Question

Consider ray tracing in an isotropic elastic Earth, with travel time function \( T(x, y, z) \) in Cartesian coordinates. Select the correct option(s).

• A. The slowness vector is tangential to the wave fronts
• B. The slowness vector is parallel to the gradient of \( T(x, y, z) \)
• C. \( T(x, y, z) \) is constant on a particular wave front
• D. \( T(x, y, z) \) is constant along the rays

Hint:

In ray theory, the slowness vector points in the direction of increasing travel time and is always normal to wavefronts.

Answer 1

The Correct Option is B, C

Step 1: Understand slowness vector. 
The slowness vector is defined as \( \nabla T(x, y, z) \), i.e., the gradient of the travel time. 
Step 2: Analyze wavefront properties. 
Wavefronts represent surfaces of constant travel time, i.e., \( T(x, y, z) = {constant} \). Rays are perpendicular to wavefronts, so the slowness vector (being the gradient) is normal to the wavefront. 
Step 3: Evaluate options. 
(A) Incorrect: Slowness is normal, not tangential.
(B) Correct: Slowness vector \( = \nabla T \).
(C) Correct: \( T(x, y, z) \) is constant on a wavefront.
(D) Incorrect: \( T \) increases along a ray path.