The fundamental components of inverse theory in the solid earth are (i) spectral perturbation, (ii) the geodesic $X$-ray transform,  (iii)the generalized Radon transform - tied to reflection tomography, and (iv) the wave-equation analogues of (ii)-(iii). Inverse surface-wave scattering yields a modification of (iii)-to-(iv). Receiver functions can be derived from (iii) & (iv). Surface-wave tomography can be derived from (i).

The goal of this course is to provide an overview of approaches -associated with time reversal - to imaging the materials properties and processes (under (iii)-(iv)). We focus on reverse-time migration
(RTM), the new notion of array receiver functions, and finite-frequency reflection tomography. Applications pertain to the crust, the transition zone and the lowermost mantle. The course will consist of 15 hours of lectures and an oral exam, in 6 days.

course material: www.math.purdue.edu/~mdehoop/10_topics

day 1

SESSION 1: introduction to imaging and inverse scattering
- an incident plane wave [ 3 hours]

day 2

SESSION 2: reciprocity, time reversal [ 2 hours]

backpropagation

day 2/3

SESSION 3: RTM acoustic [ 4 hours]

adjoint state method and waveform inversion

introduction to fast wave-packet/curvelet migration

day 4

SESSION 4: extended imaging, reflection tomography [ 3 hours]

artifacts and resolution

day 5

SESSION 5: RTM elastic, anisotropy [ 3 hours]

array receiver functions

day 6

SESSION 6: imaging via noise blending [ 1 hour ]

ORAL EXAM (material: SESSIONS 1-5) [ 2 hours]




Maarten V. de Hoop
Geo-Mathematical Imaging Group
Purdue University, West Lafayette IN 47907, USA