As a means of interpreting subsurface geophysical and petrophysical data in terms of engineering reservoir properties, the discipline of rock physics has been central to delivering value for an ever-growing pool of underground energy applications. As the industry looks in new directions, from the sequestration of carbon dioxide to the production and storage of geothermal heat and hydrogen, many new challenges arise that position rock physics as a major enabler to a new sustainable energy portfolio. Delivering on that promise will in part necessitate the ingenuity and dedication of a new generation of rock physicists as skilled in the understanding of fundamental chemo-physical processes at play as they are in the astute use of modern digital tools. But as with any great project, foundation comes first, and long-recognized challenges that have already prompted decades of rock physics modeling efforts still require our attention if we are to succeed in these new endeavors.

In this special section, three papers provide a timely overview of the state of the art in the modeling of elastic properties, addressing the issues of anisotropy, microfractures, fluid substitution, and stress sensitivity. Individually, each paper addresses a specific problem to which a modeling strategy is successfully applied. Together, they provide an ideal starting point for a deep dive into historical practical challenges in effective-medium modeling from a variety of perspectives.

Asaka tackles the problem of inferring the full vertical transversely isotropic (VTI) tensor of shale rocks from partial information derived from sonic logs. Indeed, such VTI tensor determination usually requires measurements of both P and S waves in various directions, which is typically not possible with downhole logging tools. Using a sonic data set from a vertical well in the Middle Devonian Marcellus Shale and mineralogical data obtained on rock samples from the same well, the author employs his previously published model to infer the values of the missing elastic moduli C11 and C13 by performing a brute-force matching of the measured C33, C55 (or C44), and C66. In the matching process, meaningful model parameters are generated, including two Thomsen's anisotropy parameters: δ and ε. These outputs can in turn be used to honor VTI anisotropy in seismic inversion and borehole stability analysis, while also providing further insight into gas saturation through the ε/δ ratio.

In Allo and Vernik's paper, the problem of Gassmann's fluid substitution in highly stress-sensitive materials is covered in light of recent observations that suggest that the formalism of Gassmann is inaccurate and may lead to overestimating undrained elastic moduli. These recent observations promote the use of a more general expression for the undrained compressibility of saturated porous media such as derived by Biot and by Brown and Korringa, and which involves one additional compressibility term. In this work, the authors postulate that this more rigorous expression may be conveniently and fully parameterized through the adoption of the stress-sensitive effective-medium model of Vernik and Kachanov, which considers the distinct elastic contributions of stiff pores and high-compliance features such as microcracks. Consistent with their approach, they estimate that the traditional Gassmann's result is still appropriate for media with very low crack density or at close to closure stress conditions.

Hongyan et al. study sonic log response modeling and interpretation by taking a contrasting approach to that of the previous papers. Starting from a log data set acquired in an oil shale reservoir in the Mahu area of Xinjiang, the authors endeavor to identify the most appropriate effective-medium model for their data set, within the context of known fracture presence. After evaluating a number of available options, the authors settle for a workflow involving (1) the use of the Hashin-Shtrikman bounds average for the mineral contribution, (2) a differential effective-medium approach for the porous and microcracked rock, and (3) an original inclined fracture model to honor fracture presence. The effect of the fluids is then incorporated through the standard Gassmann equation. In fitting the log data, sets of fracture angle and density values are generated that compare well statistically with those derived from borehole electrical imaging.