Acoustic Impedance

Acoustic impedance (Z) is the product of a rock's bulk density (rho) and the compressional wave velocity (Vp) through that rock: Z = rho × Vp. It is expressed in units of kg/(m²s), sometimes written as rayl (SI unit) or more commonly in oilfield usage as (g/cc) × (m/s) or (g/cc) × (ft/s). Acoustic impedance is the fundamental physical property that controls how seismic energy behaves at the boundary between two rock layers: when a seismic wave encounters a boundary between materials with different acoustic impedances, some energy is reflected back toward the surface and some is transmitted onward into the lower layer. The proportion of energy reflected is determined by the reflection coefficient (R), which depends on the impedance contrast between the layers. High impedance contrasts produce strong seismic reflections; low contrasts produce weak or invisible reflections. This relationship makes acoustic impedance the bridge between well log measurements (where density and velocity are measured as a function of depth) and seismic data (where the reflected energy is measured as a function of two-way travel time at surface receivers).

Key Takeaways

The normal-incidence reflection coefficient between two layers is R = (Z₂ - Z₁) / (Z₂ + Z₁), where Z₁ is the impedance of the upper layer and Z₂ is the impedance of the lower layer. A positive R means the lower layer has higher impedance (denser or faster, or both); the reflected wave has the same polarity as the incident wave. A negative R means the lower layer has lower impedance; the reflected wave has reversed polarity. The transmission coefficient is T = 2Z₁ / (Z₂ + Z₁), the fraction of energy transmitted into the lower layer. In the SEG (Society of Exploration Geophysicists) polarity convention, a positive reflection coefficient (impedance increase downward) is displayed as a black peak on a seismic trace with standard display settings. The AVO (amplitude versus offset) behavior of reflections at non-normal incidence depends on both P-wave and S-wave impedances and is analyzed using the Zoeppritz equations or their linearized approximations.
Typical acoustic impedance values for common formation types guide the seismic interpreter in understanding which reflections to expect. Water: Z ≈ 1.5×10⁶ kg/m²s (density 1.0 g/cc, Vp 1,500 m/s). Unconsolidated sand: Z ≈ 3 to 5×10⁶ kg/m²s. Consolidated sandstone: Z ≈ 5 to 10×10⁶ kg/m²s. Limestone: Z ≈ 8 to 18×10⁶ kg/m²s. Dolomite: Z ≈ 10 to 20×10⁶ kg/m²s. Anhydrite: Z ≈ 15 to 20×10⁶ kg/m²s. Salt: Z ≈ 12 to 15×10⁶ kg/m²s. The contrast between salt (Z ≈ 13×10⁶) and the surrounding carbonates (Z ≈ 15 to 18×10⁶) is moderate, producing a detectable reflection at the top of salt that marks the salt body boundary on seismic sections. The contrast between gas-saturated sandstone (Z ≈ 3 to 5×10⁶, because gas reduces both density and velocity) and overlying shale (Z ≈ 4 to 7×10⁶) can produce a negative reflection coefficient (gas sand has lower impedance than shale), which appears as a phase reversal on the seismic section and is one of the direct hydrocarbon indicators (DHI) used in exploration.
Gas saturation has a dramatic effect on acoustic impedance because gas is much less dense and more compressible than oil or water. Substituting gas for brine in a porous sandstone reduces the bulk modulus of the pore fluid (the Gassmann-Biot relationship) and reduces the bulk density. The combined effect reduces Vp by 10 to 30 percent and reduces density by 1 to 5 percent (depending on porosity), causing a significant drop in acoustic impedance. Even small gas saturations (10 to 20%) reduce Vp significantly because gas dominates the fluid compressibility. This means that seismic amplitude (which is proportional to the reflection coefficient, which depends on impedance contrast) is a strong indicator of gas saturation but is less diagnostic for distinguishing oil from brine, since the bulk modulus difference between oil and brine is much smaller than between gas and brine.
Seismic inversion converts a seismic section from a display of reflectivity (differences in impedance between adjacent layers) to a display of acoustic impedance as a function of depth or time. This conversion is valuable because impedance is a rock property that can be directly compared to well log measurements and used to distinguish rock and fluid types, whereas reflectivity only shows where impedance changes without revealing the absolute value. Seismic inversion removes the "ringing" effect of the seismic wavelet (which spreads energy from a single interface over several wavelengths) and attempts to recover the true impedance profile of the formation. The inversion requires a low-frequency model (the impedance trend below the resolution of the seismic data, typically from well log data) and a wavelet estimate. Poorly constrained inversions produce non-unique solutions that can be misleading; well-constrained inversions calibrated to multiple wells can reliably distinguish sandstone from shale and, in favourable circumstances, oil from gas-saturated zones.
In carbonate formations of the WCSB, acoustic impedance contrasts guide the identification of reef buildups and their associated porosity development. A Devonian Leduc reef has lower acoustic impedance than the surrounding tight Ireton shale (lower velocity and density in the porous reef rock than in the tight basinal carbonate), but higher impedance than the overlying porous inter-reef carbonates in some cases. The internal acoustic impedance variations within a reef (between porous zones, tight zones, and fluid contacts) are what create the reflections visible on seismic sections shot across reef trends. Mapping the acoustic impedance distribution within a reef using seismic inversion calibrated to wells provides a predictive porosity map that guides infill drilling and waterflood monitoring.

Computing Acoustic Impedance From Well Logs

Acoustic impedance as a function of depth is computed by multiplying the density log (in g/cc) by the velocity (in m/s, converted from the sonic log transit time by V = 1,000,000/DT where DT is in us/m). The resulting Z log (in g/cc × m/s, or g/cm²s) represents the acoustic impedance profile of the formation at the well location. This Z log is the basis for two important products: the synthetic seismogram (which simulates what the seismic section should look like at the well location) and the seismic inversion constraint (the low-frequency model that anchors the inversion result to well data).

The Z log from a single well is an accurate measurement only at the borehole. Away from the well, the impedance must be predicted from seismic data through inversion. The reliability of the inversion decreases with distance from the well control, as the seismic wavelet may change laterally (due to acquisition and processing effects), the low-frequency model may not capture structural variations, and the acoustic impedance contrasts of interest may fall below the seismic resolution limit of 10 to 20 metres at typical exploration depths.

In the Cardium Formation of west-central Alberta, acoustic impedance computed from well logs shows a clear relationship between oil saturation and impedance: oil-saturated Cardium sandstones have lower impedance than brine-saturated Cardium sandstones (approximately 6.5 versus 8.5 × 10⁶ kg/m²s in this formation), enabling seismic amplitude mapping to distinguish productive oil-charged sands from water-wet sands at the prospect scale. This impedance difference, while small, is detectable on properly processed and conditioned 3D seismic data and has guided infill well placement in mature Cardium fields.

Fast Facts

The concept of acoustic impedance in the context of seismic reflection was formalized in the work of Norman Ricker and others at Gulf Research and Development Company in the 1940s and 1950s, building on the wave physics established by Knott in 1899 and Zoeppritz in 1919 for the energy partitioning at seismic interfaces. The Zoeppritz equations, derived independently by several scientists around the same time, provide the complete solution for reflection and transmission coefficients at all angles of incidence and for both P-wave and S-wave modes — a system of four equations used in modern AVO analysis. Seismic inversion to extract acoustic impedance from reflection data was pioneered by Lavergne and Willm in 1977 and subsequently developed commercially by Hampson-Russell Software (now part of CGG Veritas), whose Strata and HRS-9 inversion products became widely used in Canadian exploration from the 1990s onward. Alberta seismic inversion studies in the Cardium, Viking, and Devonian carbonate play trends helped establish the technique's value in the WCSB context, where the impedance contrasts associated with oil-saturated Cretaceous sands versus brine-saturated equivalents are small but exploitable with adequate seismic quality.

Acoustic Impedance and AVO Analysis

Amplitude versus offset (AVO) analysis uses the variation of seismic reflection amplitude with the angle of incidence to extract additional rock and fluid information beyond what normal-incidence impedance alone can provide. At non-normal incidence, the reflection coefficient depends on both the acoustic impedance contrast and the shear impedance contrast (shear wave velocity × density). By measuring how the amplitude changes with offset (offset being proportional to angle of incidence), it is possible to separately estimate the P-wave impedance contrast (related to the stack or near-offset amplitude) and the S-wave impedance contrast (related to the gradient, or rate of amplitude change with offset).

The practical value of AVO analysis in hydrocarbon exploration is that gas sands, oil sands, and brine sands often have distinct AVO signatures. A Class III AVO anomaly (the most common gas sand indicator in the Gulf of Mexico and in the shallow Cretaceous of the WCSB) shows a large negative amplitude at zero offset that becomes more negative (more strongly negative) with increasing offset. This pattern is diagnostic of a gas sand with lower acoustic impedance than the overlying shale and a large negative gradient. In the WCSB, Class III AVO anomalies in the Cardium and Viking have been used to identify gas-charged sands and to distinguish them from brine-saturated sands with smaller amplitude anomalies and less negative gradients.

Acoustic impedance is also called seismic impedance or P-wave impedance (the last term distinguishing it from shear impedance, Z_s = rho × Vs). Related terms include reflection coefficient (R = (Z₂-Z₁)/(Z₂+Z₁), the fraction of seismic wave amplitude reflected at the boundary between two layers; determined by the acoustic impedance contrast and the fundamental quantity displayed on a seismic section), seismic inversion (the mathematical process of converting a seismic section from a display of reflectivity to a display of acoustic impedance; requires a low-frequency model from well logs and a wavelet estimate; produces a result that can be compared directly to rock properties), acoustic log (the wireline or LWD tool that measures interval transit time, from which compressional wave velocity is computed; combined with the density log to compute the acoustic impedance log at the well location), amplitude versus offset (AVO, analysis of how seismic reflection amplitude varies with the angle of incidence; used with acoustic and shear impedance to identify lithology and fluid saturation in exploration targets), and direct hydrocarbon indicator (DHI, a seismic attribute that is directly related to the presence of hydrocarbons in a reservoir; a phase reversal or amplitude brightening caused by a low acoustic impedance gas sand is one of the most reliable DHIs in exploration).

How Acoustic Impedance Mapping Guided the Discovery Well Placement on a Saskatchewan Bakken Pool

An exploration team was evaluating a prospect in the Bakken Formation in southwest Saskatchewan. 3D seismic data covered the prospect area and showed a broad structural high on the Bakken horizon with a bright amplitude anomaly in the centre. The team interpreted the bright amplitude as a hydrocarbon indicator but was uncertain whether it represented oil-saturated tight Bakken carbonate or simply a diagenetic change in the carbonate cementation pattern unrelated to hydrocarbons.

A seismic inversion was performed on the 3D dataset, constrained by two offset wells that had penetrated the Bakken but showed tight, non-productive carbonate with high acoustic impedance (12.4 × 10⁶ kg/m²s from the well log calculation). The inversion result showed a distinct low-impedance anomaly (8.8 to 10.2 × 10⁶ kg/m²s) coinciding exactly with the bright amplitude on the seismic section, surrounded by the higher-impedance values that matched the tight offset wells.