Stratigraphic Geometry Distribution And Uncertainty Analysis Based On Bayesian Machine Learning

Stratigraphic are sediments formed under complex tectonic movement and stress history in different geological ages.Therefore,the information distribution of strata in different positions in space has different degrees of differences,and usually has the characteristics of irregular stratified distribution in space.Geotechnical engineering structure design requires geological exploration in the site to obtain the required stratigraphic information,including determining the geometry and number of soil layers,and demarcating the stratigraphic boundaries between different soil layers.However,the geological data obtained through geological exploration in practical engineering are discrete,and the exploration for a specific site is usually too sparse,such as the borehole data in the exploration,to fully determine the geological data of the unexplored area in the site.In addition,due to the limitations of exploration data and site survey techniques,a comprehensive and direct observation of the subsurface formation structure is not possible,resulting in a high level of stratigraphic uncertainty,namely the uncertainty of the boundary between different layers of soil or rock.However,stratigraphic uncertainty is also critical to the reliability of the engineering design.Therefore,in order to provide sufficient and reliable basis for engineering design,it is necessary to study the geometric formation distribution and formation uncertainty analysis based on sparse drilling holes.Based on Markov random field(MRF)and Bayesian machine learning theory,stochastic geological modeling method is studied in this paper.On the basis of the model,the distribution and uncertainty of formation geometry under the condition of sparse borehole data are analyzed.The main work and conclusions are as follows:(1)Based on the newly constructed MRF model,a method is proposed to estimate the distribution and uncertainty of formation geometry by enhancing the model prior parameters under sparse drilling holes.Firstly,the model parameters were calibrated using Bayesian machine learning and visual inspection.The final formation estimation results and quantified formation uncertainty were obtained by random simulation using calibrated model parameters and sparse borehole data.Through a synthesis case and an engineering example,it is proved that this method can obtain good formation estimation and uncertainty results when facing the horizontal strata with normal deposition.(2)For inclined strata or complex strata with thin interlayers,an efficient borehole distribution scheme based on the newly constructed MRF model is proposed,and this borehole distribution scheme is used to estimate the geometric distribution of such strata and its uncertainty.Based on the analysis of the formation simulation results and the model posteriori parameters under two different borehole distribution schemes,an efficient borehole distribution scheme,namely the binary borehole distribution method(DBDA),which is driven by borehole data(independent of model prior parameters),is proposed,and the location of newly added boreholes is determined by information entropy adaptively.Examples of inclined strata and complex strata with thin interlayers demonstrate that the proposed scheme can obtain good formation estimation and uncertainty results in the face of different strata types.(3)In view of the problem that the formation initial field generated in a random way affects the formation estimation results and computational efficiency,an adaptive discriminant nearest neighbor Kharmonic mean distance(DANN-KHMD)classifier which can generate reasonable initial field is proposed.By integrating DANN-KHMD classifier,MRF theory and Bayesian framework,the MRF model is updated.The performance of the updated MRF model and other geological models in various strata is compared systematically.It is demonstrated that the model is helpful to obtain more accurate stratigraphic results and reduce the calculation cost.(4)In order to enable the updated MRF model to solve the problem of non-stationary complex strata,image warping technology(IWT)is integrated into the updated MRF model to build a model that can accurately predict non-stationary complex strata.Firstly,the borehole information of non-stationary field is transformed into the sequence of stationary field,and the result of formation geometry distribution is obtained based on the updated MRF model.Finally,the stratigraphic results are reversely transformed into non-stationary sequences by image warping technique,and the final stratigraphic distribution results are obtained.The performance of the models with and without the use of image warping technology in the face of various types of complex nonstationary field layer is systematically compared,and the superior performance of the integrated image warping technology model is verified.(5)In view of the limitations of two-dimensional geological model in dealing with practical engineering,the two-dimensional spatial correlation of soil mass is extended to three-dimensional spatial correlation,three-dimensional neighborhood system is established,and three-dimensional MRF geological model is constructed.A twodimensional research strategy for 3D problems is proposed to improve the computational efficiency of the model for 3D formation problems.By studying two different types of 3D synthesis cases and a 3D engineering example,it is proved that the 3D MRF geological model has excellent performance in different types of 3D strata.