Seismic Trace

Key Takeaways

• The convolutional model of the seismic trace (trace = wavelet convolved with reflectivity + noise) is the mathematical foundation for seismic interpretation and processing, expressing the observation that each reflector in the Earth produces a band-limited replica of the seismic wavelet at the corresponding two-way time, with amplitude proportional to the reflection coefficient at that interface; the convolutional model is derived from the assumption that the Earth behaves as a linear, time-invariant filter (the reflectivity) applied to the source wavelet, an assumption that is valid for primary (non-multiply-reflected) reflections at moderate acoustic amplitudes and short source-to-receiver distances, but that breaks down for large-offset traces (where non-hyperbolic moveout and angle-dependent amplitude effects become significant), for near-surface heterogeneity (where the wavelet shape varies laterally in ways not captured by a single stationary wavelet model), and for highly attenuative formations (where frequency content decreases with depth due to anelastic absorption, causing the wavelet to become longer and lower-frequency at depth than near the surface, violating the stationary wavelet assumption); deconvolution is the processing step that attempts to collapse the wavelet to a spike or minimum-phase wavelet by designing an inverse filter from the autocorrelation of the trace (Wiener-Levinson algorithm), improving resolution by broadening the frequency bandwidth represented on the trace.
• Seismic trace attributes derived from the complex trace representation (Taner, Koehm, and Sheriff, 1979) have become standard tools in reservoir characterization: the instantaneous amplitude (envelope) of the complex trace, computed using the Hilbert transform to construct the quadrature trace paired with the real trace, represents the reflective strength at each time sample and is used to identify bright spots (high-amplitude anomalies related to gas sands or unusual lithologies), stratigraphic pinch-outs (amplitude fade at reservoir edges), and gas-water contacts (flat-spot events at fluid boundaries); the instantaneous frequency (the time derivative of the instantaneous phase) reveals frequency anomalies associated with gas-related attenuation (the "gas chimney" low-frequency shadow below a gas reservoir caused by preferential absorption of high frequencies by gas-saturated rock), and chaotic zones of low amplitude and variable instantaneous frequency are characteristic of mass-transport complex deposits, salt welds, and highly faulted intervals that cannot be imaged coherently; these trace-based attributes require high signal-to-noise ratio to be interpretable, because noise amplification by the instantaneous frequency calculation makes low-S/N zones appear chaotically high-frequency.
• Trace-to-trace coherence (also called similarity, continuity, or semblance) is computed from the similarity of adjacent traces in a time window, providing a structural attribute that highlights faults, fractures, and erosional channels where the reflector continuity is broken and adjacent traces are dissimilar: the variance (1 minus coherence) cube computed from a 3D seismic volume is particularly effective for fault detection because fault planes appear as linear or curvilinear low-coherence features that can be extracted as fault sticks and interpreted in three dimensions in seismic interpretation software; coherence computation requires that the seismic traces have been migrated accurately so that structurally related events are correctly positioned before the similarity calculation, and that the trace spacing (bin size) is fine enough to resolve the structural features of interest -- a fault with 10 meters of throw requires a bin size of 12.5 meters or less to appear as a discontinuity on the coherence cube rather than being averaged into the surrounding coherent reflectors.
• Synthetic seismograms (also called well ties or log-to-seismic ties) are computed by convolving the reflectivity series derived from wireline log measurements (computed as the vertical derivative of acoustic impedance, where impedance = velocity times density from the sonic and density logs) with a wavelet extracted from the seismic traces adjacent to the well, producing a synthetic trace that predicts what the seismic trace at the well location should look like given the geological column logged by the well; the quality of the synthetic-to-real trace match (measured by cross-correlation coefficient, typically 0.7 to 0.95 for a good tie) validates the depth-to-time conversion (the time-depth relationship from checkshot or VSP survey), confirms the seismic polarity convention (if the synthetic tie is poor or inverted, the processing polarity may be incorrect), and calibrates the interpretation by confirming which seismic events correspond to which geological boundaries in the well; poor synthetic ties are frequently caused by cycle-skipping in the time-depth relationship (where the sonic log has been depth-shifted by an incorrect number of cycles during the tie process), wavelet non-stationarity (where the extracted wavelet does not represent the seismic response at the well location), or borehole effects on the sonic log (cycle-skipping in the raw waveform or gas effect on the compressional velocity).
• Trace sampling and Nyquist aliasing govern the maximum frequency content that can be recorded by a digital seismic system: for a sample interval of dt milliseconds, the Nyquist frequency is 1/(2*dt) Hz, above which the digital system cannot unambiguously represent wave frequencies and aliasing artifacts fold high-frequency signal energy onto lower-frequency components; standard reflection seismic surveys use a 2 ms sample interval (Nyquist at 250 Hz), appropriate for exploration seismic with dominant frequencies of 20 to 80 Hz and effective bandwidth up to 150 Hz; high-resolution shallow surveys (engineering geophysics, shallow hazard surveys, UHR marine profiling) use 0.25 to 0.5 ms sample intervals to record frequencies of 100 to 2,000 Hz for resolving thin near-surface layers; spatial aliasing (the trace-spacing equivalent of temporal Nyquist) also limits the dip and frequency content resolvable by the trace array, with spatial aliasing occurring when the apparent dip of a reflector across adjacent traces exceeds lambda/2 (half the wavelength), causing dipping reflectors to be smeared in the wrong direction during migration unless the trace spacing is fine enough relative to the dominant wavelength.