The directional pattern of sound waves scattered from an object insonified by a plane wave can be efficiently predicted using the Fourier diffraction theorem (FDT). This is achieved by sampling a circle in the discrete Fourier transform of the object/medium distribution. However, the FDT-based approach under the first-order Born approximation is only applicable to weak scattering. To improve the prediction accuracy and expand the method’s scope of applications, we introduce a second-order correction term to the solution, which is obtained by taking the first-order scattered waves as secondary incident sources, and calculate the “scattering” in the same way as in the first-order FDT-based approach. Adding the resulting correction term to the directional pattern based on the first-order Born approximation, the second-order prediction is obtained. Numerical results show that the proposed method can provide improved directional patterns of the scattered waves, and the range of applicability is significantly expanded.

Multiple autonomous underwater vehicles (AUVs) have gradually become the trend in underwater operations. Identifying and detecting these new underwater multi-targets is difficult when studying underwater moving targets. A 28-element transducer is used to test the echo of multiple AUVs with different layouts in a lake. The characteristics of the wideband echo signals are studied. Under the condition that the direction of arrival (DOA) is not known, an autofocus coherent signal subspace (ACCSM) method is proposed. The focusing matrix is constructed based on the received data. The spatial spectrum of the array signal of multiple AUVs at different attitudes is calculated. The algorithm estimates the DOA of the echo signals to overcome the shortcomings of traditional wideband DOA estimation and improve its accuracy. The results show that the highlights are not only related to the number of AUVs, but are also modified by scale and attitude. The contribution of the microstructure of the target in the overall echo cannot be ignored. Different parts of the target affect the number of highlights, thus resulting in varying numbers of highlights at different attitude angle intervals. The results have significant implications for underwater multi-target recognition.

The Huguangyan Maar Lake is caused by a volcanic eruption. The original sediments at the bottom of the lake are natural yearbooks for the evolution of the earth’s climate and environment. A multi-beam sonar technique is used to scan the full coverage on the lake surface to get fine samples of echoes form the lake bottom. The information of the bathymetric data of the lake bottom is accurately described and the results of three-dimensional geomorphology imaging are given. The results show that the lake is divided into two parts, east and west, by a north-south underwater volcanic wall, and the maximum depth of water is over 22 meters. We apply a texture feature extraction method based on multi-scale fractal dimension to describe the characteristics of the sediments and roughness. Multi-scale fractal dimensions algorithm is used to extract waveform characteristics of depth samples in different directions. General distribution of sediment at the bottom of the lake is distinguished by the width of multi-scale fractal spectrum. The results obtained can be helpful for the estimation of the physical properties of sediments.