A Quantitative Evaluation of Seismic Signals at Teleseismic Distances?II: Body Waves and Surface Waves from an Extended Source

Abstract

Summary Expressions are derived for the body wave and surface wave displacement at epicentral distances of between 30 and 100 from an extended or moving source. The source is assumed to lie entirely within a finite region on a plane. Otherwise it can be quite general. The effects of layering at the source and receiver are taken into account. Attenuation due to linear anelasticity is allowed for by an empirical factor. Propagation through the mantle is assumed to follow ray theory and the sphericity of the Earth is taken into account by the use of geometrical spreading factors. Expressions for the surface waves generated by a point source in a layered halfspace have been given by both Haskell (1964) and Harkrider (1964) using essentially the same method (i.e. the Thomson-Haskell matrix theory) but with different notations. Later on, Fuchs (1966) derived similar formulae in Harkrider's notation for the body waves radiating into the lower half-space. These correspond to the waves from a seismic source which travel through the mantle before being refracted back to the surface by the velocity gradient. A scheme by which the body wave pulse from a seismic source may be calculated, allowing for the effects of transmission through the mantle and crust, was given by Carpenter (1966). The analysis applies to the waves recorded at epicentral distances between 30 and 100; i.e. waves travelling along a ray path which lies partly in the mantle and is unaffected by the core. Kogeus (1968) applied Fuchs's results to Carpenter's theory to allow for the effects of the layered crust. He derived teleseismic waveforms due to an explosive source near the surface. A method for extending these results to sources of finite extent was indicated by Harkrider (1964) who derived expressions for the surface waves radiated from a source consisting of a horizontal point force moving with finite speed along a line. More realistic models of explosive and earthquake sources and their integration into the Thomson-Haskell theory are given by Hudson (1969) (Part I of the present Methods are, therefore, available for constructing waveforms of body waves and surface waves at distances in the range 30-100 from a wide range of source models. We shall begin by deriving expressions for the Fourier time transforms (with transform variable o) of the body waves and surface waves from a point source of