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The Zoeppritz equations consist of four equations with four unknowns [] = [ ] [ ]R P, R S, T P, and T S, are the reflected P, reflected S, transmitted P, and transmitted S-wave amplitude coefficients, respectively, =angle of incidence, =angle of the transmitted P-wave, =angle of reflected S-wave and =angle of the ...
2.5.1 Wave equations. 2.5.2 Sinusoidal solutions to the 3d wave equation. 3 See also. 4 Footnotes. 5 Sources. 6 Further reading. Toggle the table of contents.
Acoustic waves couple to deep-water waves in a three-wave interaction, [11] Vorticity waves couple in a triad. A uniform current (necessarily spatially inhomogenous by depth) has triad interactions. These cases are all naturally described by the three-wave equation. In plasma physics, the three-wave equation describes coupling in plasmas. [12]
For an incident wave traveling from one medium (where the wave speed is c 1) to another medium (where the wave speed is c 2), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be ...
(For navigation, the user receiver's clock must be synchronized with the transmitter clocks; this requires that the TOT be found.) Equation 3 is the hyperboloid described in the previous section, where 4 receivers (0 ≤ m ≤ 3) lead to 3 non-linear equations in 3 unknown Cartesian coordinates (x,y,z). The system must then solve for the ...
An indeterminate system by definition is consistent, in the sense of having at least one solution. [3] For a system of linear equations, the number of equations in an indeterminate system could be the same as the number of unknowns, less than the number of unknowns (an underdetermined system), or greater than the number of unknowns (an ...
The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
Kinematic wave can be described by a simple partial differential equation with a single unknown field variable (e.g., the flow or wave height, ) in terms of the two independent variables, namely the time and the space with some parameters (coefficients) containing information about the physics and geometry of the flow. In general, the wave can ...