A method for processing seismic data, comprising: a) predicting seismic data based on an earth model representing seismic properties of subterranean formations in the earth by determining that an earth model is an earth model in depth, simulating seismic data according to the earth model in depth, and converting the earth model in depth into an earth model in traveltime; b) determining a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data; c) projecting the difference into an earth model descent direction in depth by injecting a model of one or more seismic sources into the earth model in depth forward in time to produce a forward-propagating source wavefield, producing the earth model descent direction in depth by cross-correlating a back-propagated wavefield of the difference with the forward-propagated source wavefield, and translating the earth model descent direction in depth, using at least one processor, into an earth model descent direction in traveltime; and d) updating, using the at least one processor, the earth model in traveltime according to the earth model descent direction in traveltime, wherein the updated earth model in traveltime more accurately represents the seismic properties of the subterranean formations in the earth; and characterised in that translating the earth model descent direction in depth comprises applying an adjoint of a Jacobian of a time-to-depth function to the earth model descent direction in depth, wherein the time-to-depth function converts earth models parameterized by traveltime into earth models parameterized by depth. a) predicting seismic data based on an earth model representing seismic properties of subterranean formations in the earth by determining that an earth model is an earth model in depth, simulating seismic data according to the earth model in depth, and converting the earth model in depth into an earth model in traveltime; b) determining a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data; c) projecting the difference into an earth model descent direction in depth by injecting a model of one or more seismic sources into the earth model in depth forward in time to produce a forward-propagating source wavefield, producing the earth model descent direction in depth by cross-correlating a back-propagated wavefield of the difference with the forward-propagated source wavefield, and translating the earth model descent direction in depth, using at least one processor, into an earth model descent direction in traveltime; and d) updating, using the at least one processor, the earth model in traveltime according to the earth model descent direction in traveltime, wherein the updated earth model in traveltime more accurately represents the seismic properties of the subterranean formations in the earth; and characterised in that translating the earth model descent direction in depth comprises applying an adjoint of a Jacobian of a time-to-depth function to the earth model descent direction in depth, wherein the time-to-depth function converts earth models parameterized by traveltime into earth models parameterized by depth.