Azimuthally averaged magnetic field and its vertical gradient in the 3D MHD simulation. Panel a) represents the magnetic field as a function of normalized radial distance r/R_spot and geometrical depth d−d_photo, where d_photo denotes the average geometrical depth of the quiet Sun photosphere at log τ = 0. Panel b) displays ∂B/∂d. The lower, middle, and upper curves in panels a) and b) show the log τ = 0.0, log τ = −0.9, and log τ = −2.5 levels, respectively. The black, blue, and red curves in panel c) 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. These geometric depth positions used in estimating (ΔB/ Δd) are shown by horizontal lines in panels a) and b). Shaded areas represent standard deviations. Dotted vertical lines in all panels indicate the umbra-penumbra boundary and the outer boundary of the sunspot.