Introduction

Effective and efficient modelling of infinite media is important for the production of accurate and useful solutions for many scientific and engineering problems involving infinite domains (Bettess 1977, 1980; Chow and Smith 1981; Medina and Taylor 1983; Zhang and Zhao 1987; Zhao et al. 1989; Zhao and Valliappan 1993a, b, c, d; Astley 1996, 1998; Yang et al. 1996; Yang and Huang 2001; Yun et al. 2000, 2007; Wang et al. 2006). Some typical examples involving infinite domains are as follows: (1) earthquake wave propagation within the upper crust of the Earth in the fields of geophysics and seismology; (2) dynamic structure–foundation interaction in the fields of geotechnical, civil and dam engineering; and (3) transient pore-fluid flow, heat transfer and mass transport within the interior of the Earth in the fields of geoscience and geoenvironmental engineering.