seismic methods: seismic reflection -...

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Applied Geophysics – Seismic reflection II

Seismic reflection - II

Reflection reading: Sharma p130-158; (Reynolds p343-379)

Seismic methods:


Seismic reflection processingFlow overview

These are the main steps in processing

The order in which they are applied is variable

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Reflectivity and convolution

The seismic wave is sensitive to the sequence of impedance contrasts

The reflectivity series (R)

We input a source wavelet (W) which is reflected at each impedance contrast

The seismogram recorded at the surface (S) is the convolution of the two

S = W * R


Deconvolution

Spiking or whitening deconvolution

Reduces the source wavelet to a spike. The filter that best achieves this is called a Wiener filter

Our seismogram S = R*W (reflectivity*source)

Deconvolution operator, D, is designed such that D*W = δ

So D*S = D*R*W = D*W*R = δ*R = R

Time-variant deconvolution

D changes with time to account for the different frequency content of energy that has traveled greater distances

Predictive deconvolution

The arrival times of primary reflections are used to predict the arrival times of multiples which are then removed

…undoing the convolution to get back to the reflectivity series – what we want

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Spiking deconvolution



1 -1 Recorded waveform

Deconvolution operator

Output 0

¾

1

¼ 1 1

Recovered reflectivity series

-½

4



1 -1

0

¾

1

¼ 1 1

-½

0

Recorded waveform


Output




1 -1

0

¾

1

¼ 1 1

-½

0 0

Recorded waveform


Output


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1 -1

0

¾

1

¼ 1 1

-½

0 0 0

Recorded waveform


Output




1 -1

0

¾

1

¼ 1 1

-½

0 0 0

Recorded waveform


Output


?A perfect

deconvolution operator is of infinite length

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Source-pulse deconvolution

Deconvolution: Ringing removed

Original section

Source wavelet becomes spike-like

Examples


Deconvolution using correlation

If we know the source pulse

Then cross-correlating it with the recorded waveform gets us back (closer) to the reflectivity function

If we don’t know the source pulse

Then autocorrelation of the waveform gives us something similar to the input plus multiples.

Cross-correlating the autocorrelation with the waveform then provides a better approximation to the reflectivity function.

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MultiplesDue to multiple bounce paths in the section

Looks like repeated structure

These are also removed with deconvolution• easily identified with an autocorrelation• removed using cross-correlation of the

autocorrelation with the waveform

Sea-bottom reflections


Seismic reflection processingFlow overview

These are the main steps in processing

The order in which they are applied is variable

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Velocity analysis

Determination of seismic velocity is key to seismic methods

Velocity is needed to convert the time-sections into depth-sections i.e. geological cross-sections

Unfortunately reflection surveys are not very sensitive to velocity

Often complimentary refraction surveys are conducted to provide better estimates of velocity


Normal move out (NMO) correction

reflection hyperbolae

become fatter with depth

(i.e. velocity)

1

220

2

VxTTx +=

The reflection traveltime equation predicts a hyperbolic shape to reflections in a CMP gather. The hyperbolae become fatter/flatter with increasing velocity

210

2

2 VTxTNMO ≈∆

We want to subtract the NMO correction from the common depth point gather

But for that we need velocity…

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Stacking velocity

210

2

2 VTxTNMO =∆In order to stack the waveforms we

need to know the velocity. We find the velocity by trial and error:

• For each velocity we calculate the hyperbolae and stack the waveforms• The correct velocity will stack the reflections on top of one another• So, we choose the velocity which produces the most power in the stack

V2 causes the waveforms to

stack on top of one another


Stacking velocityMultiple layer case

A stack of multiple horizontal layers is a more realistic approximation to the Earth

• Can trace rays through the stack using Snell’s Law (the ray parameter)

• For near-normal incidence the moveout continues to be a hyperbolae

• The shape of the hyperbolae is related to the time-weighted rms velocity above the reflector

Velocity semblance spectrum

Pick stacking velocities

multiples

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Stacking velocityMultiple layer case

Stacking velocity panels: constant velocity gathers

Note: the sensitivity to velocity decreases

with depth


Multiple layers

Interval velocityi

ii tzV =

0' TZV =

∑∑=

i

iiRMS t

tVV

2

RMSn V

zxt22 4+

=

( ) ( )1

12

1,2

,int

−

−−

−−

=nn

nnRMSnnRMS

tttVtV

V

Average velocity

Root-mean-square velocity

Two-way traveltime of ray reflected off the nth interface at a depth z

The interval velocity of layer n determined from the rms velocities and the two-way traveltimes to the nth and n-1th reflectors Dix equationThe interval velocity can be determined from the rms velocities layer by layer starting at the top

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Velocity sensitivity: ExampleDeep: Two layer model: α1 = 6 km/s, z = 20 km

440031

42 222

1

xxzt +=+=α

4802

2

021

2 xt

xtNMO ==∆α

Equation of the reflection hyperbolae:

Normal move out correction:

For a 5 km offset:α1 = 6.0 km/s then 0.052 sec – correct valueα1 = 5.5 km/s then 0.062 secα1 = 6.5 km/s then 0.044 sec

Are these significant differences?

What can we do to improve velocity resolution?

Shallow: Two layer model: α1 = 3 km/s, z = 5 km

4255.11 2xt +=

60

2xtNMO =∆

For a 5 km offset:α1 = 3.0 km/s then 0.417 secα1 = 2.5 km/s then 0.600 secα1 = 3.5 km/s then 0.306 sec


Frequency filtering

Hi-pass: to remove ground roll

Low-pass: to remove high frequency jitter/noise

Notch filter: to remove single frequency

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Resolution of structure

Consider a vertical step in an interface

To be detectable the step must cause an delay of ¼ to ½ a wavelength

This means the step (h) must be 1/8 to ¼ the wavelength (two way traveltime)

Example: 20 Hz, α = 4.8 km/s then λ = 240 mTherefore need an offset greater than 30 m

Shorter wavelength signal (higher frequencies) have better resolution.

What is the problem with very high frequency sources?


Resolution of structure

When you have been mapping faults in the field what were the vertical offsets?

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Fresnel ZoneTells us about the horizontal resolution on the surface of a reflector

First Fresnel Zone

The area of a reflector that returns energy to the receiver within half a cycle of the first reflection

The width of the first Fresnel zone, w:

42

242

2

22

2

λλ

λ

+=

+=

+

dw

wdd

If an interface is smaller than the first Fresnel zone it appears as an point diffractor, if it is larger it appears as an interface

Example: 30 Hz signal, 2 km depth where α = 3 km/s then λ = 0.1 km and the width of the first Fresnel zone is 0.63 km

seismic methods: seismic reflection -...

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