“…Many forward modelling methods, most of them for the ultrasound imaging, have been developed with variable density (Kwon and Jeong, 1998; Lavarello and Oelze, 2009; Mojabi and LoVetri, 2015; Rao et al ., 2020). In recent years, some studies about integral equation methods for seismic forward modelling with variable density have been considered in several publications (Yang et al ., 2016; Yao et al ., 2016; Sun et al ., 2017; Jiménez et al ., 2018; Luo and Wu, 2018; Farshad and Chauris, 2020). Although these studies have been developed, there is still an important need to develop more accurate and efficient methods for seismic forward modelling with variable density.…”