# VẬT lý địa CHẤN 08 seismogram

Seismogram

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

Wavenumber k = --λ

Velocity v

=

f⋅λ

-----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 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.

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