利用随机多项式展开的海底声学参数反演方法

Geo-acoustic inversion using polynomial chaos expansion

为了提高地声反演算法的计算效率,探索克服地声反演结果多值性问题,本文利用宽带、多收发位置的传播损失数据结合传播损失在地声参数先验搜索区间内的随机多项式展开系数矩阵,反演得到海底纵波声速、吸收率和密度比重.使用随机多项式展开近似传播损失时,展开系数的自变量为声波频率、收发位置等参数,随机多项式的自变量为表示声速、吸收率、比重在各自搜索区间内均匀分布的随机变量.传播损失的展开系数通过嵌入随机多项式的声学宽角抛物方程结合盖辽金投影、最小角度回归算法计算求得.在低频、一定声传播水平距离以内和地声参数搜索区间长度适中时,使用随机多项式展开近似传播损失的相对误差在1%以下.仿真发现,在浅海环境中使用低频、一定声传播水平距离以内的传播损失数据,在接收信号信噪比较高、声源和水听器相对位置误差较小时,选择合适的随机多项式展开截断幂次可较准确地反演海底声速、吸收率和密度比重,且计算效率比网格遍历搜索方法提高一个数量级以上.

In order to improve the computational efficiency of algorithms while exploring the method to overcome the ambiguity problems in underwater geo-acoustic inversion,we use the data of transmission losses at the broadband sound frequencies and multiple propagating distances with the matrix of polynomial chaos expansion coefficients of transmission losses to invert the speed(c),attenuation(α) of compression sound wave and the density ratio of seabed to seawater(ρ) in their prior searching intervals.When approximating the transmission loss with the polynomial chaos expansion,the expansion coefficients are the functions of parameters including sound frequency,source and hydrophone’s position while the polynomial bases are functions of the above geoacoustic parameters which are uniformly distributed in their respective intervals.The expansion coefficients are calculated by embedding the orthogonal polynomial bases into the acoustic wide-angle parabolic equation model.After that,the coefficients are deduced using the Galerkin projection and least angel regression.Under the situations of low sound frequency,short or medium sound propagation distance and short or medium length of intervals of geo-acoustic parameters,the polynomial chaos expansion can approximate the transmission losses accurately with the relatively error less than I%.In the simulation case,with the high signal to noise ratio and the low errors of relative distances between source and receivers,the geo-acoustic parameters can be inverted accurately when the appropriate truncated powers are chosen.And the time cost is reduced by at least an order of magnitude compared with that of traversal grids searching procedure.