Transient response from a planar acoustic interface by a new point‐source decomposition into plane waves

For the wave field of a point source in full space there currently exist two classical decompositions into plane waves. The wave field can be decomposed into either (a) homogeneous and horizontally propagating (vertically attenuated) inhomogeneous plane waves by using the so‐called Sommerfeld‐Weyl integral, or (b) upgoing and downgoing homogeneous plane waves only using the Whittaker integral. Transient representations of both integrals exist. We propose a new decomposition integral that has a greater flexibility than both classical decompositions. Solutions for the point‐source reflection/transmission response from a planar interface, if based on the Sommerfeld‐Weyl integral, have for instance inherently an infinite integration limit. With the new formula, by which the wave field of a transient point source is decomposed into upgoing and downgoing homogeneous as well as horizontally propagating inhomogeneous transient plane waves, the point‐source response is directly obtained in the form of an integral with a finite integration limit. It can also be interpreted in terms of certain plane waves by which the point source is simulated in a new manner. For that matter, solutions based on the new integral readily reveal the “evanescent” or “nonray” character of the point source. The new formula may be considered an extension of the Sommerfeld‐Weyl or Whittaker integral. It can be used to compute reflection/transmission responses in a compact form in situations where the Sommerfeld‐Weyl integral was hitherto considered fundamental.