MATLAB FACILITIES FOR SIMPLE MODELLING AND RAYTRACE MIGRATION 111

4.3. MATLAB FACILITIES FOR SIMPLE MODELLING AND RAYTRACE MIGRATION 111

Figure 4.43: The seismogram of Figure 4.42 is Figure 4.44: The picks of Figure 4.43 are shown shown with picks on the image of the anticline.

migrated on top of the reflectivity section.

with the command rayvelmod(vel,dx) where vel is the velocity matrix and dx is the grid size. Then, the command eventraymig(figno), where figno is the MATLAB figure number of Figure

4.39, causes the picks to be migrated and the resulting raypaths displayed in Figure 4.44. At the termination of each raypath, a small line segment, perpendicular to the raypath, is drawn that indicates the implied reflector dip. (These do not appear perpendicular in Figure 4.44 because the (x, z) axes do not have the same scale. The command axisequal will display any figure with equal scales on all axes.)

The relative accuracy of the migrations in Figure 4.44 is instructive. The picks have all migrated to positions near the anticline but some have fallen short while others have gone too far. Among the obvious reasons for this are the difficulty in determining which phase (peak, trough, zero crossing, etc.) of the input waveform should be picked and then making a consistent pick at two points. A slight error in either case can result in a very large error in the final position. Since the material beneath the anticline has a high velocity, a pick that arrives at the anticline with a little time left (see section 4.2.2) will continue a significant distance. Thus, small errors in the pick time can make

a large error in the result. Also, an error in picking ∆t/∆x will cause the initial trajectory of the ray to be incorrect. Since sin θ 0 = .5v 0 ∆t/∆x, these emergence angle errors are also more significant in high-velocity material. Migration by normal raytracing can reveal a lot about the nature of a seismic dataset. Also instructive is the complementary process of normal-incidence raytrace modelling. This process is implemented in the function normray that is logical reverse of normraymig . The latter requires

the pick specification of (x 0 ,t 0 , ∆t/∆x) while the former needs the specification of the normal ray: (x n ,z n ,θ n ). Here, (x n ,z n ) are the coordinates of the normal incidence point and θ n is the structural dip (in degrees) at the normal incidence point. Though logically similar, it is convenient to use separate raytracing engines for these two tasks because they have different criteria for stopping the ray. In migration, the ray is terminated when it has used the available traveltime while in modelling, it is stopped when it encounters the recording surface (z = 0). These raytracing engines are shootrayvxz and shootraytosurf respectively.

As with the migration tools, it is tedious to invoke normray at the command line for each pick. Therefore, a convenience function, eventraymod is provided that automatically models any picks found in the global variable PICKS. These picks are expected to have been made on a depth section

112 CHAPTER 4. ELEMENTARY MIGRATION METHODS

Figure 4.45: The reflectivity section of Figure Figure 4.46: The picks of Figure 4.45 are shown

4.40 is shown with picks on the anticline and modelled on top of the seismic section of Figure normal rays to the surface.

though no check is made to ensure this. Figure 4.45 shows the reflectivity section of Figures 4.40 and

4.44 with a series of picks, (x n ,z n ,θ n ), made on the anticline. Also shown are the normal incidence raypaths (drawn by normray ) to the surface. Figure 4.46 shows the modelled picks, (x 0 ,t 0 , ∆t/∆x), on top of the seismic section of Figures 4.42 and 4.43.