Dix Formula

Key Takeaways

• The assumptions underlying the Dix formula limit its accuracy in practice: the formula is exact only for flat, horizontal, isotropic layers with no lateral velocity variation, where the RMS velocity model (a series of constant-velocity layers separated by flat reflectors) perfectly describes the actual subsurface; in real geological situations, layers dip, velocity varies laterally (due to facies changes, compaction gradients, or fluid substitution), and the subsurface is anisotropic (velocity varies with propagation direction due to layering and preferential alignment of minerals or fractures), all of which cause the Dix-derived interval velocities to deviate from the true layer interval velocities; the effect of dip on Dix velocities is that dipping reflectors produce NMO velocities that are higher (for updip shooting) or lower (for downdip shooting) than the true RMS velocity by the cosine of the dip angle, causing Dix inversion to produce erroneously high or low interval velocities in areas of significant structural relief; full-waveform inversion (FWI) and reflection tomography methods that directly invert the seismic waveform for the velocity model are increasingly used in exploration and production geophysics to circumvent the limitations of the Dix approximation, particularly in geologically complex areas with salt, steep dips, or strong lateral velocity gradients.
• Seismic depth conversion using Dix-derived interval velocities converts the time-domain interpretation (the horizon interpretations in two-way travel time from the seismic workstation) to the depth domain needed for reservoir volumetrics, well prognosis, and drilling depth prediction: the depth to each interpreted horizon is calculated as the integral of the interval velocity over the two-way time from the surface to that horizon, using the Dix interval velocities as the layer-by-layer velocity model; the accuracy of the depth conversion depends on both the accuracy of the Dix interval velocities (which requires good-quality velocity picks at many CMP locations to define the RMS velocity field) and the calibration of the seismic velocity model to well sonic logs and checkshot data (which measure the actual velocity at the well location and reveal any systematic bias in the Dix velocities that must be corrected before the depth map can be used for well planning); the depth conversion uncertainty (expressed as the error in the predicted depth to the target horizon at a new well location) is typically 1 to 3 percent of depth for well-constrained seismic velocity models and can exceed 5 to 10 percent in areas with poor well control, complex velocity structure, or anisotropy not accounted for in the Dix analysis.
• Interval velocity from the Dix formula as a lithology and fluid indicator uses the known velocity ranges for different rock types and fluid saturations to distinguish between prospective and non-prospective zones on seismic data: dry sandstone has P-wave velocities of 3,000 to 5,500 m/s depending on porosity, cementation, and depth; water-saturated sandstone has slightly higher velocity (because water is incompressible and stiffens the rock frame); gas-saturated sandstone has dramatically lower velocity (because gas is highly compressible and reduces the bulk modulus), creating the "bright spot" amplitude anomaly and the velocity "sag" (apparent depression of deeper reflectors below a gas sand) that are key amplitude-versus-offset (AVO) and seismic attribute indicators for gas sands; Dix interval velocities that show a low-velocity zone consistent with gas saturation within an otherwise normally compacting section are direct indicators of possible gas accumulations that warrant priority exploration attention; quantitative interpretation of Dix interval velocities for fluid and porosity prediction requires calibration against well data (sonic logs and core measurements) that establish the velocity-porosity-fluid relationships for the specific basin and lithology.
• The reciprocal of interval velocity is the interval transit time (the time for seismic waves to traverse one unit of vertical thickness of a layer), which is related to the sonic log transit time measured by acoustic logging tools in the borehole and enables direct comparison between seismic-derived interval velocities and well-based sonic measurements: a synthetic seismogram (computed by convolving the reflection coefficients derived from the sonic log and density log with a seismic wavelet) ties the well's depth-domain log measurements to the time-domain seismic data, allowing the interpreter to verify that the Dix interval velocities match the sonic log values at the well location; systematic discrepancies between Dix velocities and sonic log velocities indicate that the NMO velocity picks used in the Dix calculation are biased (too high or too low relative to the true velocities), guiding reprocessing or re-picking of the velocity analysis; the synthetic-to-seismic tie is one of the most important calibration exercises in seismic interpretation, providing both the wavelet estimation needed for inversion and the velocity calibration check for depth conversion.
• Interval velocity gradients and their variation with depth provide basin-scale information about compaction history, diagenesis, and abnormal pressure: in a normally compacted sedimentary sequence, interval velocity increases with depth as porosity is reduced by compaction and cementation; a velocity reversal (interval velocity decreasing with depth) indicates undercompaction (pore pressure above normal hydrostatic, because the excess pore pressure prevents grain-to-grain compaction), providing one of the primary seismic indicators of overpressure that is used in pore pressure prediction before drilling; the Eaton pore pressure prediction method uses the ratio of observed interval velocity (from Dix analysis or sonic log) to the expected normal compaction velocity at the same depth as the input for pore pressure estimation, directly linking the Dix formula to one of the most important applications of seismic velocity in well planning safety.