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Summary form only given. The soft magnetic underlayer is a crucial component of a perpendicular recording medium. This is because it helps the write process by intensifying the vertical component and decreasing the in-plane components of the write field. Most of our understanding of underlayers is based on the method of images. Although computationally fast, the method of images presents only an idealized case because its results do not depend on the underlayer's magnetic or geometric properties. Furthermore, the theory behind the method of images assumes that the underlayer is isotropic and does not saturate which is not true for today's underlayers. A micromagnetic model of the underlayer should provide a deeper understanding of how an underlayer performs under a diverse set of conditions. In agreement with previously reported results, our work shows that the induced image field strength in the medium decreases with track-width. Our results show, however, that under the right conditions the strength of the induced image field can be larger from a three-dimensional write field than from a two-dimensional write field.