• Journal of Korea Water Resources Association
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• v.31 no.6
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• pp.845-854
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• 1998

Following the approach of Ebersole (1985), water wave transformation is predicted using the eikonal equation and transport equation for wave energy which are reduced from the extended mild-slope equation of Massel (1993), and also the irrotationality of wave number vectors. The higher-order bottom effect terms, i.e., squared bottom slope and bottom curvature, are neglected in the study of Ebersole but are included in the present study. It was expected that, if these terms are included in this study, the approach would give more accurate solution in the case of rapidly varying topography. But, the expectation was frustrated. It is probably because, in the case of rapidly varying topography, the diffraction effect which is included in the eikonal equation does not work well and thus the solution is deteriorated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.15-21
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• 1989

A simple numerical refraction model is presented. The model takes into account refraction, shoaling and bottom dissipation. Eikonal equation and equation of energy conservation are discretized by an explicit finite-difference method, which provides wave angle and height at each grid point, respectively. Applications of the model were made to simple geometries as well as complex geometries, and some advantages on computing time and stability have been observed.

• Geophysics and Geophysical Exploration
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• v.3 no.4
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• pp.119-124
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• 2000

A new fast algorithm for travel time calculation using mono-chromatic one-way wave equation was developed based on the delta function and the logarithms of the single frequency wavefield in the frequency domain. We found an empirical relation between grid spacing and frequency by trial and error method such that we can minimize travel time error. In comparison with other methods, travel time contours obtained by solving eikonal equation and the wave front edge of the snapshot by the finite difference modeling solution agree with our algorithm. Compared to the other two methods, this algorithm computes travel time of directly transmitted wave. We demonstrated our algorithm on migration so that we obtained good section showing good agreement with original model. our results show that this new algorithm is a faster travel time calculation method of the directly transmitted wave for imaging the subsurface and the transmission tomography.