Crude Oil Price

WTI (West Texas Intermediate) price refusing to fluctuate !!!
since last 3-4 days it has hung on $97.41.
Whereas in case of Brent the case is not like that ...
it has fallen for last couple of days.

Normal Moveout Term

Before that let us understand why are we looking for a correction in our seismic data. Let us consider a situation in which we are obtaining a seismic profile for "horizontal beds", and we are having the array of source and geophones. (as shown in the figure)

Now as soon as there will be blast, the waves would be emitted from it and a part of wave would reflect back and reach to the geophone G0. Let the time recorded by this geophone be T0, and similarly let the time recorded by G1, G2 and G3 be T1, T2 and T3 respectively. One thing is clear that the T0 will be less than T1, because G1 is placed @ a greater distance than G0 w.r.t. the source. So, we can say that T0<T1<T2<T3 and so on (keep one thing in mind that this is only valid for  those reflecting surfaces which are horizontal so at this point there should be no debate over this issue).   What actually the debatable issue is...how much is the change in time that we are getting ?  T1 - To will give some ▲t T1 - To will give some ▲t  T2 - To will give some other ▲t' (▲t and ▲t' wont be in linear relationship)  AND THIS CHANGE IN TIME WHICH WE ARE GETTING IS CALLED MOVE OUT    Now all we need to do is find out these ▲t (general move out term).   So, for this purpose we first need to understand the relationship of Time(tx) and Distance(X) from source (offset), and it will be hyperbola.The equation for the hyperbolic relation betn tx and X will be : Let,  X = Distance from source '"or" offset V = Velocity of wave tx = Travel time for a wave towards X distance to = Travel time for a wave at X=0 "or" at zero offset  


(tx)² = (to)² + (X/V)²  
(tx)² = (to)² [ 1 + (X/V*to)² ]( taking to common )  
(tx)  = (to)  [ 1 + (X/V*to)² ]^½   
Expanding the term we get :  
(tx)  = (to)  [1 + ½(X/V*to)² + (higher power terms)......... ]  
Ignoring higher power terms we get :  
(tx)  = (to) + (X²/V²*to)( to is cancelled in second term )  
(tx) - (to) = (X²/V²*to)  where, (tx) - (to) is nothing but T1 - To, T2 - To and so on...    


Example:
So our NMO correction is :  
▲t = (X²/V²*to)   where, ▲t is the required NMO correction.  
Thus, we can say that ever point on the hyperbola is incremented by ▲t, with respect to it's preceding point. i.e. to = 0.5 then  t1 = 0.5 + ▲t   (where ▲t =  (X²/V²*to)    = (1²/V²*0.5)   = (2/V²)

Derivation of equation for velocity of P wave & S wave

P-wave propagates with the help of expansion and compression of the medium, so the motion of the particles is in the direction of propagation of the wave whereas the S-wave propagates with the relative perpendicular motion of the particles. P-waves are also called longitudinal wave/compressional wave and S-waves are also called transversal wave/shear wave. The derivation of equation for velocity of P-wave/S-wave is quite complicated and is very difficult to understand so here, we would only deal with the 1 dimension accoustic wave equation.
You can derive the velocity of S-wave or P-wave if you know 3 equations. First is the Newton's ssecond law of motion (F=ma), Hooke's law for elasticity and equation of sound waves. Easy, isn't it ?
Let us consider that P is the pressure that is exerted on the subsurface layer by the wave incident on it and x is the distance travelled by the wave in order to do so. þ is the density of the formation on which the given wave is incident. ø and µ are the modulus of elasticity and modulus of rigidity.
As we know that the Newton's 2nd law is given by:

dP/dx = þ* dx²/dt² (1)
As we know that as per Hooke's law, the ratio of stress and strain is equal to the modulus of elasticity; 
so,
P = ø* dy/dx (2)

differentiating equation (2) w.r.t. x, we get

dP/dx = ø* dy²/dx²

putting equation (1) in above equation, we get

þ* dx²/dt² = ø* dy²/dx²
dx²/dt² = (ø/þ)* dy²/dx²
comparing above equation with equation of sound wave we can directly obtain

V² = (ø/þ)
V = (ø/þ)^½ (3)

Now, for s-wave we can write modulus of elasticity(ø) = modulus of rigidity(µ) 
so, by replacing the above value ø in equation (3) by the above relation, we can write velocity of S-wave which is given by,

V = (µ/þ)^½
Similarly you can derive the equation of velocity of p-wave in which the modulus of elasticity is the function of modulus of rigidity and bulk modulus(K).
i.e. ø = K + (4/3µ).so, by replacing the above value ø in equation (3) by the above relation, we can write the velocity of P-wave which is given by,

V = [{K + (4/3µ)}/þ]^½

That's it !!!

Generation of a synthetic seismogram

How can we generate a synthetic seismogram?
Procedure to create a synthetic seismogram is as follows:
- Multiply the velocity (calculated from the sonic log) and density logs to generate an acoustic impedance (AI) log. When a density log is not available, the densities can be calculated from the velocities with Gardner's rule: the density is proportional to the ¼ power of the P-wave velocity.

- Calculate from the AI log the reflection coefficients (using Zoeppritz' equation)

- Determine the wavelet from the seismic data

- Convolve the wavelet with the reflection coefficient trace to generate the synthetic trace