Inverse Crimes d=Lm m=L-1 d Red Sea Synthetics

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Inverse Crimes d=Lm m=L-1 d Red Sea Synthetics From Chapter 1: Inverse problems: an introduction

Inverse Crime Definition Inverse Crime: Employing the same modeling algorithm d=Lm to generate & invert m=L-1 d the synthetic data. Avoiding Inverse Crimes: Generate synthetic data Lm by a forward solver that has no connection to inverse solver m=L-1 d=L-1 Ld.  unreallistically optimistic results. Example 1: Field data inversion. Example 2: Elastic model vs acoustic inverse. Example 3: Different discretizations

Inverse Crime Questions 1. What does the term „no connection“ mean? 2. What kind of reconstructions of the unknown parameters can one obtain when there is „no connection“ between the forward and inverse solvers? m=L-1 d=L-1 Ld 3. Are inverse crime inversions always trivial? 4. Should the inverse crime always be avoided?

Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km 6 km/s Initial model 6 km 3 km/s 0 km 20 km 0 km 5 Hz 6 km/s 6 km 3 km/s 0 km 6 km/s 10 Hz 6 km 3 km/s 0 km 6 km/s 20 Hz 6 km 3 km/s

Waveform Tomograms Initial model 5 Hz 10 Hz 20 Hz 0 km 6 km 0 km 20 km 6 km/s Initial model 6 km 3 km/s 0 km 20 km 0 km 5 Hz 6 km/s 6 km 3 km/s 0 km 6 km/s 10 Hz 6 km 3 km/s 0 km 6 km/s 20 Hz 6 km 3 km/s

Traveltime Tomogram Depth (km) 3000 2.5 Velocity (m/s) Depth (km) 3000 2.5 Velocity (m/s) Waveform Tomogram 1500 Depth (km) 2.5 X (km) 20 20

Vertical Derivative of Waveform Tomogram 3000 Waveform Tomogram Velocity (m/s) Depth (km) 1500 2.5 Vertical Derivative of Waveform Tomogram Depth (km) 2.5 X (km) 20 21

Kirchhoff Migration Images