TY - JOUR

T1 - Asymptotic Ray Method for the Double Square Root Equation

AU - Shilov, Nikolay N.

AU - Duchkov, Anton A.

N1 - Our research is supported by grant \u2116FWZZ-2022-0017 of the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/4

Y1 - 2024/4

N2 - The parabolic wave equation describes wave propagation in a preferable direction, which is usually horizontal in underwater acoustics and vertical in seismic applications. For dense receiver arrays (receiver spacing is less than signal wavelength), this equation can be used for propagating the recorded wavefield back into the medium for imaging sources and scattering objects. Similarly, for multiple source and receiver array acquisition, typical for seismic exploration and potentially beneficial for ocean acoustics, one can model data in one run using an extension of the parabolic equation—the pseudo-differential Double Square Root (DSR) equation. This extended equation allows for the modeling and imaging of multi-source data but operates in higher-dimensional space (source, receiver coordinates, and time), which makes its numerical computation time-consuming. In this paper, we apply a faster ray method for solving the DSR equation. We develop algorithms for both kinematic and dynamic ray tracing applicable to either data modeling or true-amplitude recovery. Our results can be used per se or as a basis for the future development of more elaborated asymptotic techniques that provide accurate and computationally feasible results.

AB - The parabolic wave equation describes wave propagation in a preferable direction, which is usually horizontal in underwater acoustics and vertical in seismic applications. For dense receiver arrays (receiver spacing is less than signal wavelength), this equation can be used for propagating the recorded wavefield back into the medium for imaging sources and scattering objects. Similarly, for multiple source and receiver array acquisition, typical for seismic exploration and potentially beneficial for ocean acoustics, one can model data in one run using an extension of the parabolic equation—the pseudo-differential Double Square Root (DSR) equation. This extended equation allows for the modeling and imaging of multi-source data but operates in higher-dimensional space (source, receiver coordinates, and time), which makes its numerical computation time-consuming. In this paper, we apply a faster ray method for solving the DSR equation. We develop algorithms for both kinematic and dynamic ray tracing applicable to either data modeling or true-amplitude recovery. Our results can be used per se or as a basis for the future development of more elaborated asymptotic techniques that provide accurate and computationally feasible results.

KW - asymptotic ray method

KW - double square root equation

KW - parabolic equation

KW - source–receiver migration

KW - true-amplitude imaging

KW - wave equation

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85191407184&origin=inward&txGid=33d13b3dce192ec94b58143c09b173ab

UR - https://www.mendeley.com/catalogue/28313f83-702c-3649-92d2-69a6268d9c44/

U2 - 10.3390/jmse12040636

DO - 10.3390/jmse12040636

M3 - Article

VL - 12

JO - Journal of Marine Science and Engineering

JF - Journal of Marine Science and Engineering

SN - 2077-1312

IS - 4

M1 - 636

ER -