## 1 Introduction  
Rocks undergo a range of weathering processes driven by changing environmental factors, such as climate, temperature, and precipitation. Characterization of cracks in a rock is one common way to monitor the extent of weathering. Cracks that develop during weathering can reduce the strength and stiffness of a host rock, critically reducing its durability [1; 2]. According to [PERSON] [3], cracks have sizes within the range 0.01-1 m, whereas micro-cracks have sizes less than 0.01 m. Visual observation is a common method used to find cracks in rocks, although it is not effective at identifying micro-cracks due to their small size. Given this limitation, crack density, defined as the number of cracks per unit volume of rock, is often used to estimate the number of micro-cracks in a rock instead [4], assuming that their proportions are related. Several researchers have suggested that the crack density can be calculated via the theory of elastic wave propagation [5], which provides a method to estimate the proportions of micro-cracks in the absence of independent constraints. [PERSON] [6] first established a constitutive equation for wave propagation through a porous medium with a uniform pore pressure by using a stress-strain relationship. Subsequently, [PERSON] [7] added a crack parameter to this relationship to quantify how crack density affects seismic wave velocity. This theory has since been developed with respect to circular [8] and rectangular [9] cracks, although elastic interactions between cracks must be considered in order for this parameterization to have practical applicability. [PERSON] and [PERSON] [10] expanded on this work by developing a new model for crack development in rocks, which considered elastic interactions based on self-consistent theory [11]. This parameterization was shown by [PERSON] [12] to adequately predict interactions between different petrophysical parameters in porous and cracked rocks. These theories were developed primarily to elastically predict the stress-strain relationship in a porous-cracked rock, rather than quantitatively evaluating the spatial characteristics of the cracks themselves, although some recent models have used this theory to estimate crack densities. [PERSON] [6] showed that elastic moduli and the assumption of elastic behavior are important variables in the wave propagation equation. As such, [PERSON] et al. [13] and [PERSON] [14] proposed analytical solutions to investigate changes in crack density due to variations in elastic moduli. Also, since elastic moduli can be inferred from elastic wave velocity, [PERSON] et al. [4] characterized different rock types by estimating their crack density using measured elastic wave velocity data. However, crack density is also a function of aspect ratio, and it is difficult to estimate a reliable crack density without knowing the aspect ratio of the cracks, even if elastic moduli are well constrained. Previous studies of this issue have been limited in their ability to estimate crack densities, as they assumed constant values for aspect ratios. Therefore, in this work, a new relationship is presented that relates crack density and crack aspect ratio, which was parameterized from experimental results. This allows definition of the aspect ratio as a function of the crack density, which allows either of these variables to be determined if the other can be accurately measured. As the 4 th industry technology has developed, data analysis techniques have also been improved, and machine learning (ML) techniques were proposed to reliably define correlations between two or more physical variables or to cluster them [15; 16]. The relationship of each different physical quantity is mainly analyzed based on regression analysis, and a deep neural network (DNN) is used to infer nonlinear correlation as part of a supervised learning technique.