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

Time-lapse 4-D resistivity imaging inversion with positivity constraints

© 2019 24th European Meeting of Environmental and Engineering Geophysics. All rights reserved. Time-lapse resistivity surveys are used to monitor changes in the subsurface. In some situations, it is known that the resistivity will only decrease (or increase) with time. The 4-D ERT smoothness-constrained inversion method, that includes temporal smoothness constraint, has proved to be a robust method that reduces artefacts due to noise. However, in some cases, the time-lapse inverse models might show an increase in the resistivity with time where it is only expected to decrease. We modify the 4-D ERT inverse method to include a constraint that removes this artefact. The standard 4-D ERT inversion algorithm is first used to generate an initial model. If the resistivity is expected to decrease with time, for the model cells that show a resistivity increase with time, a truncation procedure is used where the resistivities of the different time models are reset to the mean value (corresponding to zero change with time). We then use the method of transformations in the inversion method that ensures the resistivities of the later time models are always less than the first model. The constraints can be modified so that they are only applied to selected regions in the model in cases where additional information is available