Modeling the overpressure of organic shales caused by thermal maturation and its elastic responses is crucial for geophysical characterization of source rocks and unconventional shale reservoirs. Thermal maturation involves the generation of excess fluid contents (oil and gas) and can cause the overpressure if an organic shale preserves the produced fluids partly or wholly. The solid organic matter (e.g., kerogen or solid bitumen) with the potential of generating hydrocarbon presents two types of morphology in organic shales: scattered patches as pore-fillings and continuous network as load-bearings. According to the kerogen morphology, two bulk volume models are devised to simulate the elasticity of organic shales using respective rock-physics modeling schemes. The rock physics modeling combined with the density and compressibility of pore-fillings are demonstrated to effectively capture the excess pore pressure characteristics due to thermal maturation in organic shales. The basic principle of solving the overpressure is that the pore space volume equals the total volume of all components within the pores before and after the maturation. According to the modeling results, the elastic characteristics of overpressure due to thermal maturation reveal a decrease in velocity and a slight decrease in density. Besides, for an organic shale with a relatively rigid framework, it tends to yield higher overpressure than a shale with a relatively compliant framework. With proper calibration, the modeling strategy shows its potential in quantitatively interpreting the well-log data of organic shale formation within the thermal maturation window.

Knowledge of dispersion and attenuation is essential for better reservoir characterization and hydrocarbon identification. However, limited by reliable laboratory data at seismic frequency bands, the roles of rock and fluid properties in inducing dispersion and attenuation are still poorly understood. Here we perform a series of laboratory measurements on two sandstones under both dry and partially water-saturated conditions at frequencies ranging from 2 to 600 Hz. Two samples, Bentheimer and Bandera sandstones, have similar porosity of $\sim$20% but different permeability of 1830 mD and 33 mD. At vacuum-dry conditions, the bulk dispersion and attenuation in Bandera sandstone with more clay contents are distinctly larger than those in Bentheimer sandstone, suggesting clay contents might contribute to the inelasticity of the rock frame. The partially water-saturated results show the combined effects of rock permeability and fluid saturation on bulk dispersion and attenuation. Because of the high compressibility of gas, even a few percent of gas ( $\sim$5%) can substantially dominate the pore-fluid relaxation by providing a quick and short communication path for pore pressure gradients. The consequent bulk dispersion and attenuation are negligible. However, when the sample is approaching a fully water-saturated condition (gas saturation $<$5%), the gas effect gradually decreases. Instead, the rock permeability begins to play an essential role in the pore-fluid relaxation. For Bandera sandstone with lower permeability, a partially relaxed status of pore fluids is achieved when the gas saturation is lower than 5%, accompanied by significant attenuation and dispersion.