VẬT lý địa CHẤN 08 seismogram

Seismogram
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Relation between seismic trace and geology
Wavelets
Multiples
Resolution
– Vertical resolution
– Horizontal resolution


Seismogram of an earthquake
mid atlantic ridge measured in Brasil magnitude 5 (sept 2002) 3000km
Amplitude

Unfiltered:

Time (s)

Filtered:

P

PP

PcP

S

SS

Rayleigh


From geology to seismogram


Amplitude

Waves

t or x

1
Period τ ==--f

Wavelength λ
Period τ

Phase

2π
Wavenumber k = --λ

Velocity v

=

f⋅λ

2π
-----ω


Important wave forms

Zero-Phase

0 time

Minimum Phase

0 time


Minimum phase and zero-phase wavelet
Minimum phase wavelet:

Zero phase wavelet:

Energy is maximally front-loaded
(Energy does not arrive before zero time)
Symmetric with respect to zero time
and peaks at zero time
(Energy arrives also before zero time)


Important waveforms

Minimum Phase

Zero Phase


Display of Seismogram


Example of a shot

Reynolds, 1997


Multiples


Air gun record

Keary and Brooks


Surface
Riverbed
Sediment

Bedrock

Reynolds

Resolution
Resolution refers to the minimum separation
between two features such that we can tell that
there are two features rather than only one.
• Vertical resolution
• Horizontal resolution


Comparison of resolution of different data sets

30 Hz wave
at 2000 m/s

Big Ben (ca. 123 m)

gamma log
through oil field

(Emery and Myers)


Vertical resolution
Rayleigh’s-criterion:

λ
4
Vertical resolution depends on:
- Frequency
- Velocity

v
λ=
f


Resolution of two boundaries depends on wavelength


λ/4=12 ms
V1

V1
or

>

<
V2

>

<

V2

V3

V3

R12

R23

R12/R23= pos.

V1
or

>

<
V2

V1
V2
<

>

V3
V3
R12/R23= neg.

R12
R23


Horizontal resolution

z

w = 2zλ
w

for z>>λ


Sampling theorem
At least two samples per (horizontal) apparent
wavelength must be obtained in order to recognize
Features (remember the time sampling theorem!!).
For example, to recognize a stream channel on a
horizontal slice generally requires bin sizes no larger
than 1/3 or ¼ the channel width.