In this paper, we describe an implementation of the fast spherical harmonic transform (SHT) algorithm in the Yin–He global spectral model (YHGSM). A new analysis method is proposed to study the potential instability of interpolative decomposition and to evaluate the performance of fast SHT on the MilkyWay-2 supercomputer. The novel aspect of the proposed method is the use of the computational complexity analysis method by studying the properties of interpolative decompositions. Furthermore, three test cases are conducted to verify fast SHT in YHGSM. The results demonstrate that fast SHT is feasible and efficient for reducing the computational complexity and memory cost of SHT while still keeping enough accuracy.

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

Ambient noise carries abundant subsurface structure information and attracts ever-increasing attention in the past decades. However, there are lots of interference factors in the ambient noise in the real world, making the noise difficult to be utilized in seismic interferometry. The paper performs shear-wave tomography on a very short recording of ocean ambient noise with interference. An adapted eigenvalue-based filter is adopted as a pre-processing method to deal with the strong, directional interference problem. Beamforming and the noise crosscorrelation analyses show that the filter works well on the noise recorded by the array. Directional energy is significantly suppressed and the background diffuse component of the noise is relatively enhanced. The shear-wave tomography shows a 4-layer subsurface structure of the area covered by the array, with relatively homogeneous distribution of the shear-wave velocity values in the top three layers and a complicated structure in the bottom layer. Moreover, 3 high-velocity zones can be recognized in the bottom layer. The result is compared with several other tomography results using different methods and data. It demonstrates that, although the ambient noise used in this paper is very short and severely contaminated, a reasonable tomography result can be obtained by applying the adapted eigenvalue-based filter. Since it is the first application of the adapted eigenvalue-based filter in seismic tomography using ambient noise, the paper proves the effectiveness of this technique and shows the potential of the technique in ambient noise processing and passive seismic interferometry.

Bayesian seabed geoacoustic inverse problems are commonly addressed using Markov chain Monte Carlo (McMC) methods or their variants, which are computationally expensive. This study proposes an efficient Bayesian geoacoustic inversion approach based on mixture density networks (MDNs). Rather than training separate networks for each parameter, this approach models the joint posterior probability distribution of all parameters. Moreover, the classical Bayesian geoacoustic inversion framework is enhanced by utilizing the MDN theory to analytically deduce essential geoacoustic statistics from the multidimensional posterior probability density (PPD). This approach not only eliminates the computationally intensive numerical integration typically required for Bayesian inversion but also provides deeper insight into the statistical characteristics of the Bayesian PPD. Comparisons of MDN and McMC inversion results across various cases reveal that the inversion using MDN (MDN inversion) produces PPD approximations that align well with the McMC method in terms of overall trends, despite some local discrepancies. Analysis of inter-parameter correlations indicates that the MDN can capture key trade-offs between parameters. This approach offers an efficient method for solving seabed geoacoustic inverse problems within the Bayesian inference framework, making it a promising technique for real-time inversion.