Resolving details in subsurface reservoir parameters from surface waveform data is a challenging problem, particularly when a reservoir is beneath a complex overburden whose properties are also poorly known. We have developed new metrics for detecting and quantifying errors in subsurface models that are well-suited for target-oriented inversion. Our metric, when combined with state-of-the art redatuming, aims at enabling waveform inversion for target volume parameters with no need to resolve model features elsewhere (e.g., in the overburden). We refer to these metrics as "interferometric objective functions" because they rely on extrapolation from reciprocity integrals commonly used in seismic interferometry. As in seismic interferometry, wavefield extrapolation retrieves the wave response between two points by combining observed data with an extrapolator that describes the response between the subsurface and the data boundary. When the source point is outside a target volume, either forward time or reverse time extrapolation produces the same field. However, because they physically rely on different components from the boundary data, the forward time and reverse time extrapolated fields are only equal when the model used is consistent with the real subsurface within the target volume. As such, we use the difference between the forward time and reverse time extrapolated fields to define subsurface- domain metrics that quantify model errors. Our approach thus provides a new metric for target-oriented nonlinear inversion in the subsurface domain, one that fundamentally differs from other subsurface domain metrics based on, e.g., focusing or image extensions.