Making CMP’s

From chapter 16 “Elements of 3D Seismology” by Chris Liner

Outline

•Normal Moveout

•Stacking

Normal Moveout

22 2

0 2

xT T

V

22

0 0 02( ) ( )

xT x T x T T T

V

x

T

Hyperbola:

Normal Moveoutx

T

“Overcorrected”

Normal Moveout is too large

Chosen velocity for NMO is too

(a) large (b) small

Normal Moveoutx

T

“Overcorrected”

Normal Moveout is too large

Chosen velocity for NMO is too

(a) large (b) smallsmall

Normal Moveoutx

T

“Under corrected”

Normal Moveout is too small

Chosen velocity for NMO is

(a) too large

(b) too small

Normal Moveoutx

T

“Under corrected”Normal Moveout is too small

Chosen velocity for NMO is

(a) too largetoo large

(b) too small

Vinterval from Vrms

122 2

1 1interval

1

n n n n

n n

V t V tV

t t

Dix, 1955

2i i

RMSi

V tV

t

Vrms

V1

V2

V3

Vrms < Vinterval

Vinterval from Vrms

Vrms T Vinterval from Vrms ViViT VRMS from V interval1500 0 01500 0.2 1500 450000 15002000 1 2106.537443 4000000 20003000 2 3741.657387 18000000 3000

SUM 3.2 22450000

Primary seismic eventsx

T

x

T

Primary seismic events

x

T

Primary seismic events

x

T

Primary seismic events

Multiples and Primariesx

TM1

M2

Conventional NMO before stackingx

TNMO correction

V=V(depth)

e.g., V=mz + B

M1

M2

“Properly corrected”

Normal Moveout is just right Chosen velocity for NMO is correct

Over-correction (e.g. 80% Vnmo)

x

TNMO correction

V=V(depth)

e.g., V=0.8(mz + B)

M1

M2

x

TM1

M2

f-k filtering before stacking (Ryu)

x

TNMO correction

V=V(depth)

e.g., V=0.8(mz + B)

M1

M2

x

T

M2

Correct back to 100% NMO

x

TNMO correction

V=V(depth)

e.g., V=(mz + B)

M1

M2

x

TM1

M2

Outline

•Convolution and Deconvolution

•Normal Moveout

•Stacking

NMO stretching

V1

V2

T0

“NMO Stretching”

NMO stretching

V1

V2

T0

“NMO Stretching”

V1<V2

NMO stretching

V1

V2

V1<V2

0 0T T0T 1T

1 1T TNMO “stretch” = “linear strain”

Linear strain (%) = final length-original length

original length

X 100 (%)

NMO stretching

V1

V2

V1<V2

0 0T T0T 1T

1 1T T

X 100 (%)

original length = 1T final length = 0T

NMO “stretch” = 0 1

1

T TT

X 100 (%)0

1

1TT

0T

X 100 (%)0

1

1TT

stretching for T=2s,V1=V2=1500 m/s

Green line assumes

V1=V2

Blue line is for general case,

where V1, V2 can be different

and delT0=0.1s (this case: V1=V2)

Matlab code

Stacking

+ + =

+ + =

Stacking improves S/N ratio

+ =

Semblance Analysis

22

1 1 2

22

1 1 2

22

1 1 2

“Semblance”

+

22

3 33

2 2 2

X

Tw

tt (

s)

+ =

Semblance Analysis

+

X

Tw

tt (

s)

V3

V1

V2

V

Peak energy