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Direct forecasting has recently been proposed as a method for uncertainty quantification in non-linear inverse problems. The method directly forecasts a desired future response without the need for full model inversion. The method has been successfully applied to a range of subsurface field cases, such as groundwater, shallow and deep geothermal and oil/gas predictions. In this paper, we extend the framework of direct forecasting to do what it was avoided to do in the first place: model inversion. The idea is simple: replace the prediction variables with the model variables. Two challenges now occur: the model dimensions, in subsurface realm at least, are much higher than data variables. This is the case in the paper where we consider dynamic data and high-dimensional spatial models for geological structure and properties. Secondly, the regression applied in the original method, being a linear regression of prediction variables on transformed data, is unlikely to lead to models that match field observations. We address these challenges first by adding a variable selection method (through global sensitivity analysis) for the model space. More specifically, we select those model components that are most sensitive to data variables only. The linear assumption is mitigated by a sequential updating of sensitive model variables. We illustrate our method on a Libyan oil reservoir with complex geological uncertainty involving structural, petrophysical and fluid model parameters. • A method for joint inversion of both global and spatial parameters. • Extension of direct forecasting to directly invert model variables. • Application to a real field oil reservoir in Libya. [ABSTRACT FROM AUTHOR]