Seismic reflection - II Seismic reflection processing

Seismic methods:

Seismic reflection - II

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

Applied Geophysics – Seismic reflection II

Seismic reflection processing

Flow 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 Î 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

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

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 Applied Geophysics – Seismic reflection II

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Spiking deconvolution



Recorded waveform Deconvolution operator

Output

1 ¼

1

1

0

1

-1

¾

-½

Recovered reflectivity series Applied Geophysics – Seismic reflection II

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Recorded waveform

1

-1

Deconvolution operator

¼

1

1

Output

0

1

0

¾

-½



Recorded waveform

1

-1

¾


¼

1

1

1

0

0

Output

0

-½


4


Recorded waveform

1


Output

0

1

-1

¾

-½

¼

1

1

0

0

0



Recorded waveform

1

-1


Output Recovered reflectivity series

0

1

0

¾

-½

¼

1

0

0

1

?

A perfect deconvolution operator is of infinite length


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Source-pulse deconvolution Examples

Original section

Deconvolution: Ringing removed

Source wavelet becomes spike-like Applied Geophysics – Seismic reflection II

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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Multiples Due to multiple bounce paths in the section Î 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 Applied Geophysics – Seismic reflection II

Seismic reflection processing

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

Tx2 = T02 +

reflection hyperbolae become fatter with depth (i.e. velocity)

x2 V1

We want to subtract the NMO correction from the common depth point gather 2

∆TNMO ≈

x 2T0V12

But for that we need velocity…


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Stacking velocity In order to stack the waveforms we need to know the velocity. We find the velocity by trial and error:

∆TNMO =

x2 2T0V12

• 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


Multiple layer case

s tiple mul

Stacking velocity 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 Î Velocity semblance spectrum Î Pick stacking velocities


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Stacking velocity

Note: the sensitivity to velocity decreases with depth

Multiple layer case Stacking velocity panels: constant velocity gathers


Multiple layers zi

Interval velocity

Vi =

Average velocity

V '= Z

Root-meansquare velocity

ti

T0

∑V t ∑t 2

VRMS =

i

i

i

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

tn =

The interval velocity of layer n determined from the rms velocities and the two-way traveltimes to the nth and n-1th reflectors

Vint =

x2 + 4z 2 VRMS

(V

) t − (V 2

RMS , n

n

)t 2

RMS , n −1

n −1

t n − t n −1 Dix equation

The interval velocity can be determined from the rms velocities layer by layer starting at the top Applied Geophysics – Seismic reflection II

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

Deep: Two layer model: α1 = 6 km/s, z = 20 km 2 2 2 1 Equation of the 400 + x t= z2 + x = 4 3 4 α1 reflection hyperbolae:

Normal move out correction:

∆t NMO =

x2 2α t

2 1 0

=

x2 480

For a 5 km offset:

t=

2 1 25 + x 4 1.5

∆t NMO =

x2 60

For a 5 km offset:

α1 = 6.0 km/s then 0.052 sec – correct value

α1 = 3.0 km/s then 0.417 sec

α1 = 5.5 km/s then 0.062 sec

α1 = 2.5 km/s then 0.600 sec

α1 = 6.5 km/s then 0.044 sec

α1 = 3.5 km/s then 0.306 sec

Are these significant differences? What can we do to improve velocity resolution?


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 m Therefore 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? Applied Geophysics – Seismic reflection II

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Fresnel Zone Tells 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: 2

λ   w 2 d +  = d +   4  2 w2 = 2dλ +

2

λ2 4

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 Applied Geophysics – Seismic reflection II

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