Abstract We describe a method of modeling seismic waves interacting with single liquid-filled large cracks based on the Kirchhoff approximation and then apply it to field data in an attempt to estimate the size of a hydraulic fracture. We first present the theory of diffraction of seismic waves by fractures using a Green’s function representation and then compute the scattered radiation patterns and synthetic seismograms for fractures with elliptical and rectangular shapes of various dimensions. It is shown that the characteristics of the diffracted wavefield from single cracks are sensitive to both crack size and crack shape. Finally, we compare synthetic waveforms to observed waveforms recorded during a hydraulic fracturing experiment and are able to predict successfully the size of a hydraulically induced fracture (length and height). In contrast to previously published work based on the Born approximation, we model both phases and amplitudes of observed diffracted waves. Our modeling has resulted in an estimation of a crack length 1.1 to 1.5 times larger than previously predicted, whereas the height remains essentially the same as that derived using other techniques. This example demonstrates that it is possible to estimate fracture dimensions by analyzing diffracted waves.

Abstract This paper argues that the pervasive distributions of closely-spaced stress-aligned fluid-saturated microcracks in almost all rocks are a critical system close to fracture criticality and loss of shear strength. New evidence includes three examples in which observations and modelling directly imply non-linear interactive critical systems with some form of self-organised criticality (SOC). These are a direct calibration of anisotropic poro-elasticity (APE) by monitoring and modelling the response of a reservoir to a high-pressure injection. Monitoring and modelling velocity and attenuation dispersion in a rock physics laboratory. Monitoring the effect of the build-up of stress before earthquakes and volcanic eruptions, including the successful stress forecast of the time and magnitude of an ML=5 (MS ≈ 6) earthquake in southwest Iceland. These new results from three very different fields strongly suggest that the earth's crust is a critical interactive non-linear system with self-organised criticality (SOC). Some effects are subtle and easily ignored. Others are so common and familiar that we have developed one-off explanations in terms of conventional deterministic physics to describe their behaviour and occurrence. We suggest that the identification of the sub-critical physical processes is one reason for the success of APE-modelling. Recognition of (crack) criticality leads to a new understanding of low-level (pre-fracturing) deformation that has massive implications for almost all dynamic processes in the crust. These include reservoir characterisation, hydrocarbon recovery, monitoring the progress of fluid-fluid fronts, and the build-up of stress before fracturing, faulting, and earthquakes, and the movement of magma before volcanic activity. The implications will be discussed and the arguments presented.