Markov chain Monte Carlo algorithms are commonly employed for accurate uncertainty appraisals in non-linear inverse problems. The downside of these algorithms is the considerable number of samples needed to achieve reliable posterior estimations, especially in high-dimensional model spaces. To overcome this issue, the Hamiltonian Monte Carlo algorithm has recently been introduced to solve geophysical inversions. Different from classical Markov chain Monte Carlo algorithms, this approach exploits the derivative information of the target posterior probability density to guide the sampling of the model space. However, its main downside is the computational cost for the derivative computation (i.e. the computation of the Jacobian matrix around each sampled model). Possible strategies to mitigate this issue are the reduction of the dimensionality of the model space and/or the use of efficient methods to compute the gradient of the target density. Here we focus the attention to the estimation of elastic properties (P-, S-wave velocities and density) from pre-stack data through a non-linear amplitude versus angle inversion in which the Hamiltonian Monte Carlo algorithm is used to sample the posterior probability. To decrease the computational cost of the inversion procedure, we employ the discrete cosine transform to reparametrize the model space, and we train a convolutional neural network to predict the Jacobian matrix around each sampled model. The training data set for the network is also parametrized in the discrete cosine transform space, thus allowing for a reduction of the number of parameters to be optimized during the learning phase. Once trained the network can be used to compute the Jacobian matrix associated with each sampled model in real time. The outcomes of the proposed approach are compared and validated with the predictions of Hamiltonian Monte Carlo inversions in which a quite computationally expensive, but accurate finite-difference scheme is used to compute the Jacobian matrix and with those obtained by replacing the Jacobian with a matrix operator derived from a linear approximation of the Zoeppritz equations. Synthetic and field inversion experiments demonstrate that the proposed approach dramatically reduces the cost of the Hamiltonian Monte Carlo inversion while preserving an accurate and efficient sampling of the posterior probability. 相似文献
海洋水深信息对研究珊瑚礁海域资源与环境具有重要作用。南海珊瑚礁海域测深数据受多种条件限制施测困难,在时间与空间方面数量非常有限。文章针对南海岛礁海域以I类水体为主导的海水光学特性,以南沙群岛库归沙洲海域为例,使用Sentinel-2多光谱卫星遥感影像和同期过境的MODIS卫星数据,构建底质光谱,采用半分析半经验模型计算海水表面遥感反射率与海水叶绿素浓度,通过对数比值模型进行该地区光学浅水海域遥感水深反演分析,并进一步通过多时相反演水深融合提升精度。经与多波束实测水深数据验证,研究区域反演水深总体均方根误差和平均相对误差分别为2.68 m 和9.99%。该方法通过叶绿素浓度推演部分海水光学特性,可以从多光谱卫星影像中快速获取南海岛礁光学浅水海域初步水深信息,供相关海洋领域分析与应用。 相似文献