Q-Factor Calculator: Seismic Attenuation via the Spectral Ratio Method

Every seismic wave loses energy as it travels, not just from geometric spreading but from the rock itself absorbing high frequencies faster than low ones. The seismic quality factor, Q, is how geophysicists measure that intrinsic attenuation. A low Q means a rock volume is soaking up energy fast, which shows up on a seismic section as dulled, lower frequency reflections at depth. Use the calculator above to estimate Q from two amplitude readings and see how the amplitude spectrum changes with travel time.

What the Q-Factor Measures

Q is defined from the fractional energy lost per cycle of wave oscillation. A high Q rock, like a tight, well cemented carbonate, barely attenuates seismic energy and Q can run into the hundreds. A low Q rock, like an unconsolidated sand or a gas charged reservoir, can have Q below 50 and will visibly dull the seismic wavelet as it passes through. Because attenuation is frequency dependent, with higher frequencies lost faster than lower ones, Q also controls how much resolution you lose with depth.

The Spectral Ratio Method

The most common way to estimate Q from field or well data is the spectral ratio method. You compare the amplitude spectrum of the same frequency component at two different travel times, one shallower and one deeper. Assuming Q stays roughly constant over that interval, the ratio of the two amplitudes at a given frequency decays exponentially with both frequency and travel time difference:

Q = pi f (t2 – t1) / ln(A1 / A2)

Here f is frequency in Hz, t1 and t2 are the two travel times in seconds, and A1 and A2 are the amplitudes at those times for that same frequency. The calculator above also converts Q into an attenuation coefficient in dB per 100 meters, and into a loss per wavelength figure, which is often the more intuitive way to think about how much a signal fades over one full oscillation.

Typical Q Values by Rock Type

• Unconsolidated sand or gas charged sediment: Q of about 20 to 50
• Shale and typical clastic sedimentary sequences: Q of about 50 to 150
• Well cemented sandstone or limestone: Q of about 150 to 300
• Tight, low porosity carbonate or crystalline basement: Q above 300

Worked Example

The default example in the calculator uses a 40 Hz component with amplitude 1.0 at 500 ms and amplitude 0.35 at 1200 ms. Plugging into the equation gives Q around 84, which the chart shows as a visibly steeper amplitude drop off at higher frequencies for the deeper time curve compared to the shallow one. That places this interval on the lower end of the typical sedimentary rock range, a moderately attenuative section rather than a tight, well cemented rock.

Why Q Matters in Seismic Interpretation

Attenuation is not just noise to filter out. Anomalously low Q zones are sometimes used as a direct hydrocarbon indicator, since gas saturated rock tends to attenuate high frequencies more strongly than the same rock fully saturated with brine. Q also matters for processing, since inverse Q filtering is used to restore high frequency content and sharpen deep reflections that would otherwise look smeared out. Ignoring attenuation can bias amplitude versus offset analysis and make deep targets look weaker than they really are.

Related Calculator and Reference

For another look at how rock properties shape seismic response, see the Acoustic Impedance Calculator. The spectral ratio method and typical Q value ranges used here follow the summary in the SEG Wiki entry on the seismic quality factor Q.