Head Wave

Key Takeaways

• The crossover distance is where head waves overtake direct waves and become the first arrivals — at short source-receiver distances (offsets), the direct wave traveling through the upper layer at velocity V1 arrives at the receiver before the head wave because the head wave path is longer (down to the interface, along it, and back up); at greater offsets, the head wave's higher velocity along the interface more than compensates for its longer path, and it becomes the first arrival; the crossover distance (Xcross = 2z × sqrt[(V2+V1)/(V2-V1)], where z is the depth to the interface) is the offset at which direct and head wave arrival times are equal; recording seismic data at offsets beyond the crossover distance is required to observe head wave arrivals and perform refraction analysis — too-short geophone spreads that don't extend beyond crossover will miss the head wave completely and cannot map the refracting layer; in shallow investigations, crossover distances of a few tens of meters are typical, while deep crustal studies may require offsets of tens to hundreds of kilometers to observe head waves from the Moho and other deep interfaces.
• The t-x diagram (travel time versus distance plot) reveals layer velocities directly from head wave slopes — when head wave arrival times are plotted against receiver offset on a linear t-x graph, the head wave arrivals from a single interface form a straight line with slope equal to the reciprocal of the refractor velocity (1/V2); the y-intercept of this line gives the intercept time (ti = 2z × cos(ic)/V1), from which the depth to the interface can be calculated if the upper layer velocity V1 is known; in a multi-layer earth, each interface produces a separate head wave with its own slope and intercept time on the t-x diagram, allowing sequential determination of each layer's velocity and the depth increments between layers; this direct, graphical interpretation of refraction t-x data makes head wave analysis particularly straightforward compared to reflection processing, which requires complex velocity analysis and normal moveout correction before structural imaging; the simplicity of t-x analysis is one reason refraction seismology became practical decades before reflection seismology and remains the standard method for rapid, low-cost shallow velocity profiling in engineering and environmental applications.
• Near-surface velocity anomalies (the "weathering layer" problem) in reflection seismic processing require head wave analysis for correction — the earth's surface is typically covered by a low-velocity zone (LVZ) of weathered, fractured, or dry rock (the weathering layer) that has seismic velocities much lower than the consolidated rock below; seismic waves traveling through this zone are delayed relative to waves traveling through the high-velocity rock below, creating time delays (called statics shifts) that vary from trace to trace depending on the thickness and velocity of the weathering layer beneath each receiver and source point; these static shifts, if uncorrected, blur the stacked reflection image by misaligning reflections in the CMP gather before stacking; first-arrival refraction analysis uses head waves from the base of the weathering layer to map its velocity and thickness at each shot and receiver point, providing the refraction statics corrections that are applied before reflection processing; in areas with severe weathering variability (desert sand dunes, karst terrain, permafrost), refraction statics can be the single most important processing step for reflection data quality.
• Seismic first-arrival tomography uses head wave picks to invert for near-surface velocity models — rather than interpreting head waves using the simple layer-cake t-x method, modern near-surface characterization uses first-arrival travel time tomography: the travel times of first arrivals (dominantly head waves and direct waves at different offsets) are picked for thousands of source-receiver pairs, and an iterative inversion adjusts the velocity model until the modeled travel times match the observed picks; the result is a 2D or 3D velocity model of the near-surface zone that captures lateral velocity variations (buried channels, karst dissolution, permafrost boundaries) that the layer-cake refraction method would average over and miss; first-arrival tomography is now routinely applied in marine acquisition to model seafloor velocity variations that affect reflection processing, and in land acquisition to build the near-surface model for static corrections in areas with complex geology that defies simple layer interpretation.
• In offshore seismic, water-bottom refracted waves are the head waves used to quality-control cable depth and water velocity — in marine seismic acquisition, the water column has a nearly uniform velocity of approximately 1,480-1,530 m/s (varying with temperature, salinity, and pressure), and the seafloor (if it is harder and faster than the water) generates head waves that travel along the seafloor at the seabed sediment velocity; the water column direct wave arrives at all near offsets first, and the seafloor head wave appears as a linear first-arrival trend at longer offsets on the record; the slope of this seafloor head wave directly measures the compressional velocity of the near-surface seabed sediment, which is important for refraction statics in shallow-water surveys; simultaneously, the direct water wave travel time at known cable offsets provides a direct measurement of the water column velocity at the acquisition time, used to calibrate the marine velocity model for processing.