Normal Incidence: Zero-Offset Reflection Coefficient, Acoustic Impedance Contrast, and Synthetic Seismograms in WCSB Exploration
Normal incidence is the case in which a seismic wavefront is parallel to a subsurface interface and its raypath is perpendicular, or normal, to that interface as the wave impinges upon it. In other words, the energy strikes the boundary head-on at an angle of incidence of zero degrees, the simplest geometry in reflection seismology and the foundation on which most basic seismic interpretation is built. When a downgoing wave meets a boundary between two layers of different acoustic properties, part of its energy reflects back up and part transmits across into the lower layer. The fraction reflected at normal incidence is governed entirely by the contrast in acoustic impedance across the boundary, where acoustic impedance is the product of a rock's bulk density and its seismic velocity. The normal-incidence reflection coefficient is expressed as the difference in impedance across the interface divided by the sum of the impedances of the two layers, so a large velocity or density jump produces a strong reflection and a small contrast produces a weak one. The sign of the coefficient also matters: a wave passing from a low-impedance layer into a high-impedance layer produces a positive reflection, while the reverse produces a negative reflection with a polarity flip, information interpreters use to distinguish, for example, a hard carbonate from an overlying soft shale or a gas-charged sand from brine-filled rock. Normal incidence is an idealization, since in real surveys the source and receiver are separated by an offset and rays strike interfaces at a range of angles, but it remains central for two reasons. First, the zero-offset trace, the trace that would be recorded if source and receiver were at the same point, is what conventional stacked seismic sections approximate after normal-moveout correction and stacking, so the everyday seismic image is effectively a normal-incidence display. Second, the synthetic seismogram, the bridge between a well and the seismic volume, is built by convolving a wavelet with a normal-incidence reflectivity series computed from the well's sonic and density logs. In the Western Canadian Sedimentary Basin, this is the workhorse of exploration and development geophysics. Interpreters generating synthetics from Montney and Duvernay well logs use the normal-incidence reflectivity to tie formation tops to seismic reflectors, calibrate the wavelet, and map reservoir geometry. The departure of real, finite-offset amplitudes from the normal-incidence value, the basis of amplitude-versus-offset analysis, is itself only meaningful when measured against the zero-offset reference that normal incidence defines.
Key Takeaways
- Head-on geometry, zero degrees: Normal incidence means the raypath is perpendicular to the interface and the angle of incidence is zero. The wavefront is parallel to the boundary and strikes it head-on, the simplest possible reflection geometry and the reference case for nearly all introductory seismic theory.
- Impedance contrast sets the reflection: The normal-incidence reflection coefficient equals the impedance difference across the interface divided by the sum of the two impedances, where impedance is density times velocity. A large contrast, such as shale over tight carbonate, yields a strong reflection; matched layers yield almost none.
- Polarity carries lithology and fluid information: A wave entering a higher-impedance layer reflects with positive polarity; entering a lower-impedance layer it flips to negative. WCSB interpreters read this sign to separate hard carbonates from soft shales and to flag gas-charged sands, which lower impedance and produce characteristic negative responses.
- Stacked sections approximate zero offset: After normal-moveout correction and stacking, a conventional seismic section approximates the zero-offset, normal-incidence trace. The everyday interpreted seismic image is therefore effectively a normal-incidence display, which is why the concept underpins routine mapping rather than only theory.
- Foundation of the synthetic seismogram: Synthetics that tie wells to seismic are built from a normal-incidence reflectivity series computed from sonic and density logs, then convolved with a wavelet. In the WCSB this tie calibrates depth-to-time conversion and confirms which reflector corresponds to which formation top.
Computing the Reflection Coefficient From Logs
To build a synthetic for a Duvernay well, an interpreter first computes acoustic impedance at every depth by multiplying the sonic-derived velocity by the bulk density log. The normal-incidence reflectivity at each interface is then the impedance contrast across it normalized by the sum of the bounding impedances. Strong positive spikes appear where soft shale overlies tight, fast carbonate or dense siltstone, and negative spikes appear at the reverse transitions. This reflectivity series, sampled in time rather than depth via a check-shot or sonic integration, is convolved with an estimated wavelet to produce the synthetic trace that is then matched against the field seismic at the well location.
Normal Incidence Versus Amplitude-Versus-Offset
Real WCSB surveys record reflections over a spread of source-receiver offsets, so rays hit interfaces at increasing angles away from normal. The variation of reflection amplitude with that angle, described by the Zoeppritz equations and their approximations, is the basis of amplitude-versus-offset, or AVO, analysis. AVO is powerful for detecting gas and characterizing fluids, but its starting point is always the normal-incidence intercept, the modelled zero-offset amplitude. The gradient, how amplitude changes with offset, is measured relative to that intercept. Without a sound normal-incidence reference, the offset-dependent behaviour that flags a Montney or Nikanassin gas sand cannot be quantified.
Fast Facts
The full mathematics of how seismic energy partitions at an interface were worked out by Karl Zoeppritz and published in 1919, shortly after his death, in equations that remain the backbone of reflection seismology more than a century later. The normal-incidence reflection coefficient is simply the zero-angle solution of those equations, the one clean case where the messy trigonometry of converted shear waves and angle-dependent partitioning collapses to a single ratio of impedances, which is why it became the entry point for teaching and the anchor for every synthetic seismogram generated since.
Related Terms
Normal incidence defines the zero-offset reflection used throughout seismic reflection surveying, the primary geophysical method for imaging WCSB reservoirs. The strength of a normal-incidence reflection is set by the contrast in acoustic impedance, the product of density and velocity that interpreters compute from well logs. That impedance series feeds the synthetic seismogram used to tie wells to seismic, and the deviation of real amplitudes from the normal-incidence value underlies amplitude-versus-offset fluid analysis.
Real-World WCSB Scenario: Tying a Montney Well to 3D Seismic
An interpreter working a Montney play near Dawson Creek, British Columbia, needed to confirm which strong reflector on a new 3D volume corresponded to the top of the Montney before committing a horizontal landing depth. Using the well's sonic and density logs, the team computed a normal-incidence reflectivity series, converted it to time with a check-shot survey, and convolved it with a wavelet extracted from the seismic to generate a synthetic trace.
The synthetic matched the field data cleanly, locking the Montney top to a specific peak and resolving an earlier ambiguity of about 15 m in the time-depth conversion. With the tie secured, the operator placed the horizontal in the target interval with confidence, avoiding a mispick that on a multimillion-dollar WCSB pad could have landed the lateral in the wrong zone.