Sonic Measurement

Key Takeaways

• Compressional slowness (DTC, delta T compressional) is the foundational sonic measurement that provides porosity through the time-average relationship — for clean sandstones with quartz matrix, the relationship is DTC = (1-phi) × DTM + phi × DTF, where DTM is matrix slowness (~55.5 microseconds/ft for quartz), DTF is fluid slowness (~189 microseconds/ft for water), and phi is the formation porosity; the resulting Wyllie equation provides porosity estimates from sonic logs that complement the porosity from density and neutron logs in standard formation evaluation; for non-clean formations and complex lithologies, more sophisticated rock physics models supplement the basic Wyllie equation; sonic-derived porosity is particularly valuable in fractured reservoirs and in some carbonate applications where the density-neutron porosity may have specific issues with the rock fabric.
• Shear slowness (DTS) provides additional rock physics information that complements compressional slowness — the ratio of compressional to shear slowness (Vp/Vs ratio = DTS/DTC) reflects the rock's elastic properties and is sensitive to rock type, porosity, and fluid type; for typical sandstones, Vp/Vs is approximately 1.6-1.8; for typical carbonates, Vp/Vs is approximately 1.8-2.0; for shales, Vp/Vs is approximately 1.7-2.5 depending on clay content and pore fluid; for gas-bearing formations, Vp/Vs decreases substantially due to the strong effect of gas on compressional velocity vs shear velocity; the Vp/Vs analysis supports lithology identification, gas identification, and other applications that require shear measurement capability.
• Array sonic tools record the full waveform at multiple receivers (typically 8-13 receivers in modern tools) at typical receiver spacings of 0.5 ft, providing the data redundancy needed for sophisticated processing — slowness-time coherence (STC) processing analyzes the multi-receiver waveforms to identify the slowness of each wave mode propagating through the formation, with the resulting analysis providing compressional, shear, and Stoneley slownesses simultaneously; the STC analysis is more accurate than first-motion detection because it uses information from the entire waveform rather than just the leading edge, and is more robust against noise and interference; modern sonic logging routinely uses STC processing as the standard analytical approach.
• Stoneley wave analysis provides additional information about formation properties and fractures — Stoneley waves are interface waves that propagate along the borehole-formation boundary, with their slowness depending on borehole fluid properties and formation elastic properties; Stoneley wave attenuation provides information about formation permeability (more attenuation in higher-permeability zones) and fracture density (substantial attenuation increase across natural fractures crossing the wellbore); modern dipole sonic tools include Stoneley wave processing that extends the analytical applications of sonic logging to include permeability and fracture characterization; the Stoneley analysis is particularly valuable for fractured reservoir characterization where conventional logging methods provide limited fracture information.
• Geomechanical applications of sonic measurement include rock strength estimation (from compressional and shear velocities through standard rock physics relationships), elastic modulus calculation (Young's modulus, Poisson's ratio, bulk modulus, shear modulus from the velocities and density), and pore pressure prediction (from compressional slowness analyzed through specific pore pressure prediction models); the geomechanical analysis supports drilling decisions (wellbore stability prediction), completion design (hydraulic fracturing parameters), and production engineering (compaction-related concerns); modern integrated geomechanical workflows combine sonic measurement with density logs, image logs, and core data to provide comprehensive rock mechanics characterization.