EXTENDED SEISMIC DATA PROCESSING-

DMOSEISMIC DATA PROCESSING

Last lecture we discussed the f-k domain filtering. Today we make swift review and then move to dip move out DMO. F-K domain is a transformation from t-x domain. The transformation is done using Fourier transform for both frequency and wavenumber. The subject seems complex but let’s start with the mathematical formula:

𝑢 (𝑘 ,𝜔 )=∬−∞

∞

𝑈 (𝑥 , 𝑡 )𝑒−𝑖 (𝜔𝑡+𝑘𝑥 )𝑑𝑥𝑑𝑡

As we are recording the wavefield at geophones distributed at the earth’s surface with certain intervals, we are actually sampling that wavefield in both space and time. Hence, all considerations pertinent to time are also valid for space ‘x’. Terminology changes only, for space domain, transform moves me to the wavenumber domain. Mathematically: 𝑘=

2𝜋𝐿

Where L is the wavelength

Now back to yesterday example

DMO, the problem

From the figure it is visible also that the CMP points do not lie at the mid-distance between the source and the receiver, the midpoints are smeared in the up-dip direction. The intention here is find that extra term that corrects for the dipping of the reflector.The distance between the source and receiver can be derived using the following equation:

To get rid of dR we use :

Substituting

The travel time then becomes:

The true velocity is related with the apparent velocity (dip-dependent) with the relation

Cdip can give good nmo correction although that the velocity is not true. The problem arise more when we deal with the so called conflicting dip case as in the next figure.

Now correction for DMO using the formula

Where

The time correction is thus given by

DMO flowchart