Seismic Data ProcessingLecture 13

Stacking and migration

Dr Amin KhalilSchool of Physics, USM

Factors controlling seismic Velocity

Seismic velocities of common rock types

•Seismic reflection data often show bad Signal to Noise ratio S/N, not only because of the high amplitude of coherent energy of surface waves but also due to non coherent noise as well.

•In order to increase S/N ratio CMP gather and sorting, then NMO correction then stacking are the basic operation to do so.

•In stacking, the CMP gathered traces are corrected for NMO then summed to give one single trace

Why Stacking?

We have two types of stacking:

1- Horizontal stacking: In which we apply CMP, NMO correction then adding traces together to get single trace for certain points in the subsurface.

2- Vertical stacking: In which at the same shot and geophone locations we shot number of times and then the traces are averaged.

Types of Stacking

Stacking Illustrated

CMP gather, velocity analysis and stacking

Drawback of stacking

Reflection depends on the angle of incidence, which mean change of the angle of incidence contains information about the lithology, fluid contents, ... etc.

In stacking we are averaging over the various incidence angles, which result in data only at kx =0. This situation is similar to average of time series in time domain which results in DC content only i.e. F=0

What we benefit from stacking isSignal to Noise ratio is enhanced, despite the stretching and averaging of incident angles.

In the stacked section below do you realize something wrong?!!!

Stacking reduce data volume.

Filter in seismicIn seismic we have 4 types of filters:• Low Pass• High Pass• Band Pass• Band reject

Migration

In migration we want to remove the wave phenomena so that our section resemble the shape of the subsurface, thus we can model the earth more accurately.

One of the wave phenomena problems is the diffraction of seismic waves. (discussed earlier)

Statement of the problem

In CMP-NMO-Stacking sequence we assume that all the traces are reflected on common point in the reflector. This is the case for flat horizontal reflector (i.e. the ideal case). In reality there reflectors may be dipping or irregular. Hence the CMP gather doesn’t represent single point in the reflector.Despite this problem CMP-NMO-Stacking sequence is consider powerful tool for signal to noise ratio enhancement.

Migration is thus applied to solve this problem.

In ordinary seismic reflection practice, we fire the shot at time t=0, then seismic ray propagates to the reflector where it is reflected back and recorded by the geophone on the surface. In exploding reflector model we assume that shot is at the reflector and the energy is propagating up to the geophone with half the wave speed. To get good amplitude, the strength of each source is related to the reflection coefficient at the point

Cont’d

By tracing in time domain to to we can image the reflector by defining the places of the shots. The condition of to is called the imaging condition.

Kinematically, Zero-offset section can be considered a record of exploding reflector model.

Seismic Diffraction

Seismic Diffraction

More complicated example

The time for a diffracting point located at (xd , Zd ) is given by:

This equation represent hyperbola like the one seen at the following figure.

This figure shows the diffractor to the left and its corresponding time on the zero offset seismic section.

Diffraction stacking Cont’d

In early days, Before the computer era, people used stacking along the hyperbola in order to obtain the diffraction point. This require the knowledge of the velocity to carry out stacking. In case that we have more than one diffraction point with different velocities we apply stacking for each hyperbola with its proper stacking velocity.

Diffraction stacking Cont’d

In early computer age the following relation is used:

Four points diffractor

If the points separation is infinitely small, a reflector then can be mapped.

Thank you