Linearization Error Polina Zheglova DNOISE Seminar, October 16, - - PowerPoint PPT Presentation

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Linearization Error Polina Zheglova DNOISE Seminar, October 16, 2013 1/7 Linearization Error Velocity Model c = v + v v = vr v = v ( z ) is smooth r = r ( z ) is oscillatory random Standard deviation of r is 5% 2/7 Linearization Error

SLIDE 1

Linearization Error

Polina Zheglova

DNOISE Seminar, October 16, 2013

1/7 Linearization Error

SLIDE 2

Velocity Model

c = v + δv δv = vr v = v(z) is smooth r = r(z) is oscillatory random Standard deviation of r is 5%

2/7 Linearization Error

SLIDE 3

Smooth Background and Oscillatory Perturbation

Figure :

Left: background model v. Right: perturbation r.

3/7 Linearization Error

SLIDE 4

Data from Smooth Model / Linearized Data

Figure :

Left: F[v] . Right: F[v]r.

4/7 Linearization Error

SLIDE 5

Oscillatory Background and Smooth Perturbation

c = v1 + δv1 r1 = δv1 v1 Oscillatory background: v1 = 95%v + δv Smooth perturbation: δv1 = 5%v

5/7 Linearization Error

SLIDE 6

Data from Smooth Model / Linearized Data

Figure :

Left: F[v1] . Right: F[v1]r1.

6/7 Linearization Error

Linearization Error

Polina Zheglova

DNOISE Seminar, October 16, 2013

Velocity Model

c = v + δv δv = vr v = v(z) is smooth r = r(z) is oscillatory random Standard deviation of r is 5%

Smooth Background and Oscillatory Perturbation

Figure :

Left: background model v. Right: perturbation r.

Data from Smooth Model / Linearized Data

Figure :

Left: F[v] . Right: F[v]r.

Oscillatory Background and Smooth Perturbation

c = v1 + δv1 r1 = δv1 v1 Oscillatory background: v1 = 95%v + δv Smooth perturbation: δv1 = 5%v

Data from Smooth Model / Linearized Data

Figure :

Left: F[v1] . Right: F[v1]r1.

Linearization Error

Figure :

Left: Error for F[v] . Right: Error for F[v1].