Cross-hole resistivity inversion method constrained by prior information of incomplete boundary

The cross-hole electrical resistivity tomography method is a refined detecting method, and it has been well applied in the exploration of small and medium-sized geological anomalies such as caves and boulders. However, it’s poor in identifying the interfaces of geological anomalies. By geological drilling, seismic or ground penetrating radar methods,it is able to recognize the distinct lithological interface more clearly than the cross-hole electrical resistivity tomography. From the perspective of constrained inversion theory, a new cross-hole resistivity inversion method constrained by prior information of incomplete boundary is proposed. Firstly, the complete description of the "virtual internal region" radiated from the known partial boundary is defined, which is usually the interface of the geological anomaly detected by the ground penetrating radar. The construction of morphological constraints are then achieved by setting the external constraints with "same smoothness",boundary constraints of "anisotropic smoothness" and internal constraints of "gradient smoothness". Further, by adding these prior information constraints into the cross-hole resistivity inversion equation,the new inversion method carrying with known incomplete boundary information is formed. A numerical inversion test and a physical model test on detection of boulders are used to verify the effectiveness and feasibility of the new method. The tests results show that the new method has a significant improvement on the boundary recognition of the anomalous body.