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The most important resources to fulfill today's energy demands are fossil fuels, such as oil and natural gas. When exploiting hydrocarbon reservoirs, a detailed and credible model of the subsurface structures is crucial in order to minimize economic and ecological risks. Creating such a model is an inverse problem: reconstructing structures from measured reflection seismics. The major challenge here is twofold: First, the structures in highly ambiguous seismic data are interpreted in the time domain. Second, a velocity model has to be built from this interpretation to match the model to depth measurements from wells. If it is not possible to obtain a match at all positions, the interpretation has to be updated, going back to the first step. This results in a lengthy back and forth between the different steps, or in an unphysical velocity model in many cases. This paper presents a novel, integrated approach to interactively creating subsurface models from reflection seismics. It integrates the interpretation of the seismic data using an interactive horizon extraction technique based on piecewise global optimization with velocity modeling. Computing and visualizing the effects of changes to the interpretation and velocity model on the depth-converted model on the fly enables an integrated feedback loop that enables a completely new connection of the seismic data in time domain and well data in depth domain. Using a novel joint time/depth visualization, depicting side-by-side views of the original and the resulting depth-converted data, domain experts can directly fit their interpretation in time domain to spatial ground truth data. We have conducted a domain expert evaluation, which illustrates that the presented workflow enables the creation of exact subsurface models much more rapidly than previous approaches.