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 (sept 2002) 3000km Amplitude Unfiltered: Time (s) Filtered: P PP PcP S SS Rayleigh From geology to seismogram Amplitude Waves t or x Period τ == f Wavelength λ Period τ Phase 2π Wavenumber k = λ Velocity v = f⋅λ 2π -ω Important wave forms Zero-Phase time Minimum Phase 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 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  .. .Seismogram of an earthquake mid atlantic ridge measured in Brasil magnitude (sept 2002) 3000km Amplitude Unfiltered: Time (s) Filtered: P PP PcP S SS Rayleigh From geology to seismogram. .. (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