Array Sonic: Definition, P-wave, S-wave, and Formation Slowness
An array sonic tool is a multi-receiver wireline or LWD logging instrument that records compressional (P-wave), shear (S-wave), and Stoneley wave acoustic modes simultaneously from an array of eight to thirteen axially spaced receiver stations, each separated by 6 to 12 inches along the tool mandrel, allowing the formation slowness (Delta-t, the reciprocal of velocity in microseconds per foot) to be extracted from the differential arrival times across the receiver array through a semblance-based velocity analysis algorithm rather than from a single transmitter-receiver travel time. Unlike legacy borehole compensated sonic (BHC) tools that use only two receivers and are susceptible to cycle-skipping in slow or poorly cemented formations, an array sonic tool simultaneously records waveforms at all receivers for each transmitter firing, processes the full waveform suite through slowness-time coherence (STC) or modified matrix pencil algorithms, and extracts P-wave, S-wave, and Stoneley slownesses with sub-microsecond precision from a single logging pass. The Schlumberger Dipole Sonic Imager (DSI), Sonic Scanner, Baker Hughes XMAC (Cross-Multipole Array Acoustic), and Halliburton ISONIC are the principal commercial platforms; all add cross-dipole transmitter sources that fire shear waves horizontally across the borehole to measure shear slowness in fast and slow formations and to detect azimuthal shear wave anisotropy from natural fractures and in-situ stress orientation. In the Western Canada Sedimentary Basin, array sonic logs are the primary input for geomechanical model construction in Montney, Duvernay, and Cardium horizontal completions, where compressional and shear slowness data drive the calculation of dynamic Young's modulus, Poisson's ratio, and minimum horizontal stress magnitude used to design perforation cluster spacing, pump schedule, and proppant volume in multistage hydraulic fracture treatments.
Key Takeaways
- Slowness-time coherence (STC) processing and the waveform array approach: When the array sonic transmitter fires a broadband acoustic pulse, the wavefront travels through the borehole and formation and arrives at each receiver in the array at a slightly different time. For a P-wave in a 3,000 m/s formation (slowness approximately 100 microseconds per foot), successive receivers spaced 6 inches apart detect the arrival 5 microseconds later per station. The STC algorithm cross-correlates the waveform recorded at each receiver against the waveform at the first receiver over a sliding time window and maps coherence as a function of both arrival time and slowness on a 2D colour grid. High coherence at a specific slowness-time combination identifies a mode (P, S, or Stoneley); the slowness at the peak of the coherence map is read as Delta-t for that mode. The STC approach is far superior to amplitude-threshold first-break picking because it works even when the P-wave first arrival is very weak (as in slow, high-attenuation formations like gas-saturated sands or coal layers) and because it separates overlapping modes that arrive within the same time window. Schlumberger's Sonic Scanner enhances the STC framework with "slowness-frequency analysis" (SFA) that separates dispersive Stoneley and flexural modes at different frequency bands, enabling simultaneous determination of formation slowness, borehole fluid slowness, and borehole diameter effects from a single waveform set.
- Compressional and shear slowness for mechanical property calculation: The two most important slowness outputs for geomechanical applications are Delta-tcompressional (DTC) and Delta-tshear (DTS). From these, dynamic elastic moduli are computed as: dynamic Young's modulus Edyn = rho x Vs2 x (3Vp2 - 4Vs2) / (Vp2 - Vs2), where Vp = 1,000,000/DTC (ft/s, when DTC is in us/ft) and Vs = 1,000,000/DTS, and dynamic Poisson's ratio nudyn = (0.5 x (DTS/DTC)2 - 1) / ((DTS/DTC)2 - 1). These dynamic values are then empirically corrected to static values (the relevant parameter for fracture closure stress calculations) using field-calibrated correlations that typically reduce Edyn by 20 to 50 per cent for static Young's modulus. In the Montney Formation at Dawson Creek and Groundbirch, DTC typically ranges from 58 to 72 microseconds per foot in the siltstone pay facies and DTS ranges from 90 to 115 microseconds per foot, yielding dynamic Young's moduli of 45 to 65 GPa and Poisson's ratios of 0.22 to 0.28. Brittle intervals with high Young's modulus and low Poisson's ratio are the preferred perforation cluster targets for multistage hydraulic fracture initiation.
- Cross-dipole shear and azimuthal anisotropy from natural fractures and stress: Standard monopole acoustic sources excite P-wave and Stoneley modes strongly but cannot generate pure shear arrivals in slow formations (where Vs is less than the borehole fluid velocity of approximately 1,500 m/s) because no refracted shear head wave exists under those conditions. Cross-dipole sources — a pair of orthogonal dipole transmitters oriented 90 degrees apart — fire flexural shear waves that propagate through the formation as bending waves and can be detected at cross-dipole receiver pairs to extract shear slowness in both slow and fast formations. When the formation has azimuthal shear anisotropy due to aligned natural fractures, horizontal stress anisotropy, or TIV lamination, the flexural wave in the fast shear direction (aligned with maximum horizontal stress or fracture strike) travels faster than in the slow shear direction (perpendicular to fractures), and the difference in DTSfast and DTSslow — expressed as the shear anisotropy ratio (DTSslow - DTSfast) / DTSfast — is a direct measure of the anisotropy magnitude. In the Duvernay shale at Kaybob South, shear anisotropy values of 8 to 18 per cent are routinely observed, with the fast shear azimuth oriented approximately N65E consistent with the regional maximum horizontal stress direction. This information is used to orient perforation clusters parallel to expected hydraulic fracture planes and to select the optimal frac azimuth for transverse fracture development.
- Stoneley wave slowness for permeability estimation and fracture identification: The Stoneley wave (also called the tube wave) is an interface wave that propagates along the borehole wall at a velocity slightly slower than the borehole fluid velocity. Its slowness and attenuation are sensitive to the formation permeability at the borehole wall: in permeable zones, formation fluid is driven in and out of the pore space by the oscillating Stoneley wave pressure, dissipating wave energy and slowing the wave. Schlumberger's Biot-Rosenbaum model predicts Stoneley attenuation as a function of permeability, porosity, fluid viscosity, and Stoneley frequency, and the inverted permeability from Stoneley wave measurements in homogeneous, non-fractured formations typically agrees within a factor of 2 to 3 with core permeability measurements — a useful formation permeability indicator where core is not available. In naturally fractured formations, individual fractures cause a partial Stoneley wave reflection at the fracture-borehole intersection, creating coherent down-going and up-going Stoneley events visible on the processed waveform array that can be mapped to specific depth intervals as fracture indicators. This technique, called Stoneley wave reflection analysis, identified 14 open natural fractures in a Devonian Leduc reef well in the Bonnie Glen field that were invisible on the compensated neutron-density log but produced 38 m3/day oil on test without stimulation.
- Cement bond evaluation and Stoneley wave amplitude in cased-hole applications: The array sonic tool is run as an open-hole formation evaluation instrument but can also be deployed in cased-hole mode for cement bond evaluation after casing is set. In this mode, the tool's monopole source excites a casing extensional wave that propagates along the casing wall; the amplitude of the first-arriving casing wave is attenuated by good cement bond (which couples energy from the casing into the formation and prevents a free-pipe resonance condition) and is large (low attenuation) in unbonded or gas-channelled cement. The array sonic in cased-hole mode provides a more detailed cement assessment than the conventional cement bond log (CBL) because the multiple receiver array resolves the axial bonding condition at 6-inch resolution rather than the CBL's 2-foot gate, and because the full waveform display allows the interpreter to identify micro-annulus, partial bonding, and gas migration channels from the character of the casing mode and the delayed formation arrivals. In WCSB Cardium completions where zonal isolation between the Cardium sand and the overlying shale is critical for regulatory compliance with AER Directive 083 wellbore integrity requirements, cased-hole array sonic cement evaluation is frequently required before hydraulic fracture stimulation is authorised.
Acoustic Modes in Open-Hole Array Sonic Logging
An open-hole array sonic tool excites three principal acoustic modes that are each sensitive to different formation properties. The P-wave (compressional) head wave travels along the borehole wall at the formation compressional velocity Vp after being critically refracted at the borehole wall interface; it is the fastest-arriving, highest-frequency energy on the waveform and is detected on the raw waveform train as a low-amplitude, high-frequency first arrival. The S-wave (shear) head wave propagates at formation shear velocity Vs and arrives at the receivers after the P-wave; it has lower frequency content (typically 1 to 8 kHz vs 10 to 20 kHz for P) and is identifiable on the waveform as a second coherent arrival after the P-wave. The Stoneley (tube) wave is the last major arrival and has the highest amplitude and lowest frequency (typically 0.5 to 3 kHz) of the three modes; it is an interface wave propagating at approximately 90 per cent of the borehole fluid velocity and can be identified on the waveform array by its characteristic pattern of large amplitude, low frequency, and slowness slightly above the mud slowness. In slow formations where Vs is less than Vfluid (approximately 200 microseconds per foot vs 185 microseconds per foot for water), no S-wave head wave exists and the monopole array captures only P-wave and Stoneley arrivals; shear slowness in slow formations requires the cross-dipole flexural wave measurement.
The transmitter-to-receiver array geometry varies among tool platforms but typically spans 8 to 13 feet from the nearest to farthest receiver. Schlumberger's Sonic Scanner uses a 2.5-foot lower monopole source, a 12-foot lower dipole source, a 2.5-foot upper monopole source, and 13 receiver stations spanning 8 feet from 9 to 17 feet from the lower transmitter face — a geometry that provides 8 independent slowness samples per depth increment for monopole processing and 13 samples for dipole processing. The large receiver aperture (8 feet) gives the STC algorithm excellent frequency-slowness resolution: it can distinguish P-wave slowness to within 1 to 2 microseconds per foot and shear slowness to within 3 to 5 microseconds per foot in clean formations. This resolution is critical for geomechanical work because a 5-microsecond per foot error in DTS at a DTS of 100 microseconds per foot translates to approximately a 10 per cent error in Vs and a 20 per cent error in Edyn — a significant uncertainty in hydraulic fracture model inputs.