## 1 Introduction  
While conventional reservoirs are still a very important part of the global energy supply, the progress in horizontal drilling and hydraulic fracturing technologies makes it possible to exploit unconventional reservoirs [1]. As a typical unconventional oil and gas resource, tight sandstone reservoirs have become an important target for petroleum exploration in China [2]. Effective reservoir characterization is the key to their successful exploration. The rock physics model is the bridge between elastic parameters and subsurface rock physical properties, which have been proven to be a powerful tool for studying reservoir characteristics [3, 4]. Deep-buried tight sandstone has often been affected by a series of diagenesis events, such as dissolution, mechanical compaction and cementation, forming a complex pore structure with low permeability, low porosity and abundant micro-fractures [5]. Moreover, the pore structure of rocks is usually characterized in terms of the characteristics of their geometry, connectivity and size of stiff pores and micro-fractures. However, due to the micro-scale and macro-scale heterogeneity of tight sandstone, there is no clear relationship between pore structure and physical properties of the rocks, which brings great difficulty to accurately estimating reservoir elastic parameters via rock physics models. Thus, in order to correctly explore the interrelations between different physical properties of rocks, it is essential to construct a practical rock physics models for tight sandstone. Many classical rock physics models are empirical and typically assume a linear relationship between velocity and porosity [6; 7]. Some parameters used in empirical models can be adjusted according to field data, so these models are suitable and can be applied to reservoirs with similar lithology [8]. However, due to the differences in the mineral composition, pore structure, and fluid properties of underground reservoirs in various regions, these empirical models cannot properly describe the complicated elastic behaviors of tight sandstone with heterogeneous pore structures. Some scholars consider heterogeneous porous rocks as composite materials composed of mineral particles, pores and micro-fractures [9; 10; 11; 12]. Pores and micro-fractures can be filled with different fluids: oil, gas, water, etc. In this way, it is possible to use the effective medium theory to estimate elastic properties according to the composition and microstructure of rocks at different scales [13; 14]. Under long wavelength conditions, heterogeneous mineral particles, pores and micro-fractures can be represented by ellipsoidal-shaped inclusions [15]. Some scholars use self-consistent approximation (SCA) and differential effective medium (DEM) models to determine the elastic properties of isotropic saturated porous media iteratively [16; 17]. However, the expressions of the SCA and DEM models are implicit and we need to calculate them iteratively, which reduces the computational efficiency of the model. The Kuster-Toksoz (KT) and Mori-Tanaka (MT) models are widely used in the rock physics modeling of conventional sandstone reservoirs due to their explicit expressions and high computational efficiency [18]. Inclusion-based models assume that each pore in a medium is isolated and distributed randomly, meaning that the KT and MT models may be not suitable for the tight sandstone reservoirs with complicated pore structures. Several scholars have concluded that the MT model can give more consistent results with measured samples than other equivalent medium models, through experiments. With the help of the MT model, they added dry connected pores and saturated isolated pores into a rock matrix to form a dual-connected pore model describing tight sandstone reservoirs, but this model ignores the anisotropic effects of fractures in rocks [19]. Underground fractures connecting isolated pores increase effective porosity, which can be treated as the storage space and migration pathway of tight sandstone reservoirs [20].