Application of Wavelet De-Noising for Travel-Time Based Hydraulic Tomography

Abstract

Travel-time based hydraulic tomography is a promising method to characterize heterogeneity of porous-fractured aquifers. However, there is inevitable noise in field-scale experimental data and many hydraulic signal travel times, which are derived from the pumping test’s first groundwater level derivative drawdown curves and are strongly influenced by noise. The required data processing is thus quite time consuming and often not accurate enough. Therefore, an effective and accurate de-noising method is required for travel time inversion data processing. In this study, a series of hydraulic tomography experiments were conducted at a porous-fractured aquifer test site in Goettingen, Germany. A numerical model was built according to the site’s field conditions and tested based on diagnostic curve analyses of the field experimental data. Gaussian white noise was then added to the model’s calculated pumping test drawdown data to simulate the real noise in the field. Afterward, different de-noising methods were applied to remove it. This study has proven the superiority of the wavelet de-noising approach compared with several other filters. A wavelet de-noising method with calibrated mother wavelet type, de-noising level, and wavelet level was then determined to obtain the most accurate travel time values. Finally, using this most suitable de-noising method, the experimental hydraulic tomography travel time values were calculated from the de-noised data. The travel time inversion based on this de-noised data has shown results consistent with previous work at the test site.