Mathematical models

Mathematical models

Three thin layers model

Model consists  of three thin layers. The velocity is  3 km/s in the media and  4 km/s in the layers.

 

Figure 1: Three thin layers model

Figure 2:  RTH Depth Migration Reflection  (a) and Diffraction(b).

Figure 3:  Thin slanted layers

Figure 4:  RTH Depth Migration Reflection

Figure 5:  RTH Depth Migration Reflection. Only sloped layers detected

More detail:

Erokhin G., Pestov L., Danilin A.,  Kozlov M., and Ponomarenko D., 2017,

Interconnected vector pairs image conditions: New possibilities for visualization of acoustical media, 2017,  SEG Technical Program Expanded Abstracts 2017: 4624-4629., https://doi.org/10.1190/segam2017-17587902.1

Two layers model

The velocity is  3 km/s in the upper media and  4 km/s in the  down media.

Figure 1:   Two layers model

Figure 2:  RTH Depth Migration Reflection

Figure 3:  RTH Depth Migration Diffraction

Figure 4:  RTH  Prism wave

Hard and soft diifractors model

The left diffractor  has reduced velocity by 0.1 km/s  w.r.t. background velocity 3.0 km/s  , the right one  has increased velocity by 0.1 km/s

Figure 1 : Model of “soft” and “hard” diffractors

Figure 2 : RTH Depth Migration  soft diffractor filter (a), hard diffractor filter (b), soft & hard diffractor filter  (c), RTH Dip Angle Variance (d).

More detail:

Erokhin G., Pestov L., Danilin A.,  Kozlov M., and Ponomarenko D., 2017,

Interconnected vector pairs image conditions: New possibilities for visualization of acoustical media, 2017,  SEG Technical Program Expanded Abstracts 2017: 4624-4629., https://doi.org/10.1190/segam2017-17587902.1

Marmousei2 model.

Figure 1:   Marmousei2 model

Figure 2:   Conventional RTM

Figure 3:   RTH Depth migration

Figure 4:   RTH Dip Angle Variance (part)

Gradient velocity  model

Figure 1:    The gradient initial velocity model

Figure 2: The true velocity (a), RTH velocity  (b)

Figure 3: The true velocity profile (c), RTH velocity (d)