2. 中国科学院大学, 北京 100190
2. University of Chinese Academy of Sciences, Beijing 100049, China
海洋混响是主动声呐的严重干扰之一,混响特性建模一直是水声研究的热点。对于可以利用少数简正波描述声场的浅海低频情况,特别是负梯度声速剖面条件下,海底散射是引起混响的主要因素[1]。根据对海底散射的处理方法,众多的浅海混响特性建模工作可以分为2类[2]:1)基于海底经验散射的混响模型,此类混响模型将双向传播过程和海底反向散射过程分别考虑,传播过程利用射线理论、简正波理论、抛物近似(PE)等描述,散射过程则利用经验散射函数。浅海低频远程的情况下,利用射线理论来研究混响不能给出满意的结果,在传播理论中,简正波方法对于浅海低频信道十分有效,因此利用简正波理论研究浅海混响就成了浅海混响研究的一个主要方向。早在20世纪60年代,Bucker等[3]就提出了利用简正波理论计算海洋混响的方法,该方法重点是利用射线-简正波类比,将简正波分解成上行波与下行波,下行波认为是海底散射的入射声波,海底散射满足一定形式的散射定律,比如Lambert散射定律,声波散射后回传到接收点就形成了混响;张仁和等[4]推广了这种方法,使之可以计算任意声速剖面分层介质情况下的海底混响;Ellis[5]总结了这种混响计算方法,并且利用群速度给出了时域上的混响强度变化曲线;Lepage[6]又继续发展了简正波混响建模方法,研究了收发合置混响时域特性与声源宽度、声源-接收水听器深度和波导传播特性的关系;周纪浔[7]给出了浅海混响强度的角度谱模型;Grigor′er等[8]在以往工作的基础上给出了考虑声场干涉结构的混响模型;Ellis等[9]利用绝热简正波理论和海底经验散射函数,描述了水平变化波导的混响强度模型。上述混响模型的海底散射描述都采用经验散射函数,此类模型属于混响现象模型。2)基于物理散射的全波动混响模型,20世纪80年代,高天赋[10]建立了浅海粗糙界面的全波动混响模型。之后相继出现了若干关于粗糙界面和海底不均匀性的全波动混响模型[11-14]。Ivakin[12]将2种不同散射机制纳入同一个理论体系中。尚尔昌[13]基于微扰理论给出了包含粗糙界面散射和不均匀海底介质散射的浅海混响模型,杨士莪[14]、高博等[15]提出了基于耦合简正波方法的浅海混响建模方法, Marcia[16]给出了有限元计算混响声场的方法,吴金荣[2]在全波动混响模型基础上,结合能流模型框架,建立了新能流混响模型。
近年来,基于物理散射理论的全波动混响模型主要考虑复杂环境下的混响特性建模,Tang[17]和Ivakin[18]在微扰理论的基础上,结合Ivakin[12]散射模型,给出了地形变化波导的全波动混响模型,吴金荣[19]在微扰散射的基础上,结合声场的简正波谱方法,给出了地形变化波导的解析全波动混响模型。
本文在解析全波动混响模型研究的基础上,借助浅海远程水声传播的PQ理论[20-21]和小Rayleigh参数散射研究工作[22],提出了基于集约参数的混响强度建模方法,考虑海洋环境噪声的干扰,形成了浅海低频集约参数混响强度模型。
1 浅海低频全波动混响理论浅海低频情况下,海底散射是混响的主要贡献源,海底散射通常分为2类,一类是海底粗糙界面散射,另一类是海底介质体积散射,为了简洁地描述本文提出的集约参数混响强度建模方法,这里仅考虑海底粗糙界面散射引起的全波动混响理论,海底体积散射引起的混响可以利用粗糙界面散射混响理论描述[23]。
如图 1所示,浅海波导中,声速剖面为c0(z),密度ρ0,水深为H。海底粗糙界面的起伏高度η(<η>=0),在液态海底中,声速和密度分别为cb和ρb。图 1中R0代表声源,R代表声场中的接收点,R1为海底粗糙界面η上的散射微元。
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借助Bass微绕理论,粗糙界面上声场的连续条件可以替换成平坦界面上z=H非均匀边界条件[10, 13]:
$ \frac{{\partial {u_1}(R,{R_1})}}{{\partial z}} - \frac{{\partial {u_2}(R,{R_1})}}{{\partial z}} = V({R_1}){G^i}({R_1},{R_0}) $ | (1) |
$ {\rho _0}{u_1}(R,{R_1}) - {\rho _b}{u_2}(R,{R_1}) = p({R_1}){G^i}({R_1},{R_0}) $ | (2) |
其中:
$ V({R_1}) = (k_0^2 - k_b^2/\alpha )\eta ({R_1}) + (1 - 1/\alpha ){\mathit{\boldsymbol{\nabla}} _ \bot } \cdot (\eta {\mathit{\boldsymbol{\nabla}} _ \bot }) $ | (3) |
$ p({R_1}) = ({\rho _b} - {\rho _0})\eta ({R_1})\frac{\partial }{{\partial z}} $ | (4) |
式中:波数k=ω/c0(H);密度比α=ρb/ρ0;u2、u1分别表示海底和水中的散射场。在R0点源的初始(η=0)声场Gi(R1, R0)可以写为:
$ \begin{array}{*{20}{l}} {{G^i}({R_0},{R_1}) \cong {{\left( {\frac{{2{\rm{ \mathsf{ π} i}}}}{{{k_0}{r_c}}}} \right)}^{1/2}}\sum\limits_m^M {{\varphi _m}} ({z_0}){\varphi _m}(H) \cdot }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \exp ({\rm{i}}{k_m}{r_1} - {\beta _m}{r_c})} \end{array} $ | (5) |
式中:φm(z)是归一化的本征函数;Km是复本征波数,Km=km+iβm;rc是散射区域的中心半径。
根据格林定理,在Born近似下,点源在水中的散射声场可以写为:
$ \begin{array}{*{20}{l}} {{u_1}({R_0},R) = \int {\rm{d}} {R_1}\{ G(R,{R_1})V({R_1}){G^i}({R_1},{R_0}) - }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \frac{1}{{{\rho _w}}}\frac{{\partial G(R,{R_1})}}{{\partial z}}p({R_1}){G^i}({R_1},{R_0})\} } \end{array} $ | (6) |
将式(3)~(5)代入式(6),得:
$ \begin{array}{*{20}{l}} {{u_1}({R_0},R) \cong \frac{{2{\rm{ \mathsf{ π} i}}}}{{{k_0}{r_c}}}\sum\limits_m^M {\sum\limits_n^M {{\varphi _m}} } ({z_0}){\varphi _n}(z) \cdot }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \exp [ - ({\beta _m} + {\beta _n}){r_c}]S_{mn}^R{K^R}({k_m},{k_n})} \end{array} $ | (7) |
其中:
$ S_{mn}^R \equiv {\varphi _m}(H)C_{mn}^R{\varphi _n}(H) $ | (8) |
$ \begin{array}{l} C_{mn}^R = [k_0^2 - k_b^2/\alpha + (1 + \alpha ){k_m}{k_n} + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1 - \alpha )({\alpha ^{ - 2}}){\gamma _m}{\gamma _n}] \end{array} $ | (9) |
$ {{\gamma _m} = {{(k_m^2 - k_b^2)}^{1/2}},{k_m} = {k_0}\cos {\theta _m}} $ | (10) |
$ {{K^R}({k_m},{k_n}) \equiv \int {\rm{d}} {r_1}\eta ({r_1})\exp [{\rm{i}}({k_m} + {k_n}){r_1}]} $ | (11) |
式(7)给出的散射场适用于单频连续信号(CW),对于频谱为s(ω)的脉冲信号s(t),其散射声场可以通过Fourier变换获得:
$ {u_1}({R_0},R;t) = \int {\rm{d}} \omega [s(\omega ){u_1}({R_0},R;\omega )\exp ({\rm{i}}\omega t)] $ | (12) |
将式(7)代入式(12),并且假设
$ {{r_1} = {r_c} + {r^\prime }} $ | (13) |
$ {{k_m}(\omega ) \cong {k_m}({\omega _0}) + (\omega - {\omega _0})\frac{{\partial {k_m}({\omega _0})}}{{\partial \omega }}} $ | (14) |
可以获得:
$ \begin{array}{*{20}{l}} {{u_1}({R_0},R;t) = \frac{{2{\rm{ \mathsf{ π} }}}}{{{k_0}{r_c}}}s(t - {t_c}) \cdot }\\ {\quad \sum\limits_n^M {\sum\limits_m^M {{\phi _m}} } ({z_0}){\phi _n}(z){{\rm{e}}^{ - ({\beta _m} + {\beta _n}){r_c}}}S_{mn}^R{K^R}({k_m},{k_n})} \end{array} $ | (15) |
其中:
$ {t_{mn}} = \left[ {\frac{{\partial {k_m}}}{{\partial \omega }} + \frac{{\partial {k_n}}}{{\partial \omega }}} \right]{r_c} = \left[ {\frac{1}{{{u_m}}} + \frac{1}{{{u_n}}}} \right]{r_c} \approx \frac{{2{r_c}}}{{{c_0}}} = {t_c} $ | (16) |
式(15)中,忽略了由∂2km/∂ω2引起的脉冲扩展,对于超远距离传播和非常宽频带的脉冲则该考虑次项的影响。
对水中散射声场进行统计平均<|u1(R0, R; t)|inc2>,获得混响的分相干平均强度IR(R0, R; t):
$ \begin{array}{*{20}{l}} {{I_R}({R_0},R;t) = {{\left( {\frac{{2{\rm{ \mathsf{ π} }}}}{{{k_0}{r_c}}}} \right)}^2}{s^2}(t - {t_c})(2{\rm{ \mathsf{ π} }}{r_c}) \cdot }\\ {\sum\limits_m^M {\sum\limits_n^M {\varphi _m^2} } ({z_0})\varphi _n^2(z){{\rm{e}}^{ - 2({\beta _m} + {\beta _n}){r_c}}}{{[S_{mn}^R]}^2}\varGamma ({k_m},{k_n})} \end{array} $ | (17) |
其中,某时刻对混响有贡献的区域为A=2πrcΔr,Δr$\cong$c0τ0/2,τ0是信号s(t)的长度,假设r″=r′+x,同时认为Δr远大于粗糙表面相关长度L,有:
$ \begin{array}{*{20}{l}} {\varGamma ({k_m},{k_n}) \cong (\Delta r)\sigma _\eta ^2\int_0^\infty {\rm{d}} x{R^\eta }(x)\exp ({\rm{i}}2{k_0}x) = }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} ({c_0}{\tau _0}/2){\sigma ^2}{P^\eta }(2{k_0})} \end{array} $ | (18) |
式中:Rη(x)和ση2分别是粗糙表面η的相关函数和均方值;Pη是粗糙界面η的功率谱。
将式(18)代入式(17),可得:
$ \begin{array}{*{20}{l}} {{I_R}({R_0},R;t) = {E_0}{{(2{\rm{ \mathsf{ π} }}/{k_0}{r_c})}^2}({\rm{ \mathsf{ π} }}{r_c}{c_0}) \cdot }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \sum\limits_m^M {\sum\limits_n^M {\varphi _m^2} } ({z_0})\varphi _n^2(z){{\rm{e}}^{ - 2({\beta _m} + {\beta _n}){r_c}}}\varTheta _{mn}^R} \end{array} $ | (19) |
其中E0=s2(t-tc)τ0是初始信号的能量。海底反向散射矩阵元素为:
$ \varTheta _{mn}^R = \sigma _\eta ^2{P^\eta }(2{k_0}){[S_{mn}^R]^2} $ | (20) |
全波动混响模型中未知参数多,例如海底介质分为多层,每层海底介质有厚度、声速、密度和衰减参数,海底粗糙界面有均方根高度、相关长度等参数,这些参数难以获取,且相互之间有耦合。
观测式(19),发现全波动混响强度模型中未知量主要包括简正波本征函数、本征值和海底反向散射矩阵。通常对于给定的声速剖面和海底,有很多现有程序可以计算出简正波本征函数和本征值,例如KRAKEN等。但是实际上程序输入参数,如海底分层结构及每层介质参数,很难直接测量。
声与海底的相互作用可以利用海底反射系数V(θ)描述,利用海底反射系数可以计算出水声传播格林函数[20-21],在临界角以内海底反射系数可以利用2个参数(P和Q)近似表示:
$ {\ln |V(\theta )| \approx - Q\theta } $ | (21) |
$ {\arg V(\theta ) \approx - {\rm{ \mathsf{ π} }} + P\theta } $ | (22) |
式中:P描述海底反射相位信息;Q描述海底反射损失信息。
利用WKB近似,简正波水平波数的实部km和虚部βm可以利用P和Q参数表示:
$ 2\int_0^H {\sqrt {k_0^2(z) - k_m^2} } {\rm{d}}z + P{\theta _m} = 2m{\rm{ \mathsf{ π} }} $ | (23) |
$ {\beta _m} = \frac{{Q{\theta _m}}}{{{S_m} + {\delta _m}}} $ | (24) |
式中:θm是简正波掠射角;Sm+δm为简正波的跨度:
$ {{S_m} = 2\int_0^H {({k_m}/\sqrt {k_0^2(z) - k_m^2} )} {\rm{d}}z} $ | (25) |
$ {{\delta _m} \approx P/({k_0}{\theta _m})} $ | (26) |
从式(23)可以分析获得简正波本征值的实部,利用式(24)~(26)可以获得简正波本征值的虚部。
利用波动方程分离变量之后,本征函数项可以写为:
$ \frac{{{\rm{d}}{\varphi ^2}}}{{{\rm{d}}{z^2}}} + \left( {\frac{{{\omega ^2}}}{{{c^2}(z)}} - k_{rm}^2} \right){\varphi _m}(z) = 0 $ | (27) |
海面为绝对软边界,因此本征函数在海面的值为φm(0)=0,本征函数在海底的值可以写为:
$ {{\varphi _m}(H) = \sin \left( {\frac{P}{2}\sqrt {1 - {{({k_m}/{k_0})}^2}} } \right)} $ | (28) |
$ {\frac{{{\rm{d}}{\varphi _m}(H)}}{{{\rm{d}}z}} = - \left( {\frac{P}{2}} \right){{\sin }^2}\left( {\frac{{\rm{ \mathsf{ π} }}}{P}} \right){k_m}} $ | (29) |
综合式(27)~(29),可以获得简正波的本征函数。
将式(8)代入式(20),可得海底反向散射矩阵元素:
$ \varTheta _{mn}^R = \sigma _\eta ^2{P^\eta }(2{k_0})\varphi _m^2(H){[C_{mn}^R]^2}\varphi _n^2(H) $ | (30) |
采用Goff-Jordan谱[24]表示海底粗糙界面谱:
$ {P^\eta }(2{k_0}) = {\rm{ \mathsf{ π} }}L{[1 + {(2{k_0}L)^2}]^{ - 3/2}} $ | (31) |
将海底反向散射矩阵元素式(30)写为:
$ \varTheta _{mn}^R = \varphi _m^2(H)\mu _{mn}^R\varphi _n^2(H) $ | (32) |
这里海底处简正波本征函数值φ(H)决定了海底反向散射的角度关系,定义海底反向散射项μmnR:
$ \mu _{mn}^R \approx {k_0}\sigma _\eta ^2\frac{{\rm{ \mathsf{ π} }}}{{8{L^2}}}{[c_{mn}^R]^2} $ | (33) |
$ \begin{array}{*{20}{l}} {c_{mn}^R = \{ 1 - {{({c_0}/{c_b})}^2}/\alpha + (1 - {\alpha ^{ - 1}})\cos {\theta _m}\cos {\theta _n} + }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1 - \alpha )({\alpha ^{ - 2}}) \times {{[{{\cos }^2}{\theta _m} - {{({c_0}/{c_b})}^2}]}^{1/2}} \cdot }\\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{[{{\cos }^2}{\theta _n} - {{({c_0}/{c_b})}^2}]}^{1/2}}\} } \end{array} $ | (34) |
考虑海水中声速c0=1 500 m/s,密度ρb=1 g/cm3,海深为50 m,海底类型采用第六类海底cb=1 623 m/s, ρb=1.77 g/cm3, σ=0.1 m, L=10 m,f=150 Hz的情况,如表 1所示。
从表 1可以看出,μmnR随掠射角的变化较小,可以近似为一个常数μ,因此式(19)可以写为:
$ \begin{array}{*{20}{l}} {{I_R}({R_0},R;t) = {E_0}{{(2{\rm{ \mathsf{ π} }}/{k_0}{r_c})}^2}({\rm{ \mathsf{ π} }}{r_c}{c_0})\mu \cdot }\\ {\quad \sum\limits_m^M {\sum\limits_n^M {\varphi _m^2} } ({z_0})\varphi _m^2(H)\varphi _n^2(H)\varphi _n^2(z){{\rm{e}}^{ - 2({\beta _m} + {\beta _n}){r_c}}}} \end{array} $ | (35) |
根据上述分析,浅海低频混响强度可以简写为:
$ {I_R}({R_0},R) = {E_0}f(P,Q,\mu ) $ | (36) |
考虑到混响声场存在海洋背景噪声的干扰,将浅海低频集约参数混响强度模型修正为:
$ {I_R}({R_0},R) = {E_0}f(P,Q,\mu ) + {I_N} $ | (37) |
式中IN为混响同频率带宽海洋环境噪声平均强度。
3 数值仿真分析如图 2所示,数值仿真分析中,考虑Pekeris波导,海深H=50 m,水中声速c0=1 500 m/s,海底介质利用参数P和Q表示,海底散射利用μ表示,声源深度z0=25 m,接收深度为z=25 m,考虑中心频率f=300 Hz。
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在数值仿真分析中,分别改变P、Q、μ 3个参数,观察海洋混响强度随3个参数的变化规律。3个参数的赋值。混响强度随着3个参数的变化如图 3所示。
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仿真结果表明:混响强度随着海底反射相位参数P值的提高而增加,P值主要影响海底散射的角度关系φm2(H)φn2(H),以及临界角θc=π/P,P值通过2个量间接混响强度的变化。海底反射损失参数Q主要影响混响强度的衰减快慢,Q值越大,混响强度衰减越快;海底散射系数μ决定了混响强度整体的强弱,对其衰减快慢没有影响。
在实际混响数据分析中,混响数据总是离不开海洋环境噪声的干扰,这里提出混响模型的海洋环境噪声修正方法。从能量角度看来,混响强度应写成式(37)的形式,考虑海洋环境噪声强度级为-85 dB,其对海洋混响强度的影响如图 4所示。
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图 4计算结果表明:在混响/噪声比低的情况下,海洋环境噪声对混响强度的影响较大;在混响/噪声比较高时,例如大于10 dB,海洋环境噪声的影响可以忽略。因此在混响模型海试数据验证过程中,低混响/噪声比的条件下,需要对海洋混响强度进行海洋环境噪声修正。
4 结论1) P和Q是在海底反射系数约束条件下,信息集中的参数,2参数影响混响强度衰减趋势,具有微弱的耦合关系。
2) 海底反向散射系数μ是包含了海底粗糙界面和海底非均匀介质特性的信息集中参数,直接决定混响声场整体的强弱,和混响强度衰减无关。
3) 低混响/噪声比条件下,需要利用海洋环境噪声强度对混响强度模型进行修正。
该集约参数混响强度建模方法适用于浅海低频的海底混响描述,可以推广至海底介质体积混响和海面混响的建模研究,后续将重点开展实测海洋混响数据对该模型的验证研究工作。
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