Despite over twenty years of research and application, assisted seismic history matching (ASHM) remains a challenging problem for the energy industry. ASHM attempts to optimise the subsurface reservoir model parameters by matching simulated data to the observed production and time-lapse (4D) seismic data, leading to greater confidence in the assimilated models and their predictions. However, ASHM is a difficult and expensive task that has had mixed results in industry, and a new approach to the problem is required. In this work, we examine ASHM from a different perspective by exploring the topology of the optimisation fitness landscape. Many methods for fitness landscape analysis (FLA) have been developed over the past thirty years, but in this work, we extend the use of local optima networks (LONs) to the realworld and computationally expensive ASHM problem. We found that the LONs were different for objective functions based on both production data and time-lapse reservoir maps, and for each dimensionality. Objective functions based on well pressures and oil saturation maps had the highest success rate in finding the global optimum, but the number of suboptimal funnels increased with dimensionality for all objective functions. In contrast, the success rate and strength of the global optima decreased significantly with increasing dimensionality. Our work goes some way to explaining the mixed results of real ASHM problems in industry, and demonstrates the value of fitness landscape analysis for real-world, computationally expensive problems such as ASHM.