Acoustic

In geophysics and well logging, acoustic refers to the propagation of compressional waves (P-waves) through rock, fluid, or materials, and to the measurement tools and techniques that use these wave properties to determine formation characteristics. A compressional wave is a mechanical wave in which particles oscillate in the same direction as the wave travels (alternately compressing and stretching the medium), analogous to sound in air. The acoustic log (also called the sonic log) is the wireline or LWD tool that measures the time for a compressional wave to travel a fixed distance through the formation, reported as interval transit time (delta-T, in microseconds per foot or microseconds per metre). This transit time is inversely proportional to the compressional wave velocity and is related to porosity through the Wyllie time-average equation, making the acoustic log one of the three primary porosity logs (alongside the density and neutron logs) used in formation evaluation. The acoustic principle also underpins seismic reflection surveys, where compressional waves generated at surface reflect from subsurface rock boundaries and are recorded at surface receivers, forming the foundation of petroleum exploration.

Key Takeaways

Compressional wave velocity in rock depends on the elastic properties and density of the rock and pore fluid. The acoustic velocity (Vp) equals the square root of the elastic bulk modulus (K) plus four-thirds of the shear modulus (G), divided by the density (rho): Vp = sqrt((K + 4G/3) / rho). Rocks with higher elastic stiffness and lower density have higher Vp; lighter, more compressible materials have lower Vp. In the WCSB, typical Vp values are: Devonian dolomite 5,500 to 7,000 m/s; limestone 5,000 to 6,500 m/s; sandstone 3,500 to 5,500 m/s; shale 2,000 to 4,000 m/s; anhydrite 6,000 to 7,000 m/s. The corresponding interval transit times (the reciprocal of velocity, in microseconds per foot) are: dolomite 44 to 55 us/ft; limestone 47 to 60 us/ft; sandstone 55 to 85 us/ft; shale 75 to 150 us/ft. These velocity differences create the impedance contrasts that reflect seismic waves at formation boundaries and produce the reflections visible on seismic sections.
The Wyllie time-average equation is the primary petrophysical relationship used to derive porosity from the acoustic log: 1/Vp = porosity/V_fluid + (1-porosity)/V_matrix, rearranged to: porosity = (delta_T_log - delta_T_matrix) / (delta_T_fluid - delta_T_matrix). The matrix transit time depends on the mineral: 47.6 us/ft for calcite, 43.5 us/ft for dolomite, 55.5 us/ft for quartz, 50 us/ft for anhydrite. Fluid transit time is 189 us/ft for fresh water. The Wyllie equation works well in clean, consolidated formations but overestimates porosity in unconsolidated sands (which have lower matrix velocity due to loose grain contacts) and in formations with vugs or fractures (where wave energy can travel around the voids rather than through the rock). Compaction correction factors are applied in unconsolidated sands.
The full-waveform sonic log (FWS, also called the array sonic or digital sonic log) records not just the first arrival compressional wave but the entire acoustic waveform at multiple receiver spacings. Processing the full waveform extracts: compressional wave (P-wave) velocity; shear wave (S-wave) velocity (from the S-wave arrival later in the waveform); Stoneley wave velocity (a surface wave traveling along the borehole wall, sensitive to formation permeability and fluid properties); and borehole flexural modes (used to derive shear wave velocity in soft formations where direct S-wave arrival is not separable from the P-wave). The P-wave and S-wave velocities together determine the Poisson's ratio (sigma = (Vp/Vs)² - 2) / (2 × ((Vp/Vs)² - 1)), a key mechanical property for hydraulic fracture design (high Poisson's ratio rock is harder to fracture and tends to create less complex fracture networks).
Acoustic cement bond logging evaluates the quality of the cement bond between the casing and the formation, which is critical for wellbore integrity and zone isolation. The cement bond log (CBL) uses an acoustic tool to measure the amplitude of the acoustic signal arriving at the receiver: good cement transmits energy from the casing to the formation and back, damping the casing ring; poor cement leaves the casing free to ring at full amplitude. A variable density log (VDL) displays the full waveform in a color-coded format that shows whether energy arrived at the formation (indicating a good bond) or stayed in the casing (indicating a poor bond or free pipe). These cement bond logs are run after cementing primary casing strings to verify that the cement job achieved adequate zone isolation before the well is perforated and completed.
Acoustic LWD (logging while drilling) tools use the same measurement principle as wireline sonic tools but operate in the drill collar behind the bit, transmitting data to surface by mud pulse telemetry in real time. LWD acoustic data is used for pore pressure prediction (real-time Vp monitoring can detect changes in acoustic velocity associated with overpressured zones before they cause a kick), for real-time geosteering (acoustic velocities help correlate the current drilling position to the offset well depth prediction based on sonic log correlation), and for geomechanical applications (Vp and Vs from LWD are used to calculate mechanical properties for real-time casing design updates if unexpected formation conditions are encountered). In BC Montney horizontal wells, LWD acoustic data provides a continuous velocity profile along the lateral for post-well completion design.

How the Acoustic Log Measures Formation Velocity

The acoustic tool transmits a pulse of high-frequency sound (10 to 25 kHz, in the ultrasonic range for cement bond logging, or 5 to 15 kHz for formation evaluation) from a transmitter in the tool body. The sound travels outward from the transmitter, refracts along the borehole wall through the high-velocity formation, and is detected by one or more receivers positioned 0.3 to 0.9 metres above the transmitter in the tool string. The first arrival at each receiver is the refracted P-wave traveling through the fastest (highest velocity) formation in the acoustic path.

The tool measures the slowness (interval transit time, delta-T) by timing the difference in arrival time between two receivers at known spacing. Using two receivers (or more) and computing the difference in arrival times eliminates the borehole fluid travel time that would contaminate a single receiver measurement. The result is delta-T in microseconds per foot or microseconds per metre, which is the reciprocal of formation velocity at that depth.

Cycle skipping is a common quality problem in acoustic logging. If the first P-wave arrival is too weak to trigger the detection threshold (due to a fast borehole wall, gas in the formation reducing acoustic velocity, or a washed-out borehole section), the tool triggers on a later cycle of the waveform, giving an erroneously slow transit time. Cycle skipping appears on the log as abrupt jumps to slower (higher) delta-T values that do not match the surrounding log character. Quality-controlled logs include a review for cycle skipping and either correction by the logging engineer or flagging of the affected intervals as unreliable.

Fast Facts

The acoustic log was developed in the early 1950s by Humble Oil (now ExxonMobil) and Magnolia Petroleum (now part of Exxon) researchers including G.R. Pickett, whose work established the log-lithology relationships still used today. The first commercial continuous velocity log was run by Schlumberger in 1952. The Wyllie time-average equation, introduced by Wyllie, Gregory, and Gardner in 1956, gave petrophysicists a practical porosity transform from acoustic transit time that proved reliable in clean consolidated formations and remains the standard transform used daily in formation evaluation around the world. Array sonic technology with full waveform recording was introduced commercially in the 1980s, enabling extraction of P-wave and S-wave velocities from a single pass of the logging tool. In Alberta and BC, acoustic (sonic) logging is run on virtually every exploration and evaluation well drilled into Devonian carbonate and Cretaceous clastic targets, making it one of the most frequently acquired logs in the WCSB, second only to the gamma ray in terms of universality of application.

Acoustic Impedance and Seismic Reflection

The acoustic impedance of a rock layer (Z = density × Vp) determines how strongly seismic energy is reflected at the boundary between two different rock types. The reflection coefficient at a boundary is R = (Z₂ - Z₁) / (Z₂ + Z₁), where Z₁ and Z₂ are the acoustic impedances of the layers above and below the boundary. A high impedance contrast (large difference in density × velocity between the two layers) produces a strong reflection visible on the seismic section. A small impedance contrast produces a weak reflection or no detectable reflection.

This acoustic impedance relationship is the bridge between the well log (measured at the wellbore as a function of depth) and the seismic section (measured at surface as a function of two-way time). A synthetic seismogram is constructed from well log data by converting the acoustic and density logs to an impedance log, computing the reflection coefficient series, and convolving that series with a seismic wavelet (an estimate of the transmitted seismic pulse shape and bandwidth). The resulting synthetic seismogram can be overlaid on the seismic section at the well location for calibration: if the synthetic seismogram matches the observed seismic trace at the well, the depth-to-time conversion (using the acoustic velocity from the log) is accurate, and the seismic interpretation of reflectors elsewhere in the section can be tied to specific formation tops identified in the well.

Acoustic in the petroleum context often specifically means P-wave or compressional, distinguishing it from elastic (which includes both P-wave and S-wave properties) or seismic (which is commonly used for both P-wave-dominated and multi-component data). Related terms include sonic log (the wireline or LWD tool that measures acoustic interval transit time as a function of depth in the borehole; the same measurement as the acoustic log under a different name; most commonly used for porosity evaluation and synthetic seismogram construction), interval transit time (delta-T or DT, the acoustic log measurement in microseconds per foot or microseconds per metre; the reciprocal of compressional wave velocity; the primary output of the sonic log used for porosity calculation and velocity-depth conversion), acoustic impedance (the product of rock density and compressional wave velocity, in kg/m²s; controls the strength of seismic reflections at formation boundaries; the quantity computed from the acoustic and density logs to construct a synthetic seismogram), cement bond log (CBL, an acoustic tool run in cased holes to assess the quality of cement between casing and formation; uses acoustic amplitude and full waveform data to detect free pipe and poor bond zones that indicate inadequate zone isolation), and synthetic seismogram (a simulated seismic trace constructed from well log data, used to tie seismic reflections to formation tops at the well and calibrate the depth-to-time conversion for seismic interpretation).

How Acoustic Log Correlation Resolved a Depth Discrepancy Between Two Viking Wells in Saskatchewan

An operator was developing a Viking Formation oil pool in southwest Saskatchewan using a series of horizontal wells drilled from two pads 4 kilometres apart. The geological team was correlating Viking Formation markers between wells to build a structural map for the next infill well location. The gamma ray logs showed good correlation of the Viking C zone between the first pad's wells, but when the team attempted to correlate the structure to the second pad's wells, the Viking C marker appeared 8 metres deeper in the second pad's vertical pilot wells than the structural model predicted.

The discrepancy could represent either a real structural step-down of 8 metres (a fault or monocline between the pads) or a velocity error in the seismic depth conversion used to design the second pad's well locations. If real, the infill horizontal wells at the second pad would need to be adjusted 8 metres deeper in TVD. If the depth discrepancy was a seismic velocity error, the wells should be drilled to the original seismic depth prediction.