Attenuation: Definition, Seismic Q Factor, and Formation Permeability Indicator

Key Takeaways

• Geometrical spreading (1/r) versus intrinsic absorption: two independent attenuation mechanisms: Geometrical spreading is the amplitude decay that occurs because a seismic wavefront expands outward, distributing constant total energy over an increasing surface area. For a spherical wavefront, energy per unit area falls as 1/r squared, so amplitude falls as 1/r. This decay is entirely predictable from geometry, requires no rock physics model, and is corrected in all seismic processing workflows by applying a divergence correction (gain proportional to t or t squared, depending on velocity gradient) before any amplitude-sensitive analysis. Intrinsic absorption is a material property that varies by lithology, fluid type, effective stress, and temperature. It is not corrected by a divergence correction and must be addressed separately through inverse Q filtering if bandwidth recovery is desired. The distinction matters enormously for amplitude interpretation: a geophysicist who applies only a divergence correction has not corrected for intrinsic absorption, and deep reflections from gas-charged sands may appear to have lower amplitude than shallower brine-saturated equivalents purely because higher absorption has reduced the wavelet peak amplitude at depth, potentially causing false-negative DHI classification if the amplitude interpretation is not Q-compensated.
• Q factor definition, typical rock values, and gas saturation as a DHI: The seismic quality factor Q is defined formally as Q = 2 pi times E divided by delta E, where E is the peak elastic strain energy per unit volume and delta E is energy dissipated per cycle of oscillation. Equivalently, the amplitude at time t due to intrinsic absorption is A = A0 times e to the power of (negative pi times f times t divided by Q), where f is frequency in Hz. This equation shows that high-frequency components are attenuated faster than low-frequency components by a factor directly proportional to f, which is why dominant seismic frequency decreases systematically with depth. Typical Q values: dry consolidated sandstone 80 to 150; brine-saturated sandstone 30 to 80; gas-saturated sandstone 5 to 20; heavy oil or tar sand 5 to 15; marine unconsolidated sediment 10 to 50; massive limestone 60 to 200. The gas-saturation effect is the physical basis for Q as a DHI: the compressibility contrast between gas and brine in the pore space drives vigorous squirt flow during wave-induced pressure oscillation, dissipating energy viscously. Even partial gas saturation of 5 to 10 percent pore space can reduce Q from 60 to 80 (fully brine-saturated) to 20 to 40, a readily detectable change using spectral decomposition or Q tomography on high-quality seismic data.
• Stoneley wave attenuation on array sonic logs: permeability indicator and fracture detection: Stoneley waves are guided borehole waves propagating at approximately 0.9 times the shear wave velocity along the borehole-formation interface, driven by borehole fluid pressure oscillations against the formation wall. When a Stoneley wave encounters a permeable formation interval, borehole fluid is alternately forced into and extracted from the pore space in synchrony with the wave's pressure cycle, dissipating energy viscously and attenuating the Stoneley arrival recorded at the array sonic receivers above the permeable zone. The attenuation coefficient of the Stoneley wave can be inverted using the Biot-Rosenbaum model to estimate formation permeability, providing a continuous log-scale permeability indicator not obtained from conventional neutron-density or resistivity suites. Open natural fractures produce sharp, discrete Stoneley attenuation events that differ from gradual permeable-zone attenuation in being spatially concentrated over approximately one wavelength (1 to 3 metres) above and below the fracture depth; the ratio of transmitted to incident Stoneley amplitude at the fracture gives a transmission coefficient directly related to fracture hydraulic aperture. Combined with fracture orientation from FMI image logs and in-situ stress orientation from wellbore breakout analysis on caliper logs, Stoneley attenuation provides a quantitative estimate of fracture hydraulic conductivity that is critical for hydraulic fracture stimulation design in naturally fractured carbonates and tight clastic reservoirs in the Duvernay, Montney, Nisku, and Leduc formations of the WCSB.
• Inverse Q filtering: restoring bandwidth lost to absorption for deep thin-bed resolution: Inverse Q filtering (also called Q compensation or absorption compensation) applies a time-variant, frequency-dependent gain to seismic traces that is the inverse of the forward intrinsic absorption operator, partially restoring high-frequency content lost during propagation and improving vertical resolution at depth. The gain function amplifies higher frequencies relative to lower frequencies in proportion to their estimated absorption loss along the propagation path through the estimated Q model. Q models for the inversion are built from VSP spectral ratio analysis (the most direct method, comparing downgoing wave amplitude spectra at successive depth levels in a borehole), from array sonic Q measurements, or from surface seismic Q tomography. Because any inverse filter also amplifies noise at high frequencies where signal-to-noise ratio is lowest, stabilization is applied as a water-level or frequency-dependent gain cap to prevent noise amplification beyond the recoverable bandwidth. In practice, Q compensation improves the dominant frequency of deep events by 15 to 30 Hz, sharpening reflections and enabling identification of thin-bed packages in the 10 to 30 metre range that fall below the tuning thickness (approximately one-quarter wavelength) on non-compensated data. For Duvernay and Montney shale reservoirs in Alberta and British Columbia, where productive intervals may be as thin as 8 to 20 metres, Q compensation is frequently the processing step that determines whether individual benches can be resolved for targeted perforation and stimulation planning.
• LWD electromagnetic wave attenuation for real-time formation resistivity measurement: In logging while drilling (LWD) operations, propagation resistivity tools measure the attenuation of electromagnetic (EM) waves between a transmitter and two receivers spaced along the drill collar to determine formation resistivity in real time, near the bit, during drilling. The EM wave attenuates as it propagates radially outward from the transmitter into the formation at rates controlled by the formation's electrical conductivity (the reciprocal of resistivity): high-resistivity hydrocarbon-bearing formations attenuate the EM wave slowly (large amplitude ratio between receivers), while conductive brine-saturated or clay-rich formations cause rapid attenuation (small amplitude ratio). By recording both the phase shift (related to the real part of the complex wave number) and the attenuation (related to the imaginary part) between the two receivers, the LWD tool independently determines formation resistivity from two different depths of investigation in real time. This dual-measurement approach mirrors the split between phase-based and attenuation-based resistivity readings on array propagation resistivity tools deployed at 400 kHz to 2 MHz, and enables invasion correction and formation resistivity determination without requiring a full invasion model. LWD attenuation resistivity logs are used for real-time geosteering decisions in horizontal Montney, Cardium, and Viking wells in the WCSB, enabling the driller to stay within the target reservoir by monitoring real-time attenuation contrast between reservoir and bounding shales as the bit advances.