CE 5310 Lecture Notes - Lecture 15: Physics Today, Aseismic Creep, Cross-Correlation
Document Summary
The goal of this chapter is to understand how the rtm algorithm generates an image and to discuss the advantage and disadvantage of the technique. Arrays of transducers can re create a sound and send it back to its source as if time had been reversed. The signal from the transmitter arrives at the receiver after being modified by the medium where it travels. In chapter 1, we demonstrated the solution of the 1d wave equation as showing different sign in the exponential term as where u is displacement, a is amplitude of the signal, k is a wave number, w is angular (cid:1873)(cid:3404)(cid:1827)(cid:1857)(cid:3036)(cid:4666)(cid:3038)(cid:3051)(cid:2879)(cid:3050)(cid:3047)(cid:4667) (cid:4666)(cid:883)(cid:4667) frequency, t is time, and (cid:1861)(cid:3404) (cid:3398)(cid:883). The wave equation is also valid with another solution (cid:1873)(cid:3404)(cid:1827)(cid:1857)(cid:3036)(cid:4666)(cid:3038)(cid:3051)(cid:2878)(cid:3050)(cid:3047)(cid:4667). (cid:4666)(cid:884)(cid:4667) Since the meaning of sign represents the direction of wave propagation, the solutions indicate that two waves with opposing direction are mathematically valid solutions to one wave equation.
