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In the early 1930's, Dr. Evjen wrote a treatise on “The Geometry of Refraction and Reflection Shooting” which to this day remains a classic in its field. Most of the seismologists of the Shell Companies over the entire world have learned part of their trade from this treatise. The book was released to Dr. Evjen after he left the service of Shell, but circumstances have prevented him from publishing it, wholly or in parts. It was, therefore, an honor as well as a genuine pleasure for this writer to condense, with Dr. Evjen's permission, one of the chapters of the book. It deals with monotonic increases of velocity with depth in a way which is entirely satisfactory from both the practical and the theoretical points of view.

  • V1 =

    velocity at the surface.

  • Vz =

    velocity at depth Z.

  • q =

    dimensionless constant.

  • L =

    a constant with the dimension of length.

  • T, X =

    time and distance on a time-distance curve.

  • T, x=

    time and horizontal distance from shotpoint to any point on a trajectory.

  • i =

    angle between raypath and vertical at any point of path.

  • i1 =

    value of i at surface.

  • U =

    dX/dT= V1/sin i1 = Vz/sin i = reciprocal of slope of T–X graph.

  • Z =

    depth below datum.

  • ds =

    element of raypath.

A velocity distribution or a family of velocity increases with depth must fulfill two requirements—integrability of the time and distance integrals and ease of construction of the trajectories. Although many velocity

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