Channel design for ultra-high-density perpendicular magnetic recording requires fast and precise modeling to generate readback signals corrupted by media noise. In this paper, we present a geometric-dependent approach to model random readback pulses, where a three-dimensional head and media combination for 1 Tb/in 2 density design is considered in the micromagnetic simulation. A systematic approach is developed to extract media noise statistics from micromagnetic modeling and generate readback pulses based on a fast microtrack model incorporating nonlinear effects. The feasibility of the proposed model is demonstrated through bit-error-rate (BER) simulation of a turbo equalization scheme over a low-density parity-check (LDPC) coded, general-partial-response (GPR) equalized perpendicular recording channel.