Acoustic Log

The acoustic log is a wireline or logging-while-drilling (LWD) measurement of an acoustic property of the subsurface formation or the borehole, recorded as a function of depth. The most common acoustic log measurement is the compressional wave (P-wave) interval transit time (also called slowness or delta-T), expressed in microseconds per foot or microseconds per metre, which is the reciprocal of the compressional wave velocity through the formation. The acoustic log is frequently called the sonic log, and the two terms are used interchangeably in oilfield practice. In its basic form, the acoustic log provides formation porosity (through the Wyllie time-average equation), synthetic seismogram calibration (converting well depth to seismic two-way time), and mechanical property inputs (P-wave velocity for the elastic moduli used in geomechanical analysis). Advanced versions of the acoustic log — the full-waveform sonic log, the array sonic, the dipole shear imager (DSI) — record the complete waveform at multiple receiver spacings, enabling extraction of both compressional and shear wave velocities, Stoneley wave permeability indicators, and borehole flexural wave data for slow-formation shear velocity.

Key Takeaways

The borehole compensated sonic (BHC) tool design, standard from the 1960s onward, uses two transmitters and two receivers in a four-element array that cancels the effect of borehole rugosity (irregular borehole diameter) and tool tilt on the transit time reading. In an uncompensated single-transmitter, single-receiver design, tilting the tool or crossing a borehole enlargement would change the path length between transmitter and receiver, introducing an apparent transit time change unrelated to the formation velocity. The BHC design computes the average of two measurements made in opposite directions along the borehole, which cancels the geometric error. Modern array sonic tools (eight or more receivers) use moveout analysis across the receiver array to pick the formation slowness, providing even better borehole compensation and the ability to identify and separate different wave modes (P-wave, S-wave, Stoneley) arriving at different times after the transmitter firing.
The dipole shear sonic (DSI or similar trade names) generates shear wave information in slow formations where the shear velocity is less than the mud velocity. In a fast formation (shear velocity greater than mud velocity), the refracted shear wave arrives at the receiver before the direct borehole fluid wave and can be measured directly. In a slow formation (Vs less than Vmud, common in unconsolidated sands and gas-saturated zones), there is no refracted shear wave because Snell's law requires that the refracted wave travels faster than the incident wave. The dipole source generates a flexural wave (a bending oscillation of the borehole wall) that propagates at the formation shear velocity even in slow formations; processing the flexural wave arrival gives the shear slowness needed for calculating Poisson's ratio and completing the elastic property set. In Montney and Duvernay tight formation evaluation, dipole shear data is critical for calibrating hydraulic fracture models because Poisson's ratio controls fracture width and net pressure response.
Cycle skipping is the primary quality problem in acoustic logging. When the first P-wave arrival is too weak (due to gas, fractures, or poor borehole contact) to trigger the detection threshold, the tool detects a later cycle of the waveform and records a transit time that is one or more full cycles slower than the true value. On the log, cycle skipping appears as abrupt jumps to anomalously slow (high DT) values that look like a notch or spike on the DT curve. Cycle skipping in gas-bearing zones can cause the acoustic log to show extremely slow transit times (greater than 200 us/ft in extreme cases) that would indicate very high porosity if taken at face value. Quality control of the acoustic log requires comparing it to the density-neutron crossplot porosity to identify intervals where the sonic porosity is anomalously high relative to other indicators, flagging those intervals as cycle-skip-affected and either correcting them by visual splicing or excluding them from the porosity interpretation.
The acoustic log plays a central role in geological correlation between wells. Because acoustic velocity varies systematically with lithology (carbonates are fast, shales are slow, sandstones are intermediate), the acoustic log provides a distinctive fingerprint of the stratigraphic sequence that can be matched from well to well even when the gamma ray log (the other primary correlation tool) shows ambiguity between clean shales and radioactive sands. In the Cretaceous clastic sequences of Alberta and Saskatchewan, where Viking, Cardium, and Mannville sandstones alternate with silty and shaly intervals, the acoustic log often provides sharper contrast between formation units than the gamma ray, improving correlation confidence in areas where the log spacing is large or where the wells are structurally complex.
Cement bond logging is a specialized acoustic log that uses high-frequency (20 to 35 kHz) acoustic energy to evaluate the quality of the cement annulus between the production casing and the formation. The cement bond log (CBL) measures the amplitude of the acoustic signal at a receiver 1 metre above the transmitter: good cement (fully bonded to both casing and formation) strongly attenuates the casing resonance (the "ring") because acoustic energy is efficiently coupled from the casing into the cement and formation. Poor cement (a microannulus, channelling, or no cement at all) leaves the casing free to ring at its full amplitude. The variable density log (VDL) displays the full waveform across the perforated interval at a larger receiver spacing (typically 5 feet), showing both the casing resonance and the formation arrivals, providing a complete picture of the cement bond quality and the acoustic coupling between the wellbore and the formation.

Deriving Porosity From the Acoustic Log

The Wyllie time-average equation converts acoustic transit time to porosity: porosity = (DT_log - DT_matrix) / (DT_fluid - DT_matrix). The matrix transit time (DT_matrix) depends on the dominant mineral: 47.5 us/ft for calcite, 43.5 us/ft for dolomite, 55.5 us/ft for quartz (sandstone). The fluid transit time (DT_fluid) is 189 us/ft for fresh water, slightly higher for gas (because gas has high compressibility and very slow acoustic velocity). These values are plugged into the formula at each depth level to produce a continuous porosity curve.

The Raymer-Hunt-Gardner equation is an alternative to Wyllie that performs better in unconsolidated formations and gives a more accurate result in the 0 to 30% porosity range: Vp = (1 - porosity)² × V_matrix + porosity × V_fluid. This equation does not require a compaction correction factor, which the Wyllie equation needs for shallow unconsolidated formations where the matrix transit time is effectively higher than the pure mineral value due to loose grain contacts. In practice, the Wyllie equation with a compaction correction of 0.85 to 0.90 is still widely used in WCSB evaluations because of its historical familiarity, with the Raymer-Hunt-Gardner equation applied in unconsolidated Cretaceous sands and shallow Viking plays.

Gas effect on the acoustic log is weaker than on the density and neutron logs. Gas reduces the transit time (increases apparent porosity) modestly because the bulk modulus of gas is much lower than water, but the effect saturates quickly at low gas saturations (10 to 20% gas saturation has nearly the same effect as 100% gas saturation on the P-wave velocity). This gas insensitivity of the acoustic log makes it useful as a "crosscheck" porosity tool: when the density-neutron crossplot shows a large gas effect (neutron-density separation in the gas direction), the acoustic porosity provides a gas-free porosity estimate that helps quantify how much of the neutron-density separation is gas and how much is true formation porosity.

Fast Facts

The first commercial continuous-recording sonic log was introduced by Schlumberger in 1952, following theoretical and experimental work by G.R. Pickett and colleagues at Humble Oil who published the fundamental relationships between acoustic velocity and rock properties in the 1950s. The borehole compensated sonic (BHC) tool was introduced in the 1960s, dramatically improving the reliability of the transit time measurement by eliminating borehole size and tool tilt effects. Long-spacing sonic tools (with transmitter-receiver spacings of 3 to 5 feet rather than 1 to 2 feet) were developed in the 1970s to investigate the formation beyond the altered zone around the borehole. The dipole shear sonic (Schlumberger's DSI, Baker Hughes' MRIL, Halliburton's XMAC) was commercialized in the 1980s and 1990s to provide shear velocity in slow formations. Array processing of multi-receiver waveform data became standard in the 2000s. In Alberta, the acoustic log is run on virtually every exploration and appraisal well drilled into carbonate or clastic reservoirs, making it one of the most commonly acquired logs in the province after the gamma ray.

The Acoustic Log in Geomechanical Applications

Compressional and shear velocities from the acoustic log, combined with the bulk density from the density log, provide the dynamic elastic moduli of the formation: Young's modulus (E = rho × Vs² × (3Vp² - 4Vs²) / (Vp² - Vs²)), Poisson's ratio (nu = (Vp² - 2Vs²) / (2Vp² - 2Vs²)), and shear modulus (G = rho × Vs²). These dynamic moduli are used in geomechanical models for hydraulic fracture design, wellbore stability analysis, and reservoir compaction assessment.

Dynamic moduli from the acoustic log typically overestimate the static moduli measured in laboratory triaxial tests (which are the values that actually control in-situ deformation) because the acoustic measurement samples the formation at seismic frequency and very small strain, while reservoir deformation and fracturing involve larger strains and slower processes. Empirical correlations convert dynamic to static moduli, with typical ratios (static/dynamic Young's modulus) ranging from 0.3 to 0.8 depending on formation type. In tight carbonate formations like the Montney dolomite, dynamic-to-static conversions calibrated to triaxial test data from Montney core samples are essential inputs to the fracture pressure and net pressure models used for completion design.

The acoustic log is also called the sonic log, interval transit time log, DT log, or velocity log. Related terms include interval transit time (DT or delta-T, the measured quantity of the acoustic log in microseconds per foot or microseconds per metre; the reciprocal of the compressional wave velocity through the formation), full-waveform sonic (a variant of the acoustic log that records the complete pressure waveform at multiple receiver spacings rather than just the first-arrival time; enables extraction of P-wave slowness, S-wave slowness, Stoneley wave, and borehole flexural mode information), synthetic seismogram (a simulated seismic trace constructed from acoustic log transit time and density log data; used to tie seismic reflections to formation tops at the well and calibrate the seismic depth-to-time conversion), cycle skip (a quality problem in acoustic logging where the tool detects a later wave cycle instead of the first arrival, recording an anomalously slow transit time; appears as a spike or notch on the DT curve and must be corrected before the log is used for porosity or synthetic seismogram construction), and dipole shear sonic (a tool that generates a flexural wave mode using a dipole (push-pull) source to measure shear wave velocity in slow formations where the direct refracted shear wave is not detected; essential for Poisson's ratio calculation and geomechanical modelling in soft or gas-saturated formations).

How an Acoustic Log Caught a Density Log Washout Error in a Devonian Carbonate Well

A log analyst was evaluating a Devonian Nisku Formation carbonate well in the Pembina area. The density log showed an anomalously low bulk density of 1.95 g/cc over a 4-metre interval at the top of the Nisku, which, when used in the density-neutron porosity crossplot, indicated porosities of 28 to 32% in that interval. The gamma ray was very clean (below 20 API units), suggesting this was clean carbonate and not a shale washout. The analyst was about to flag this interval as high-porosity carbonate reef vug development, which would be an important discovery for this well.

Before finalizing the interpretation, the analyst compared the acoustic log transit time over the same interval. If the density of 1.95 g/cc represented true vuggy porosity in dolomite, the expected sonic transit time should be approximately 65 to 75 us/ft (corresponding to 28 to 32% porosity in dolomite using the Wyllie equation). The actual sonic transit time over the interval was 52 us/ft, corresponding to only 12% porosity in dolomite. There was a large discrepancy between the density porosity (28 to 32%) and the acoustic porosity (12%).