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Stacking and Velocity Analysis

The data are stacked to emulate a

common source receiver geometry. Data traces from common midpoints are

added to improve the signal to noise ratio. To do this, the seismic velocity must first

be found.

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Stacking creates a seismic section that emulates

a common source-receiver geometry that can beinterpreted.

Shot and receiver in same spot!

Works best if layer is flat.

The CMP section

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Constant Velocity Stack

Lets assume the rocks all have the same

seismic velocity constant velocity assumption. What is the travel time for a raypath bouncing off

a flat layer at depth?

x

d

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x

d

The hyperbolic travel-time2

2 2 2xTotal raypath distance = 2 +d (2 )2

x d

= +

0

dwhere t =2 is the zero offset traveltime

v

2 2 2

2 2 201 2Total raypath traveltime = x +(2d)

vx d x td v d = + = +

2

2

0

xt t

v

= +

So the normal move out equation is

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HyperbolicMoveout

Near shot trace,

intercept is t0

Hyperbolas flatten

at longer times

x

Moveout is the way thereflection appears at later

times for more distant traces.

This is the equation of a

hyperbola. with its apex at t=t0

2

2

0

xt t

v

= +

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HyperbolicMoveout

The amount of moveoutdetermines what velocity

should be used.

This is called thestacking velocity

The best stacking velocity

is the one that producesthe most coherent

reflections after stack!

Near shot trace,

intercept is t0

Hyperbolas flatten

at longer times

x

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NMO correction

The travel time is:

So, to correct, we adjust each point on

each trace by:

2

2

0

xt t

v

= +

2

2

0 0 0( ) x

t t x t t t v

= = +

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NMO correction

t

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NMO correction

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Velocity varies with depth

If the velocity varies with depth, we must

adjust the stacking velocity to vary as afunction of time: v(t)

We still use a modified stacking equation:

2

20

( )xt t

v t = +

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Stacking velocity

Stacking velocity is the best apparent

velocity to stack with. It depends on all the layer velocities above

the reflector so it is an average velocitythat turns out to be the rms velocity

2

10

i

1

where t is the two-way travel time in layer i

N

stack rms i i

i

v v v t t =

= =

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Dipping layer velocity

x

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Dipping layer velocity

Modify velocity by

dividing by cos

22

2

0

cosxt t v

= +

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3D dipping layer velocity

2 2

/(1 sin cos )stackingv v =

Must modify even more if layer is

dipping in 3D

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Finding the stacking velocity

If we know the velocities and dips, we can

find the nmo correction for the reflectionhyperbola

But we dont know either the velocities ordips.

We try different stacking velocities and use

the one that works best.

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Methods to find stacking velocity

Try different stacking velocities on cmp

gathers and pick the best one Try different stacking velocities on cmp

stacked section and pick the best one Try measuring the coherency of the

reflections for different stacking velocities

and plot them

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Effect of stacking velocity on cmp

gathers

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Effect of stacking velocity on cmp

gathers

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Effect of stacking velocities on

stacked section

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Constant velocity stacks

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Velocity spectrums

We can estimate the stacked trace strength for

different stacking velocities and then plot them To do this for a specific cmp gather

Take gather and make nmo correction for a specific

velocity Measure the rms (root-mean-square) of cmp gather at

specific times

Do this for different velocities

Plot these up and contour

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Velocity

spectrum

For each velocity

NMO is applied to flatten reflectors

RMS strength is found at each time

strength is plotted and contoured

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Velocity spectrum

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Velocity spectrum

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Velocity spectrum for different line

lengths

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Velocity analysis processing

The velocityanalysis is

typically carriedout for every100 or somidpoints and

then the modelis interpolatedto get aregionally

varying modelthat is used tostack the cmpdata.