Mathematics & Physics 2015, 8(4), 442–453 УДК 519.21 System Mathematical Models for the Formation of Signals and Synchronous Interference with the Use of Pulsed Non-explosive Seismic Sources Georgy Ya. <...> Shaidurov∗ Danil S. Kudinov† Siberian Federal University Kirenskogo, 26, Krasnoyarsk, 660074 Russia Received 06.08.2015, received in revised form 07.09.2015, accepted 06.10.2015 The theory of linear systems is applied to simulate and describe signals and synchronous noise registered by seismic sensors. <...> An algorithm is proposed to reduce the effect of the inhomogeneous upper layer and of regular interference associated with the low velocity zone. <...> The materials from this paper can be helpful in developing algorithms to process data acquired primarily by nonexplosive pulsed and vibrational seismic survey technologies. <...> DOI: 10.17516/1997-1397-2015-8-442-453 Introduction The fundamental physical processes initiated in geological environment by induced seismic vibrations, including those generated by nonexplosive sources, according to the current theory of seismic surveying can be simulated by a linear model described by a set of differential equations with constant coefficients [1, 2, 3, 4, 5, 6]. <...> Assuming this approach, the characteristics that are sufficient to describe the model embrace the transfer function (TF), amplitude-frequency characteristic (AFC), phase-frequency characteristic (PFC), and transient response (TR) or pulse characteristic (PC), all being mathematically uniquely interdependent via integral Fourier and Laplace transforms [3]. <...> The excitation transfer function of seismic vibrations and propagation of the latter in a geological structure can roughly be described by the characteristics of an oscillatory circuit (Shneerson and Mayorov, 1988) [7, 8, 9]. 1. <...> Linear model of seismic signals formation Fig. 1 illustrates a simplified linear pattern of formation of a seismic signal shown as a sequence of individual stages of transfer of the excitation signal I(t) generated by a nonexplosive source [10, 11, 12, 13]. <...> The transmitting properties of the "source-ground surface" system are modeled by the pulse characteristic (PC)FG(p) and its counterpart TRFG(p), where t is the current time, P = C ±j ∗GShaidurov@sfu-kras.ru †KudinovDanil@yandex.ru ⃝ Siberian Federal University. <...> Shaidurov, Danil S.Kudinov System Mathematical Models for . <...> A linear <...>