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In this paper, we propose a theoretical calculation method for the displacements of transient wave excited by a linear array coupled to an elastic solid with a longitudinal wave couplant. Firstly, the vertical and horizontal displacements excited by a vertical line source are solved based on exact and analytical solutions of transient elastic waves induced by a line source normally acting on an elastic half-space. Secondly, in this case, the displacements from a linear array can be determined by the superposition of the solutions of a number of discrete line forces mentioned above. All the theoretical results are compared to the finite element simulation results. The theoretical results are consistent with finite element simulation data. Therefore, the calculation method can save a lot of computing time. This paper provides a fast and accurate calculation method of transient wave displacements in a half-space generated by a linear array. The calculation method can be used to explore the sound field characteristics of a linear array transducer in the future

Calculation of displacements in a half-space from a linear array based on analytical solutions of transient wave