Tomography with sparseness regularisation for ultrasonic velocity imaging

Abstract

Abstract Ultrasonic tomography, which is widely used in the study of the fracturing process of rocks, often exhibits low resolution due to insufficient ray coverage, particularly while evaluating the three-dimensional (3D) fractures. To resolve this issue, we adopted sparseness regularisation in tomography to reconstruct the ultrasonic velocity of rocks. Both numerical and laboratory experiments demonstrate that tomography with sparseness regularisation generates velocity images with clear fracture morphology than that with Tikhonov regularisation. Dynamic monitoring of the fracturing process of a granite slab with two-dimensional (2D) velocity images can reveal the accurate development of the fracturing process. The experiment on the internal structure of tight sandstone after hydraulic fracturing reveals demarcated low-velocity regions in the 3D ultrasonic velocity images of tomography with sparseness regularisation. These low-velocity regions correspond to the positions of the fractures when compared to the X-ray scanning images. Thus, tomography with sparseness regularisation can improve the resolution of ultrasonic velocity images, which can be used to accurately describe the fracture development and strain localisation during rock deformation.