Joint 3D seismic travel time and full channel electrical resistivity inversion with cross gradient structure constraint

Abstract:

Near surface geophysical exploration for the purpose of engineering design or construction，For this reason, geophysical imaging demands a higher resolution and a better quantitative interpretation. Seismic travel time tomography and direct current resistivity tomography are two main methods for the near surface survey. Because of the limited coverage of observation system and the complex physical relationship between physical parameters and observations, individual geophysical method suffers issues of non-uniqueness and resolution limitation to some degree.

We have developed a joint inversion method to combine seismic travel time tomography and full channel resistivity tomography. For the full channel resistivity survey, it uses two electrodes for power supply and all the other electrodes for recording. Compared with the traditional resistivity method, it collects more data and has a better model converge. Our joint inversion strategy relies on the structure constraint enforced through minimizing cross gradients between seismic velocity and resistivity models (Gallardo, 2003). For resistivity tomography, sensitivity kernels are obtained through the adjoint method by solving the electrostatic field equation with the finite-difference method. For seismic travel time tomography, ray paths and travel times are calculated using the fast marching method.

We have tested our joint inversion method for a 2D cross-hole problem where two small zones with high and low velocity/resistivity anomalies. Seismic/electrical sources/receivers are installed in two boreholes. For separate seismic inversion, the smearing effect is evident and two anomaly zones are distorted and misplaced. For separate electric resistivity inversion, although two anomaly zones are positioned correctly their values are not accurate. By joint inversion, two velocity anomaly zones are clearly imaged and the smearing effect is greatly reduced. In comparison, for the resistivity model, the two anomaly zones have more accurate resistivity values but their structures are only slightly changed. Compared to separate inversions, joint inversion actually produces two models that better fit their respective data and at the same time are more similar in structure.