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Amplitude

Time

Dip

Pattern

Other Attributes

Lithology

Depth

Structure

DepositionalEnvironment

Pore Fluid

Inverse Modelling from wiggles to rocks

Forward ModellingForward Modelling

From Rocks to Wiggles

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The Synthetic Seismogram: The SimpleGram Model

TheRocks

Impedance Log Reflectivity Log (z) Reflectivity (t)

I(Z) R(Z) R(t)

2

1 Reflectivity R(t)

The Wavelet

The wavelet comprises the effects ofthe Source, Receiver, Geophone, andInstruments

W(t)

12

120

II

IIR

+

=VI =

Z

T

Components of the Seismic Trace

V

Z

2T

=

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V

GasSand

Water SS

Shale

Logs and Lithology

Sonic ( s/ft) Density (g/cc)

190 150 100 2.52.0

Gas

Water

Shale

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The Simplegram Model continued

Putting the components together byconvolution

r(t) w(t) = s(t)

Each reflection coefficient stick is replaced by w(t)

=

S(t)

r(t) w(t)

Wheres the RESOLUTION ability to see individual reflections ?

What happens if the wavelet changes how will this affect COHERENCY ?

0

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The Convolutional Model

R(t,x) - Reflectivity

A(t,x)

RA

W(t,x) V(t,x)

[RA] W V

N(t,x)Randomand Coherent Noise

{[RA] W V}+ N

Spherical DivergenceSpreading Loss

AttenuatedReflectivity

The Wavelet

(source, near surface,geophone, instruments)

Time-varying filter: Q, IBM

+

The Seismic Trace

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Recovering the Reflectivity

Inverting the Convolutional Model

R(t,x) - Reflectivity

A(t,x)

RA

W(t,x) V(t,x)

[RA] W V

N(t,x)Randomand Coherent Noise

{[RA] W V}+ N

Spherical DivergenceSpreading Loss

AttenuatedReflectivity

The Wavelet

(source, near surface,geophone, instruments)

Time-varying filter: Q, IBM

The Seismic Trace

+

- N

W -1 V -1

A -1

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Exercise: Synthetic Seismogram

5 = 4.0

V5 = 8000

4 = 2.0

V4 = 16000

3 = 2.0V3 = 8000

2

= 2.0

V2 = 12000

1 = 2.0V1 = 8000

8000

8600

9000

9800

Z

2.0 2.1 2.2 2.3

t

R(t)

R(Z)

2.0 2.1 2.2 2.3

t

2.0 2.1 2.2 2.3

(B) Computeand show R(t)

(C) Compute andshow R(t)W(t) for

the wavelets below

(A) Compute R(Z) and plot at the right.

Note: the reflection from

8000 feet occurs at 2.0 s.

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Exercise: Synthetic Seismogram

5 = 4.0

V5 = 8000

4 = 2.0

V4 = 16000

3 = 2.0V3 = 8000

2

= 2.0

V2 = 12000

1 = 2.0V1 = 8000

8000

8600

9000

9800

Z

2.0

2.1

2.2 2.3

t

R(t)

R(Z)

2.0 2.1 2.2 2.3

t

2.0 2.1 2.2 2.3

(B) Computeand show R(t)

(C) Compute andshow R(t)W(t) for

the wavelets below

(A) Compute R(Z) and plot at the right.

Note: the reflection from

8000 feet occurs at 2.0 s.

20812

812R .=

+

=

20812

128R .=

+

=

3330816

816R .=

+

=

00216000048000

216000048000R .

(.).(

)(.).(=

+

=

V

Z2T

=

T=0.1

T=0.1

T=0.1

.2

-.2

.33

0

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Exercise: Synthetic Seismogram

5 = 4.0

V5 = 8000

4 = 2.0

V4 = 16000

3 = 2.0V3 = 8000

2

= 2.0

V2 = 12000

1 = 2.0V1 = 8000

8000

8600

9000

9800

Z

2.0

2.1

2.2 2.3

t

R(t)

R(Z)

2.0 2.1 2.2 2.3

t

2.0 2.1 2.2 2.3

(B) Computeand show R(t)

(C) Compute andshow R(t)W(t) for

the wavelets below

(A) Compute R(Z) and plot at the right.

Note: the reflection from

8000 feet occurs at 2.0 s.

20812

812R .=

+

=

20812

128R .=

+

=

3330816

816R .=

+

=

00216000048000

216000048000R .

(.).(

)(.).(=

+

=

V

Z2T

=

T=0.1

T=0.1

T=0.1

.2

-.2

.33

0

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A.I. Log

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A.I. Log

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