Full Wave Form Inversion for Seismic Data

In seismic wave inversion, seismic waves are sent into the ground and then observed at many receiving points with the aim of producing high-resolution images of the geological underground details. The challenge presented by Saudi Aramco is to solve the inverse problem for multiple point sources on the full elastic wave equation, taking into account all frequencies for the best resolution. The state-of-the-art methods use optimisation to find the seismic properties of the rocks, such that when used as the coefficients of the equations of a model, the measurements are reproduced as closely as possible. This process requires regularisation if one is to avoid instability. The approach can produce a realistic image but does not account for uncertainty arising, in general, from the existence of many different patterns of properties that also reproduce the measurements. In the Study Group a formulation of the problem was developed, based upon the principles of Bayesian statistics. First the state-of-the-art optimisation method was shown to be a special case of the Bayesian formulation. This result immediately provides insight into the most appropriate regularisation methods. Then a practical implementation of a sequential sampling algorithm, using forms of the Ensemble Kalman Filter, was devised and explored

Efficient modeling in transversely isotropic inhomogeneous media

An efficient modeling technique for transversely isotropic, inhomogeneous media, is developed using a mix of analytical equations and numerical calculations. The analytic equation for the raypath in a factorized transversely isotropic (FTI) media with linear velocity variation, derived by Shearer and Chapman, is used to trace between two points. In addition, I derive an analytical equation for geometrical spreading in FTI media that aids in preserving program efficiency; however, the traveltime is calculated numerically. I then generalize the method to treat general transversely isotropic (TI) media that are not factorized anisotropic inhomogeneous by perturbing the FTI traveltimes, following the perturbation ideas of Cerveny and Filho. A Kirchhoff-summation-based program relying on Trorey`s (1970) diffraction method is used to generate synthetic seismograms for such a medium. For the type of velocity models treated, the program is much more efficient than finite-difference and general ray-trace modeling techniques

Monitoring increases in fracture connectivity during hydraulic stimulations from temporal variations in shear wave splitting polarization

Hydraulic overpressure can induce fractures and increase permeability in a range of geological settings, including volcanological, glacial and petroleum reservoirs. Here we consider an example of induced hydraulic fracture stimulation in a tight-gas sandstone. Successful exploitation of tight-gas reservoirs requires fracture networks, either naturally occurring, or generated through hydraulic stimulation. The study of seismic anisotropy provides a means to infer properties of fracture networks, such as the dominant orientation of fracture sets and fracture compliances. Shear wave splitting from microseismic data acquired during hydraulic fracture stimulation allows us to not only estimate anisotropy and fracture properties, but also to monitor their evolution through time. Here, we analyse shear wave splitting using microseismic events recorded during a multistage hydraulic fracture stimulation in a tight-gas sandstone reservoir. A substantial rotation in the dominant fast polarization direction (ψ) is observed between the events of stage 1 and those from later stages. Although large changes in ψ have often been linked to stress-induced changes in crack orientation, here we argue that it can better be explained by a smaller fracture rotation coupled with an increase in the ratio of normal to tangential compliance (ZN/ZT) from 0.3 to 0.6. ZN/ZT is sensitive to elements of the internal architecture of the fracture, as well as fracture connectivity and permeability. Thus, monitoring ZN/ZT with shear wave splitting can potentially allow us to remotely detect changes in permeability caused by hydraulic stimulation in a range of geological settings