###### Abstract  
The expressions of wave structure function (WSF) and long-exposure modulation transfer function (MTF) for laser beam propagation through non-Kolmogorov turbulence were derived in our previous work. In this paper, based on anisotropic maritime atmospheric non-Kolmogorov spectrum, the new analytic expression of WSF for Gaussian-beam waves propagation through turbulent atmosphere in a horizontal path is derived. Moreover, using this newly derived expression, long-exposure MTF for Gaussian-beam waves is obtained for analyzing the degrading effects in an imaging system. Using the new expressions, WSF and MTF for Gaussian-beam waves propagating in terrestrial and maritime atmospheric turbulence are evaluated. The simulation results show that Gaussian-beam waves propagation through maritime turbulence obtain more degrading effects than terrestrial turbulence due to the humidity and temperature fluctuations. Additionally, the degrading effects under anisotropic turbulence get less loss than that of isotropic turbulence.  
wave structure function; modulation transfer function; maritime atmospheric turbulence 20202  
probability density function of the intensity for the optical wave propagating through the maritime environment [16]; [PERSON] et al. did the research on the effect of turbulent atmosphere on [PERSON]'s Flattened Gaussian beams [17]. [PERSON] et al. evolved receiver-aperture-averaged scintillation index for Gaussian waves by extending the power spectrum on non-Kolmogorov maritime atmospheric turbulence [18]. Using this non-Kolmogorov power spectrum, [PERSON] et al. derived on-axis scintillation index and analyzed the bit error rate of a partially coherent flat-topped optical wave [19]; [PERSON] el al. obtained the spreading properties of multi-Gaussian Schell-model beam array [20]; [PERSON] and [PERSON] developed the temporal phase covariance of the plane and spherical waves for evaluating the temporal frequency spread when the optical wave propagating through the terrestrial and maritime atmospheric turbulence [21].  
Recently, the degrading effects of laser beam propagation through turbulent atmosphere have attracted researchers' attention. These effects can be determined by the wave structure function (WSF) and the long-exposure modulation transfer function (MTF). [PERSON] has derived new expressions of plane and spherical waves for the WSF to analyze the spatial coherence radius when the optical waves propagate through a homogeneous and isotropic oceanic turbulence [22]. [PERSON] et al. have derived the long-exposure MTFs, angle-of-arrival fluctuations, and irradiance fluctuations for plane waves and spherical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence [23] and maritime atmospheric turbulence [24; 25]; [PERSON] and [PERSON] also have derived a new long-exposure MTF for Gaussian-beam waves propagating through isotropic non-Kolmogorov atmospheric turbulence [26]. However, study of the WSF and long-exposure MTF of Gaussian-beam waves propagating in anisotropic maritime atmospheric turbulence has not been reported, so far. Hence, in this study using the power spectrum proposed by [PERSON] et al. in [18], we will derive new WSF and long-exposure MTF expressions for the Gaussian-beam waves that propagate in the anisotropic non-Kolmogorov maritime atmospheric turbulence. The WSF and degrading effects of Gaussian-beam waves under terrestrial and maritime atmospheric turbulence are also evaluated. The evaluations are performed by using sets of numerical simulations and the degrading effects are analyzed in terms of the transmitter beam parameters, Fresnel ratio \(\Lambda_{0}\), and the curvature parameter \(\Theta_{0}\). In addition, the influences of the power law exponent \(\alpha\), the turbulence strength \(\sigma_{R}^{2}\), the turbulence scale \(L_{0}\), and the anisotropic factor, \(\zeta\), are also carefully analyzed.