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Keywords = geodesics as ray pathing

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24 pages, 2260 KiB  
Article
Application of Riemannian Seismic Ray Path Tracing in Salt Dome Prospecting
by Gabriela Yáñez, Jorge Javier Hernández-Gómez, Alfredo Trujillo-Alcántara and Mauricio Gabriel Orozco-del-Castillo
Appl. Sci. 2024, 14(13), 5653; https://doi.org/10.3390/app14135653 - 28 Jun 2024
Viewed by 910
Abstract
Within the geophysical exploration utilising seismic methods, it is well known that if the explored distances are much greater than the wavelength of the seismic waves with which the exploration is carried out, the ray approach of the wave theory can be used. [...] Read more.
Within the geophysical exploration utilising seismic methods, it is well known that if the explored distances are much greater than the wavelength of the seismic waves with which the exploration is carried out, the ray approach of the wave theory can be used. In this way, when the rays travel through an inhomogeneous medium, they follow curved trajectories, which is imperative to determine the geological features that produce reflection and refraction phenomena. In this paper, a simple algorithm for the calculation of the trajectory of a seismic beam through an inhomogeneous stratum is presented. For this, the construction of a pseudo-Riemannian metric is required from the function of P-wave velocities of the geological stratum. Thus, the problem is inverted because instead of finding the curved trajectory of the seismic beam in a background with a Euclidean metric, it is proposed that the beam follows a geodesic of a curved space-time specific to each stratum, becoming a simple and automatic process using the differential geometry apparatus. For the reader to gain insight into this tool, different geological setups from idealised ones up to a salt dome are presented. Full article
(This article belongs to the Special Issue Recent Advances in Exploration Geophysics)
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19 pages, 7297 KiB  
Article
On the Effect of Horizontal Refraction Caused by an Anticyclonic Eddy in the Case of Long-Range Sound Propagation in the Sea of Japan
by Mikhail Sorokin, Pavel Petrov, Maxim Budyansky, Pavel Fayman, Aleksandr Didov, Aleksandr Golov and Yuri Morgunov
J. Mar. Sci. Eng. 2023, 11(9), 1737; https://doi.org/10.3390/jmse11091737 - 2 Sep 2023
Viewed by 1527
Abstract
The precision of acoustic ranging and navigation depends on the accuracy of the information about the sound speed field in the area of interest. Large-scale inhomogeneities in the bottom relief and water column can significantly affect the horizontal rays corresponding to vertical modes [...] Read more.
The precision of acoustic ranging and navigation depends on the accuracy of the information about the sound speed field in the area of interest. Large-scale inhomogeneities in the bottom relief and water column can significantly affect the horizontal rays corresponding to vertical modes (in the framework of Burridge–Weinberg formalism), which can lead to delays in the acoustic signal modal components, as compared to propagation along the geodesics on the Earth’s surface. In this study, the influence of horizontal refraction on the delay times of the modal components is considered. In particular, it is studied to what extent the presence of a synoptic eddy near the source–receiver path increases the effective propagation distances due to horizontal refraction. The elongation of horizontal eigenrays relative to the geodesic connecting the source and the receiver is also estimated. The influence of hydrological inhomogeneities on the propagation time of different modal components of a broadband acoustic signal is investigated. This is accomplished by the integration of the group slowness (reciprocal to the group speed) along the horizontal eigenrays connecting the locations of the source and the receiver. Implications for improving the accuracy of the solution of acoustic ranging problems are discussed. Full article
(This article belongs to the Special Issue Direct and Inverse Problems of Sound Scattering and Propagation in Underwater Acoustics)
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