Trans-dimensional Bayesian geoacoustic inversion in shallow water
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摘要:
为解决海底沉积层分层结构未知时的反演问题, 提出了一种变维粒子滤波方法, 利用声场的互谱密度, 估计沉积层分层结构以及地声参数。仿真结果表明：变维粒子滤波在沉积层分层结构未知时, 能有效反演沉积层层数以及地声参数, 粒子的并行计算能使其相较于可逆跳蒙特卡洛马尔可夫链(rjMCMC)更加高效。利用变维粒子滤波, 对南海垂直线阵列接收到的线性调频信号进行处理, 反演结果与rjMCMC反演得到的沉积层层数和地声参数结果相近, 说明了此方法能有效估计沉积层层数的同时反演浅海地声参数, 得到可靠的参数后验概率密度。
Abstract:To deal with the inversion problem when the spatial structure of seafloor sediments is unknown, a trans-dimensional particle filter method is proposed in this paper, where the cross-spectral density of the pressure field is used to estimate the sediment layering structure and geoacoustic parameters. The simulation results show that the number of sediment layers and geoacoustic parameters can be effectively estimated using the proposed method, and the parallel particle calculation make this method more efficient than reversible jump Monte Carlo Markov chain (rjMCMC) sampling. A linear frequency-modulated signal received by a vertical line array in the South China Sea is processed using the proposed trans-dimensional particle filter. The inversion results of the sediment layers and geoacoustic parameters are similar to those acquired by rjMCMC inversion. The number of sediment layers and the posterior probability density of parameters can be effectively estimated using this method.
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Key words:
- Geoacoustic inversion /
- Geoacoustic model /
- Bayesian theory /
- Uncertainty analysis
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图 4 各参数敏感度(蓝色实线表示225 Hz的参数敏感度, 红色虚线表示240 Hz的参数敏感度, 黄色点线表示255 Hz的参数敏感度, 紫色虚点线表示265 Hz的参数敏感度, 绿色点线表示真值)
表 1 仿真采用的反演参数真实值、反演上下界、GA反演结果和MAP
反演参数 真值 反演区间 GA MAP 声源深度$ \left(\mathrm{m}\right) $ 50 [45 55] 50.22 49.95 声源距离$ \left(\mathrm{k}\mathrm{m}\right) $ 1 [0.8 1.2] 0.996 1.00 阵列倾斜角 (°) −10 [−20 20] −9.87 −9.84 水深$ \left(\mathrm{m}\right) $ 113 [110 120] 112.87 112.83 沉积层1深度$ \left(\mathrm{m}\right) $ 5 [0 40] 5.80 4.74 沉积层2深度$ \left(\mathrm{m}\right) $ 10 [0 40] 11.05 10.22 沉积层1声速$(\mathrm{m}/\mathrm{s})$ 1580 [1500 1700] 1583 1571 沉积层2声速$ (\mathrm{m}/\mathrm{s}) $ 1620 [1500 1700] 1655 1619 基底声速$ (\mathrm{m}/\mathrm{s}) $ 1800 [1600 1900] 1815 1785 沉积层密度$ (\mathrm{g}/\mathrm{c}{\mathrm{m}}^{3}) $ 1.5 [1.2 2.0] 1.55 1.49 
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表 2 实验采用的反演上下界、GA反演结果和MAP
真值 反演区间 GA MAP 声源深度$ \left(\mathrm{m}\right) $ [45 55] 50.80 50.36 声源距离$ \left(\mathrm{k}\mathrm{m}\right) $ [0.8 1.4] 1.268 1.275 阵列倾斜角 (°) [−20 20] −10.96 −10.73 水深$ \left(\mathrm{m}\right) $ [110 125] 118.21 118.40 沉积层1深度$ \left(\mathrm{m}\right) $ [0 50] 8.47 8.43 沉积层2深度$ \left(\mathrm{m}\right) $ [0 80] 39.25 36.78 沉积层1声速$ (\mathrm{m}/\mathrm{s}) $ [1500 1700] 1550.0 1562.3 沉积层2声速$ (\mathrm{m}/\mathrm{s}) $ [1500 1700] 1633.9 1637.2 基底声速$ (\mathrm{m}/\mathrm{s}) $ [1550 1900] 1663.0 1661.4 沉积层密度$ (\mathrm{g}/\mathrm{c}{\mathrm{m}}^{3}) $ [1.2 2.0] 1.60 1.71
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