Reconstruction des images bidimensionnelles de leves de radar geologique en forage (French text).

摘要

In this thesis, a new GPR tomographic method based on geostatistical cokriging and cosimulation is proposed.; Commonly used crosshole radar velocity tomography algorithms estimate 2D slowness models (reciproqual velocity) in the plane between the boreholes using the measured direct wave travel times from the transmitter (located in one of the hole) to the receivers (located in the other hole).; In this study, three classical tomography algorithms are used (LSQR, CG, SIRT). These algorithms do not explicitly consider the spatial structure of the slowness field and the correlation between the travel times.; Using the straight ray approximation, a method to estimate the slowness covariance model by using the experimental covariances of the travel times is presented. The slowness covariance model is chosen to provide a close match between the computed and the experimental time covariances. Then cokriging of the slowness field using time data is performed. The cokriging provides a smooth interpolation. To obtain inverted fields with more realistic variations, conditional geostatistical simulations are realized. This enables identifying stable features of the inverted fields.; Cells with known velocities, for example the cells crossed by the holes, provide velocity constraints which are easily implemented. The proposed approach is compared to the classical LSQR algorithm using a synthetic model and real data collected for geotechnical evaluation in a karstic area. In each case, constrained and non-constrained LSQR, cokriging and simulation were performed. The tomographies on synthetic model show that geostatistical methods provide comparable to or better results than LSQR. The geostatistical simulations also allow computing the standard deviation of the slowness within each cell of the inverted field. Stable characteristics and uncertain features of the inverted models can then be easily identified.; The linear relation between travel time and slowness is valid until the true raypaths are known. At first iteration, it is not the case, because the raypath depends on the velocity field distribution. A well known technique is to update the raypath after each iteration taking into account the velocity cell constrasts. The raypath are used to compute a new cokriging and simulation estimate. The iterative process ends as the difference between computed and measured travel times becomes small enough. It is possible to linearize the relation between amplitude and attenuation. The same algorithms developped for velocity tomography are used.; For both method, additional velocity constraints reduce uncertainty and improve spatial resolution of the inverted velocity field. Also, the simulation on synthetic model increases the spatial resolution compared to LSQR. It is demonstrated that the method is robust with regard to an acceptable level of random noise on velocity constraints. (Abstract shortened by UMI.)