The Penetration of Highly Directional Acoustic Beams into a Sedimentary Bottom. Part I

The following theoretical problem is solved. What is the pressure field in an underlying medium when a highly directional acoustic beam in water impinges on the bottom sediments. The acoustic velocity in the bottom is larger than that of the water, and the velocity ratio is such that plane wave theory predicts total internal reflection (in the absence of attenuation) at a grazing angle near 28 degrees. The incident beam is represented by a bundle of plane waves, and an approximate expression for the resulting pressure field in the bottom is obtained by the principle of stationary phase. In Part I it is assumed that all of the plane waves in the bundle have the same phase. In Part II a phase structure will be introduced in order to represent the nearfield of the source. (Modified author abstract)