Advanced techniques for subsurface imaging Bayesian neural networks and Marchenko methods

Abstract

Estimation of material properties such as density and velocity of the Earth’s subsurface are important in resource exploration, waste and CO2 storage and for monitoring changes underground. These properties can be used to create structural images of the subsurface or for resource characterisation. Seismic data are often the main source of information from which these estimates are derived. However the complex nature of the Earth, limitations in data acquisition and in resolution of images, and various types of noise all mean that estimates of material parameters also come with a level of uncertainty. The physics relating these material parameters to recorded seismic data is usually non-linear, necessitating the use of Monte Carlo inversion methods to solve the estimation problem in a fully probabilistic sense. Such methods are computationally expensive which usually prohibits their use over areas with many data, or for subsurface models that involve many parameters. Furthermore multiple unknown material parameters can be jointly dependent on each datum so trade-offs between parameters deteriorate parameter estimates and increase uncertainty in the results. In this thesis various types of neural networks are trained to provide probabilistic estimates of the subsurface velocity structure. A trained network can rapidly invert data in near real- time, much more rapidly than any traditional non-linear sampling method such as Monte Carlo. The thesis also shows how the density estimation problem can be reformulated to avoid direct trade-offs with velocity, by using a combination of seismic interferometry and Marchenko methods. First this thesis shows how neural networks can provide a full probability density function describing the uncertainty in parameters of interest, by using a form of network called a mixture density network. This type of network uses a weighted sum of kernel distributions (in our case Gaussians) to model the Bayesian posterior probability density function. The method is demonstrated by inverting localised phase velocity dispersion curves for shear-wave velocity profiles at the scale of a subsurface fluid reservoir, and is applied to field data from the North Sea. This work shows that when the data contain significant noise, including data uncertainties in the network gives more reliable mean velocity estimates. Whilst the post-training inversion process is rapid using neural networks, the method to estimate localised phase velocities in the first place is significantly slower. Therefore a computationally cheap method is demonstrated that combines gradiometry to estimate phase velocities and mixture density networks to invert for subsurface velocity-depth structure, the whole process taking a matter of minutes. This opens the possibility of real-time monitoring using spatially dense surface seismic arrays. For some monitoring situations a dense array is not available and gradiometry therefore cannot be applied to estimate phase velocities. In a third application this thesis uses mixture density networks to invert travel-time data for 2D localised velocity maps with associated uncertainty estimates. The importance of prior information in high dimensional inverse problems is also demonstrated. A new method is then developed to estimate density in the subsurface using a formulation of seismic interferometry that contains a linear dependence of seismic data on subsurface density, avoiding the usual direct trade-off between density and velocity. When wavefields cannot be measured directly in the subsurface, the method requires the use of a technique called Marchenko redatuming that can estimate the Green’s function from a virtual source or receiver inside a medium to the surface. This thesis shows that critical to implementing this work would be the development of more robust methods to scale the amplitude of Green’s function estimates from Marchenko methods. Finally the limitations of the methods presented in this thesis are discussed, as are suggestions for further research, and alternative applications for some of the methods. Overall this thesis proposes several new ways to monitor the subsurface efficiently using probabilistic machine learning techniques, discusses a novel way to estimate subsurface density, and demonstrates the methods on a mixture of synthetic and field data.