Hessian kernels plotted at the surface of the Earth. The position δv_S1 is indicated by ○. Top row: The individual Hessian kernels and (from left-hand side to right-hand side). The kernel has two contributions, labelled F and S. Contribution F represents the primary influence zone that corresponds to the approximate Hessian. Contribution S, encircled by a dotted curve, is a secondary influence zone where second-order scattering affects the measurement. (In Section 5.1, we show how the approximate Hessian can be computed separately.) Bottom row: Composite Hessian kernel . The the contribution from second-order scattering is again encircled by a dotted curve and marked with S.