First-break traveltime tomography is based on the eikonal equation. Because the eikonal equation is solved at fixed-shot positions and only receiver positions can move along the raypath, the adjoint-state tomography relies on inversion to resolve possible contradicting information between independent sho...
joint utility function of travel time T and travel cost M in Scenario i under risky conditions, p and q represent the probability of occurrence of two outcomes, and π+(⋅) and π−(⋅) are the corresponding weight functions for the gain and loss, respectively, given by equation (2...
where\(\rho =\sqrt{{x}^{2}+{\tau }^{2}}\)andθ = arctan(x/τ) are the polar coordinates on thex–tplane,Jlis thel-order Bessel function of the first kind, andτ = t − z/vgis the retarded time in pulse frame wherevgis the group velocity. Equation (2) shows...
The master equation for the residence time pdf is derived and solved analytically, providing expressions for travel and residence time pdf's as a function of input/output fluxes and of the relevant mixing. Our solutions suggest intrinsically time-variant travel and residence time pdf's through a ...
THREE-DIMENSIONAL TRAVELTIME AND AMPLITUDE COMPUTATION USING THE SUPPRESSED WAVE EQUATION ESTIMATION OF TRAVELTIME (SWEET) ALGORITHM By using the property of the damped wavefield in the Laplace domain, we calculate the traveitime and the amplitude of first arrival events in three dimensi... D Yang...
However, when the LTI is applied to a 3-D model, the least traveltime equation used in forward processing is a transcendental equation that cannot be solved by an analytical formula, as is used for a 2-D model. Many attempts have been made to solve this problem. For example, Peng and...
terms in the equation of motion. We then discuss some methodologies for the numerical implementation of the method in the time domain and to present a variational formulation for the construction of different misfit functions. We here define a new misfit travel-time function that allows us to ...
Waves propagating away from and back to the tunnel face are assumed to travel in a homogeneous medium ignoring eventual stratification of the medium and the massive influence of the tunnel itself on wave propagation. Download: Download high-res image (154KB) Download: Download full-size image ...
Also, the KSP problem to be solved is constrained by the total travel time. The goal of this research is to provide sound route choice options to the travelers in order to assist their route choice decision process, during which process the overlap and travel time deviation issues between the...
The travel distance and time of different transport modes between each node from “O” to “D” are shown in Table 1 and Table 2, respectively. Table 1. Transport distance parameters between node cities. Serial number City nodeTransportation distance (unit: km) RailwayWaterwayHighway 1 1-2 ...