Continuum intensity (panel a) and the magnetic field gradient maps from a 3D MHD simulation of a sunspot computed by Rempel (2012). Panels b–d) depict (ΔB/ Δd) estimated between d−d_photo = 384 km  and 192 km, d−d_photo = 192 km  and 0  km,  and d−d_photo = 0 km  and –192 km, respectively. Here d_photo signifies the depth at which on average τ = 0 is reached in the quiet Sun. White circles in all panels represent the averaged umbra-penumbra boundary and the outer boundary of the sunspot.