*Article* **Fast Computation of Green Function for Layered Seismic Field via Discrete Complex Image Method and Double Exponential Rules**

**Siqin Liu 1,2, Zhusheng Zhou 1,2,\*, Shikun Dai 1,2, Ibrar Iqbal 3 and Yang Yang 3**


**Abstract:** A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for the computation of the finite part. Estimation of signal parameters via rotational invariance techniques (ESPRIT) is used to improve the accuracy and efficiency of extracting DCIM compared to the generalized pencil of function (GPOF). Due to the symmetry of the horizontal layered media, the Green function, representing the seismic fields due to a point source, can be written in the form of Sommerfeld integral in cylindrical coordinate system and be calculated by the proposed method. The performance of the method is then compared to the DE rules with weighted average partition extrapolation (WA), which shows a good agreement, with computational time reduced by about 40%.

**Keywords:** DE rules; Green function; DCIM; Sommerfeld integral
