Seismogram Relation between seismic trace and

geology Wavelets Multiples Resolution

Vertical resolution Horizontal resolution

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

P PP PcP S SS Rayleigh

Unfiltered:

Filtered:

Time (s)

Amplitude

From geology to seismogram

Wavelength Period Phase

Amplitude

Velocity v f=

Period 1f---

2------==

Wavenumber k ---=

t or x

Waves

2

0 time 0 time

Zero-Phase Minimum Phase

Important wave forms

Energy is maximally front-loaded(Energy does not arrive before zero time)

Minimum phase and zero-phase waveletMinimum phase wavelet: Zero phase wavelet:

Symmetric with respect to zero time and peaks at zero time(Energy arrives also before zero time)

Minimum Phase

Zero Phase

Important waveforms

Display of Seismogram

Example of a shot

Reynolds, 1997

Multiples

Air gun record

Keary and Brooks

Bedrock

Sediment

Riverbed

Surface

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

(Emery and Myers)

30 Hz waveBig Ben (ca. 123 m)

gamma log through oil fieldat 2000 m/s

Comparison of resolution of different data sets

Rayleigh’s-criterion:

Vertical resolution depends on:

- Frequency

- Velocity

Vertical resolution

4

λ

f

vλ

Resolution of two boundaries depends on wavelength

V1

V2

V3

<<

V1

V2

V3

>>or

R12

R23

V3 V3

V1

V2

<>

V1

V2

><

or R12

R23

R12/R23= neg.

R12/R23= pos.

/4=12 ms

Horizontal resolution

w

2zλw

z

for z>>

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 largerthan 1/3 or ¼ the channel width.

Sampling theorem