Implementing positivity constraints in 4-D resistivity time-lapse inversion

Over the last 25 years 2-D and 3-D resistivity surveys have been used for a wide range of engineering, environmental, hydrological and mineral exploration surveys (Loke et al. 2013). In some surveys, the purpose includes the monitoring of subsurface changes with time (Chambers et al. 2014). The 4-D smoothness-constrained inversion method (Loke et al. 2014) has proved to be a stable and robust method for the inversion of time-lapse data sets. This method inverts the data sets measured at different times simultaneously and it includes a temporal smoothness constraint to ensure that the resistivity changes in a smooth manner with time. In some surveys, such as infiltration experiments (Kuras et al. 2016), it is known that the subsurface resistivity should only decrease (or increase) with time. As the standard 4-D inversion method does not explicitly constrain the direction of the changes with time, this could result in artefacts where an increase in the resistivity is obtained in the inverse model while it is only expected to decrease (or vice versa). In this paper we describe a modification of the 4-D smoothness-constrained inversion method to remove such temporal artefacts.