Simulations of large-scale neural activity are powerful tools for investigating neural networks. Calculating measurable brain signals like local field potentials (LFPs) bridges the gap between model predictions and experimental observations. However, accurately simulating LFPs from large-scale models has traditionally required highly detailed multicompartmental neuron models, posing significant computational challenges. Here, we demonstrate that a kernel-based method can efficiently and accurately estimate LFPs in a state-of-the-art multicompartmental model of the mouse primary visual cortex (V1). Beyond its computational efficiency, the kernel method aids analysis by disentangling contributions of individual neuronal populations to the LFP. Using this approach, we found that LFPs in the V1 model were dominated by external synaptic inputs, with local synaptic activity playing a minimal role. Our findings establish the kernel method as a powerful tool for LFP estimation in large-scale network models and for uncovering the synaptic mechanisms underlying brain signals.