Integrated geophysical data and Bayesian evidential learning approach for rockhead estimation and uncertainty quantification

Abstract

Rockhead estimation and uncertainty quantification are essential for underground constructions such as tunneling. However, deep boreholes that are required for rockhead determination are not always available at every site due to their high cost and logistical challenges. Furthermore, geological profiling using solely borehole data can introduce biases, especially when boreholes are sparsely distributed or limited in coverage. This study proposes a method that integrates geophysical data with borehole data for rockhead estimation and uncertainty quantification. Seismic surface wave data, specifically the Horizontal-to-Vertical Spectral Ratio (HVSR), are utilized for rockhead investigation. The Bayesian Evidential Learning (BEL) method employs the rockhead positions determined using HVSR to update the initial rockhead estimates derived from boreholes. The proposed HVSR-BEL approach was initially validated using a hypothetical case and applied subsequently to two real sites in Singapore for rockhead estimation, with results verified against nearby boreholes. The analysis of geophone spacing indicates that the ratio of geophone spacing to site size of 0.3 is cost-effective for achieving accurate rockhead estimation. When the ratio increases from 0.3 to 0.4, the relative difference of uncertainty reduction is most significant, reaching approximately 28 %. For Site 1, the uncertainty in rockhead estimation along the geophone lines using the proposed method is significantly reduced by 40 % to 60 % as compared with prior variance estimates. For Site 2, uncertainty reductions in the range of 5 % to 40 % are primarily observed near the geophone locations. The accuracy of the estimated rockhead at both sites is acceptable, with an average absolute error of 2.7 m. The proposed HVSR-BEL approach can provide reliable estimation of rockhead profile.