Runtime diagram

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Time- of- flight diagram in seismics and seismology is the graphic representation of seismic wave propagation , more precisely the distance covered by seismic wave trains (travel distance), over time. Usually, the distance is plotted on the x-axis and the time on the y-axis.

The underlying principle is the length of time it takes a seismic wave to travel a certain distance. The illustration represents a linear chain of seismometers that record the seismic signal with increasing distance from the source location (e.g. earthquake , detonation , hammer blow ). Since seismic waves propagate differently underground, different phases reach the measuring instrument at different times. The relationship between the distance and time of an individual phase is referred to as the transit time curve (or transit time branch). It allows conclusions to be drawn about the speed profile of the ground. The runtime curves of various phases together form the runtime diagram.

Time diagram in seismics

Schematic transit time diagram of various seismic waves with the associated beam paths . Blue: direct seismic wave, green: head wave , red: subcritically reflected wave, brown: supercritically reflected wave.

In seismics, the time-of-flight diagram is used to investigate the distribution of seismic velocities under the earth's surface. In the figure, the schematic beam paths (below) and the associated time-of-flight curves are shown separately in color for a simple 2-layer case (the top layer has the thickness  z 0 and the speed v 0 ; the layer below has the speed v 1 > v 0 ):

  • the direct wave is shown in blue. This spreads over the shortest route from the source to the recipient. The slope of the straight line in the transit time diagram indicates the reciprocal value  1 / v 0 of the velocity of propagation .
  • The straight line is intersected by another straight line (green). This transit time branch belongs to the head wave , a refracted wave that hits the boundary to the second layer at the critical angle , propagates along the boundary with the speed of the lower layer and continuously radiates energy back to the surface. Correspondingly, the slope indicates the reciprocal value 1 / v 1 <1 / v 0 . The point of intersection of the two straight lines is called the inflection point . Since the head wave only exists when the critical angle is reached, it can only be registered from a certain distance from the signal source. Their beginning is designated as the critical point in the runtime diagram.

In addition to these two wave types, reflected waves are also measured:

  • Reflections at a shorter distance than the critical point are shown in red, which are correspondingly referred to as subcritical or steep angle reflections . The associated transit time curve connects to the use of the head wave as a reflection hyperbola .
  • at greater distances one speaks of a supercritical or wide-angle reflection (shown in brown). The associated transit time curve has a parabolic shape and approaches the straight line of the direct wave with increasing distance.

In seismology

Several different phases of seismic waves that pass through the interior of the earth and reach a measuring location at different times.

Time-of-flight diagrams are also used in seismology, which are based on the same principle, but with a much larger distance scale; the triggers of the waves are earthquakes with correspondingly high energy and further wave propagation. With seismological time-of-flight curves, the distances are usually specified as angles (in degrees) in order to take account of the curvature of the earth's surface and other boundary layers. The angle is measured between the connecting lines source location ( hypocenter ) - center of the earth and the measuring station - center of the earth.

As in seismics, the shape of the individual runtime branches depends on the speed structure in the earth's interior. The registered seismic phases allow conclusions to be drawn about the global structure of the earth's interior, as measurement points are compiled from records from several decades. The averaged velocity models valid today for the interior of the earth were derived from this, e.g. B. PREM or IASP91 .