Arrival Time: Definition, Seismic Travel Time, and Acoustic Logging
Arrival time is the elapsed time between the firing of a seismic or acoustic source and the detection of a specific wave event at a receiver, and it is the foundational measurement in both surface seismic exploration and downhole acoustic logging, underpinning nearly every velocity and depth calculation performed in subsurface characterisation. In surface seismic surveys, arrival times are measured in milliseconds from a surface shot or vibroseis sweep to a geophone or hydrophone, and the two-way travel time of a reflected wave is converted to depth using an assumed or calibrated velocity function. In downhole check-shot surveys and vertical seismic profiles (VSPs), arrival times are one-way travel times from a surface source to a receiver clamped at discrete depths in the wellbore, directly measuring the interval velocity of each formation unit without the velocity uncertainty introduced by surface-to-surface two-way travel. In borehole array sonic logging, arrival time refers to the time at which the compressional, shear, or Stoneley wave from the transmitter is detected at each receiver station along the array; the differential arrival times across the receiver array (not the absolute travel time from transmitter to receiver) are processed to extract formation slowness (Delta-t in microseconds per foot). Across all three applications, the accuracy of arrival time measurement controls the accuracy of every derived product — interval velocity, time-depth conversion, formation slowness, and ultimately the depth prognosis for exploration targets and the completions engineering parameters derived from acoustic log data.
Key Takeaways
- Two-way travel time (TWT) in surface seismic and its conversion to depth: Surface seismic records reflection arrival times as two-way travel time (TWT) in milliseconds — the time for the acoustic wave to travel from the surface source down to a reflecting interface and back to the surface receiver. For a horizontal reflector at 2,000 metres depth with a velocity of 3,000 m/s above it, the TWT is 2 x 2,000 / 3,000 = 1.333 seconds (1,333 ms). Converting TWT to depth requires an accurate velocity model: the simple formula depth = velocity x TWT/2 is valid only for a single horizontal layer with uniform velocity. Real seismic sections require interval velocity analysis using the Dix equation Vint = sqrt((t2 x Vrms22 - t1 x Vrms12) / (t2 - t1)) applied at each reflector, where Vrms is the root-mean-square stacking velocity estimated from semblance analysis of common-midpoint gathers. In the WCSB, time-depth conversion uncertainty is the primary source of well-to-well depth prognosis scatter: in the Montney at Dawson Creek, seismic depth conversion uncertainty is typically plus or minus 15 to 30 metres at 2,400 metres TVD using standard NMO-based interval velocity analysis, and plus or minus 5 to 10 metres when well-calibrated check-shot velocities are incorporated into the depth model.
- Check-shot survey — one-way travel time measurement and time-depth calibration: A check-shot survey directly measures the one-way travel time from a surface seismic source (usually a dynamite shot or vibroseis sweep) to a geophone clamped against the borehole wall at a specific depth, providing a noise-free, high-accuracy travel time measurement at each clamping depth. The one-way travel time at depth d is equal to TWT/2 at the same depth in the seismic section, providing the critical calibration relationship between the seismic time domain and the well depth domain. A standard WCSB check-shot survey runs 20 to 50 clamp depths from below surface casing to near total depth, spacing stations 50 to 100 metres apart in the formations of geophysical interest (typically through the Cretaceous section and into the producing Devonian carbonates). Interval velocities computed from consecutive one-way times are typically accurate to within 1 to 2 per cent of true formation velocity — compared to 5 to 15 per cent uncertainty for NMO-derived velocities — because the downhole receiver eliminates uncertainty from near-surface velocity heterogeneity that affects surface seismic ray paths. The check-shot time-depth table is the primary calibration input for synthetic seismogram generation: the wireline sonic log is integrated to produce a travel-time log (integrated travel time, ITT, in seconds), and the ITT is stretched or squeezed in the time domain to match the check-shot arrival times, producing a synthetic trace that ties directly to the 3D seismic volume.
- Acoustic log arrival time — transmitter-to-receiver travel time and Delta-t extraction: In borehole sonic logging, the raw measurement is the arrival time of the acoustic wave at each receiver from the transmitter firing. For a standard borehole compensated sonic (BHC) with a near-receiver 3 feet from the transmitter and a far-receiver 5 feet from the transmitter in a 10-ohm-m sandstone with Vp = 4,500 m/s (Delta-t = 67 microseconds per foot), the near-receiver arrival time is tnear = 3 ft x 67 us/ft = 201 microseconds and the far-receiver arrival time is tfar = 5 ft x 67 us/ft = 335 microseconds. The formation slowness is computed as Delta-t = (tfar - tnear) / (dfar - dnear) = (335 - 201) / (5 - 3) = 67 microseconds per foot. This differential approach cancels the travel time through the borehole fluid and the mud cake on both sides, making the calculation independent of borehole fluid velocity and borehole diameter provided the same fluid path is encountered at both receivers. Array sonic tools extend this approach from two receivers to 8 to 13 receivers, extracting slowness from the slope of arrival time vs receiver position through the semblance-coherence STC algorithm, achieving sub-microsecond slowness precision in clean formations.
- First-break arrival time picking in seismic refraction statics: Before any seismic reflection image can be produced, near-surface velocity heterogeneity must be corrected through a process called statics, which requires accurate picking of the first-arrival (refraction) wave event on each seismic trace. The first-break arrival time at a receiver offset x metres from the source, for a two-layer model with surface velocity V1 and refractor velocity V2, is t(x) = x/V2 + 2h x cos(ic) / V1, where h is the depth to the refractor and ic is the critical angle arcsin(V1/V2). In the WCSB Peace River lowlands, the near-surface velocity inversion from Quaternary peat bogs and muskeg over glacial till causes dramatic first-break time anomalies — traces recorded over peat may show first arrivals 500 to 800 ms later than adjacent traces over till, causing severe reflection statics of 100 to 200 ms that would render the subsurface reflections unintelligible without correction. Automated first-break pickers use cross-correlation, neural network classifiers, or energy ratio detectors to pick arrival times on tens of thousands of traces per survey, and the resulting time maps are inverted through refraction tomography to compute the near-surface velocity model used for static corrections.
- Vertical seismic profile (VSP) arrival times for corridor stack and direct tie: A zero-offset VSP records downgoing compressional wave arrival times from a surface source at a downhole receiver clamped at multiple depths in the wellbore — essentially a series of one-way check-shot arrivals plus the full downgoing and upgoing wavefields. The upgoing wavefield (created by reflected waves bouncing back up from deeper reflectors) provides a seismic image in the vicinity of the well that can be directly tied to the surface 3D seismic cube: the "corridor stack" derived from the upgoing VSP traces within the interference-free corridor (avoiding multiples) produces a synthetic seismic trace anchored precisely to well depth and arrival time. VSP one-way arrival times at each clamp depth provide the most accurate possible time-depth pairs for depth conversion because they measure the actual ray path in the well environment rather than inferring velocity from surface-to-surface moveout. In WCSB Montney exploration wells where the relationship between seismic two-way time and TVD controls the success of step-out well depth prognosis, zero-offset VSPs with sub-millisecond arrival time accuracy at 50-metre depth intervals have reduced Montney depth uncertainty from plus or minus 40 metres to plus or minus 8 metres in several Fox Creek area campaigns.
Measuring Arrival Time: First-Break Picking, STC Processing, and Check-Shot Methodology
The precision required for arrival time measurement depends on the application. In surface seismic data, the reflection two-way time must be accurate to within 1 to 4 milliseconds to correctly position reflectors in depth within 2 to 10 metres — the typical tolerance for structural trapping in WCSB development. Modern vibroseis data acquisition records data at 1 or 2-millisecond sample intervals, and after correlation with the pilot sweep the absolute timing accuracy depends on the precision of the GPS timing system on the recording truck: current industry-standard GPS timing achieves sub-microsecond absolute accuracy, making arrival time measurement essentially exact relative to the shot instant. Phase positioning errors in the vibroseis sweep correlation are the primary residual source of TWT uncertainty — pilot sweep phase calibration errors of 5 to 10 milliseconds are periodically encountered and must be detected through quality control comparison with nearby explosive shots.
In borehole check-shot surveys, the one-way arrival time is measured from the instant the surface shot or vibroseis sweep is fired to the moment the downhole geophone detects the first-break on the downgoing wave. The source-to-receiver GPS timing link achieves sub-millisecond synchronisation — 0.25 ms is typical — and the dominant accuracy limitation is the first-break pick on the downhole geophone waveform. In a clean, high-velocity Nisku carbonate at 2,800 metres, the P-wave first break is a sharp, high-amplitude onset that can be picked to within 0.1 to 0.2 ms. In slow, attenuating formations like Colorado Group shale, the first break may be gradual and ambiguous, with pick uncertainty of 1 to 3 ms. The check-shot analyst applies a consistent picking criterion (typically the first positive zero crossing or the first half-cycle amplitude threshold) across all depths and documents the pick uncertainty as an error bar on the time-depth table.
In array sonic logging, arrival time resolution is fundamentally limited by the acoustic sampling interval of the waveform digitizer: at 10-microsecond sampling and a formation P-wave velocity of 5,000 m/s (slowness 61 microseconds per foot), the theoretical arrival time resolution is plus or minus 5 microseconds, equivalent to plus or minus 0.08 feet (1 inch) of receiver spacing uncertainty. In practice, the STC coherence algorithm applied across the multi-receiver array improves this to approximately 1 to 2 microseconds per foot in high-SNR conditions — approaching the theoretical limit set by formation velocity dispersion. The primary source of arrival time error in array sonic logging is cycle-skipping: when the formation signal is very weak (due to high attenuation, gas saturation, or borehole rugosity), the amplitude threshold picker or the STC coherence peak may latch onto the second or third cycle of the waveform rather than the first arrival, recording an arrival time that is exactly one or two cycles late. In a 10 kHz waveform, one cycle skipped corresponds to 100 microseconds of error — equivalent to reading slowness as 100 microseconds per foot higher than the true value, which can shift a formation from "reservoir" to "tight seal" in a porosity calculation using the Wyllie time-average equation.