Time-lapse joint inversion of geophysical data is required to image the evolution of oil reservoirs during production and enhanced oil recovery, CO_2 sequestration, geothermal fields during production, and to monitor the evolution of contaminant plumes. Joint inversion schemes reduce space-related artifacts in filtering out noise that is spatially uncorrelated, and time-lapse inversion algorithms reduce time-related artifacts in filtering out noise that is uncorrelated over time. There are several approaches that are possible to perform the joint inverse problem. In this work, we investigate the structural crossgradient (SCG) joint inversion approach and the crosspetrophysi?al (CP) approach, which are appropriate for time-lapse problems. In the first case, the inversion scheme looks for models with structural similarities. In the second case, we use a direct relationship between the geophysical parameters. Time-lapse inversion is performed with an actively time-constrained (ATC) approach. In this approach, the subsurface is defined as a space-time model. All the snapshots are inverted together assuming a regularization of the sequence of snapshots over time. First, we showed the advantage of combining the SCG or CP inversion approaches and the ATC inversion by using a synthetic problem corresponding to crosshole seismic and DC-resistivity data and piecewise constant resistivity and seismic velocity distributions. We also showed that the combined SCG/ATC approach reduces the presence of artifacts with respect to individual inversion of the resistivity and seismic data sets, as well as with respect to the joint inversion of both data sets at each time step. We also performed a synthetic study using a secondary oil recovery problem. The combined CP/ATC approach was successful in retrieving the position of the oil/water encroachment front.
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