be Ψ _Pl . This is the transfer function of propagation between the two points. The function _Pl can be derived using various theoretical models such as normal mode theory and sound ray theory. For example, when expressed as a superposition of normal mode waves, the following equation is obtained. However, the present invention can be applied to general sound field strength calculations and is not limited to normal mode.

Ψ _Pl (r, Z _Rp , Z _Sl ; f) = iπ _∞ 〓 ⁿ⁼⁰ U _o (Z _Sl ) Un (Z _Rp ) H ₀ ⁽¹⁾ (knr) (18) Point (r , 0, Z _Rp ) can be obtained by multiplying Ψ _Pl by the weight of the sound source element and superimposing the result with respect to l, as follows.

P _p (r)=Ψ ^T _p W _S ^* (19) (* is a sign that means a conjugate complex number, the same applies hereafter) Here, W _S = (W _S0 , W _S1 , ..., W _S,NS-1 ) ^T (20) ψ _p = (ψ _p0 , ψ _p1 , ..., ψ _p,NS-1 ) ^T (21). Here P(r) = [P ₀ (r), P ₁ (r), ..., P _NR-1 (r)] ^T
(22) Ψ(r)=(ψ ₀ , ψ ₁ , ..., ψ _NR-1 ) ^T (23) When defined, equation (19) can be expressed as follows.

P(r)=Ψ(r)W _S (24) The received wave output of the equivalent linear array receiver is calculated by multiplying equation (19) by the weight W _Rp of the wave receiving element, and applying the result for all wave receiving elements. Obtained by superimposing. Expressed using the vector expression W _R = (W _R0 , W _R1 ,..., W _R,NR-1 ) ^T (25), the received wave output V(r) is V(r) = P ^T (r)・W _R ^* (26).

V(r) for sample distances r ₀ , r ₁ , ..., r _{K-1
To find the value of} ..., P(r _K-1 )] ^T (28
), equation (26) can be rewritten as V=PW _R (29).

Hereinafter, for simplicity, vector representation will be used for the following quantities.

D _S = (D _S0 , D _S1 ,…, D _S,NS-1 ) ^T (30) D _R = (D _R0 , D _R1 ,…, D _R,NR-1 ) ^T (31) Z _SA = ( Z _S0 , Z _S1 , ..., Z _S,NS-1 ) ^T (32) Z _RA = (Z _R0 , Z _R1 , ..., Z _R,NR-1 ) ^T (33) Next, regarding the embodiments of the present invention explain. FIG. 1 is an explanatory diagram of an embodiment of the present invention. In the figure,
1 is the input terminal for sound source information (sound source depth, directivity),
2 is an input terminal for receiver information (wave reception depth, directivity),
3 and 4 are interpolators that input the sound source/receiver information and output the directional sample values and the element positions of the equivalent linear array; 5 and 6 input the directional sample values and output the element positions of the equivalent linear array; a discrete Fourier transformer that outputs the weight of each element; 7, 8, and 12 are registers;
Reference numeral 9 indicates an input terminal for environmental information; 10 indicates a sound wave propagation analyzer which inputs the sound source depth, receiving depth, and environment information, and outputs the transfer function of the sound wave between the sound source and the receiver position for each sample distance; 11 , 13 is a matrix/vector multiplier that calculates the product of a matrix and a vector, 1
4 is an output terminal of the receiver output.

The operating principle of this device will be explained. Sound source information input from input terminal 1 is sent to interpolator 3.
The interpolator 3 calculates the spatial frequency interval Δη _S from the sound source information.
Create sound source directional sample data D _S ,
The element spacing Δζ and element depth Z _SA of the equivalent linear array sound source are calculated using equations (16) and (17). The sound source directivity sample data D _S is DFTed with Δη _S and Δζ _S
The element depth Z SA is transferred to the circuit 5 , and the element depth Z _SA is transferred to the sound wave propagation analysis device 10 . The DFT circuit 5 calculates the weight vector W _S of the equivalent linear array sound source from the D _S , Δη _S , and Δζ _S transferred from the interpolator 3 according to equation (14), and transfers it to the register 7 .

On the other hand, receiver information input from the input terminal 2 is sent to the interpolator 4. The interpolator 4 generates receiver directivity sample data D _R with a spatial frequency interval Δη _R from the receiver information, and further calculates the element spacing Δζ _R and element depth Z _RA of the equivalent linear array receiver. . D _R is transferred to the DFT circuit 6 along with Δη _R and Δζ _R , and Z _RA is transferred to the sound wave propagation analysis device 10. The DFT circuit 6 calculates the weight vector W _R of the equivalent linear array receiver from the receiving directivity sample data D _R , the spatial frequency interval Δη _R , and the element interval Δζ _R sent from the interpolator 4. Calculate and transfer to register 8. Environmental information such as a sound speed profile, wind speed, seabed characteristics, etc. is inputted from the input terminal 9 and sent to the sound wave propagation device 10.

In the sound wave propagation analysis device 10, based on the environmental information input from the input terminal 9,
For each value of r _j , j=0, 1, ..., K-1, the l-th element Z _Sl of the depth vector Z _SA of the array sound source
When _an omnidirectional point sound source with a weight of 1 is _placed at a _depth of Transfer function matrix Ψ with ψ _pl as p−l element
(r _j ) [Equation (23)] is formed. Ψ(r _j ) is transferred to the matrix/vector multiplier 11 _j .

The matrix/vector multiplier 11 _j uses the transfer function matrix Ψ(r _j ) transferred from the sound wave propagation analysis device 10.
is multiplied by the weight vector W _S of the arrayed sound source taken out from the register 7, and the sound pressure vector P (r _j ) is obtained.
[Equation (24)] is calculated and transferred to the register 12.

In register 12, matrix/vector multiplier group 1
Sound pressure vector P(r _j ) transferred from 1, j=0,
1,...,K-1 in order, vector P
A sound pressure matrix P is formed in which the p-th element of (r _j ) is the i-p element. Once matrix P is formed, register 12 sends P to matrix-vector multiplier 13.

In the matrix/vector multiplier, the sound pressure matrix P transferred from the register 12 is multiplied by the weight vector W _R of the array receiver taken out from the register 8 to calculate the receiver output vector V, which is output from the output terminal 14. Output.

(Effects of the Invention) As explained above, in the embodiment of the present invention, an arrayed sound source/arrayed receiver having vertical directivity equivalent to a directional sound source/receiver is provided under the defining conditions of the directivity ( Since it is produced under a homogeneous infinite medium,
It is possible to correctly evaluate directivity disturbances due to inhomogeneity of the medium or discrepancy in sound speed with the definition conditions, and even when using a normal mode model as a sound wave propagation model, the concept of equivalent sound rays is required. The advantage is that the effect can be accurately evaluated for any directivity, including cases where the directivity is asymmetrical with respect to the horizontal axis.

In addition, by cumulatively adding up the output when the sound field from each element of the array sound source is received by each element of the array receiver for all sound source elements and all receiver elements, directional sound source Since the received wave output of a directional receiver placed in a sound field is calculated by , any theoretical model can be applied as a sound wave propagation model.

The present invention has the advantage that the directivity effect of a directional sound source/receiver can be accurately evaluated even under environments different from the conditions that define the directivity, so it is suitable for audio equipment whose usage environmental conditions vary widely. It is useful for on-site performance evaluation of sonar equipment used in the ocean, etc.

[Brief explanation of drawings]

FIG. 1 is an explanatory diagram of an embodiment of the present invention, FIG. 2 is an explanatory diagram of the present invention using cylindrical coordinates, and FIG. 3 is a diagram showing the relationship between directivity and a linear sound source. 1... Sound source information input terminal, 2... Receiver information input terminal, 3, 4... Interpolator, 5, 6... DFT circuit, 7, 8... Register, 9... Environment information input terminal, 10 ...Sound wave propagation analysis device, 11 ₁ ,...,1
1 _K , 13...matrix/vector multiplier, 14...
Output terminal.

Claims (1)

[Claims] 1. In a sound wave propagation simulation method that simulates the sound wave propagation phenomenon in a heterogeneous medium,
Equivalent linear array calculation means for calculating the position and weight of each element of an equivalent vertical linear array sound source/receiver having the vertical directivity pattern for a given frequency and vertical directivity pattern of the directional sound source/receiver. For a set plurality of sound source-receiver distances, the transfer functions for all combinations of the arrayed sound source elements and the arrayed receiver elements are calculated based on the environmental conditions given by the sound wave propagation analysis means. For each sound source-receiver distance, the output calculation means multiplies the transfer function for each depth of the receiving element by its weight and adds the result. A sound wave propagation simulation method characterized in that the output of a directional receiver placed in a sound field caused by a directional sound source is calculated by further multiplying and adding the weights of all the receiver elements.