Abstract
Abstract. The hydraulic and mechanical characterization of fractures is crucial for a wide range of pertinent applications, such as geothermal energy production, hydrocarbon exploration, CO2 sequestration, and nuclear waste disposal. Direct hydraulic and mechanical testing of individual fractures along boreholes does, however, tend to be slow and cumbersome. To alleviate this problem, we propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian Markov chain Monte Carlo (MCMC) inversion of full-waveform tube-wave data recorded in a vertical seismic profiling (VSP) setting. The solution of the corresponding forward problem is based on a recently developed semi-analytical solution. This inversion approach has been tested for and verified on a wide range of synthetic scenarios. Here, we present the results of its application to observed hydrophone VSP data acquired along a borehole in the underground Grimsel Test Site in the central Swiss Alps. While the results are consistent with the corresponding evidence from televiewer data and exemplarily illustrate the advantages of using a computationally expensive stochastic, instead of a deterministic inversion approach, they also reveal the inherent limitation of the underlying semi-analytical forward solver.
Highlights
Tube waves are interface waves propagating along the borehole wall
The goal of our stochastic inversion approach is to estimate the posterior probability density function (PDF) p(m|d), which in stochastic terms describes the adequacy of a model m given the observed data d
To improve the estimation of the fracture compliance Z, we have extended the forward operator of Minato and Ghose (2017) to include transmission losses of P waves across fractures, by using the angle-dependent transmission coefficient described by the linear slip theory (Schoenberg, 1980)
Summary
Tube waves are interface waves propagating along the borehole wall. Primary sources of tube waves are ground roll passing over the well head (e.g., Hardage, 1981) or body waves encountering open fractures intersecting the borehole (e.g., Minato and Ghose, 2017; Greenwood et al, 2019b). A number of analytical techniques to calculate the tube-wave velocity (e.g., Chang et al, 1988; Norris, 1990) as well as semi-analytical methods to simulate complete waveforms (e.g., Cheng and Toksöz, 1981) have been published. GPa GPa GPa m m m m Pa−1 m Pa−1 m Pa−1 mmmms – is considered to be reached if Ris smaller than 1.2 for all parameters In this example, considering a burn-in phase of 30 % of the complete chains, we get R < 2 for most parameters, but only approximately a third of the parameters reach R < 1.2. Longer chains would be necessary to ensure a comprehensive exploration of the posterior PDF
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