histamine dihydrochloride Motivation and significance The im
Motivation and significance The imaging method of seismic full waveform histamine dihydrochloride (FWI) aims at utilizing the complete information content of measured seismic waveforms for deriving an earth model. Established methods iteratively derive a series of models converging to the solution of the inverse problem by minimizing a waveform misfit criterion. Starting off with an initial model of sufficient quality, in each iteration first the seismic forward problem is solved, i.e. seismic wave propagation is simulated with respect to model assuming the mechanisms of the involved seismic sources as known (or inverting for source properties jointly). On the basis of the observed residual between the measured seismic waveforms and the synthetic ones computed with respect to model , then a model is derived which best reduces the misfit criterion in use. One group of currently used methods are based on the (pre-conditioned) conjugate gradient of the misfit functional with respect to the model parameters [1–4]. Another group of currently used methods minimize the misfit criterion by Newton-like [5–7] or Gauss–Newton methods [8–11] which utilize (approximations of) higher order derivatives of the misfit functional with respect to the model parameters for deriving a model update. These generally have faster convergence properties than gradient-based methods but can be subject to higher computational costs. Established FWI codes (for gradient-based as well as Newton-like or Gauss–Newton methods) infer derivatives of the misfit criterion by combination of the wavefield originating from the seismic source with the wavefield of backpropagated residuals originating from the receiver positions. Thus, solving the forward problem, i.e. simulating seismic wave propagation, is strongly interwoven with computing the derivatives and is usually implemented in the same code which thereby has a rather monolithic character. Seismic FWI is a complex problem that requires demanding numerical computations as well as handling of large amounts of data on high-performance computing systems. Thereby, complex workflows arise that need to be handled by researchers in a consistent and flexible way. From a geophysical point of view, FWI applications may have a wide range in terms of scale (from global to ultra-sonic), considered wave types and frequencies. Hence, it is desirable to have modular and extendable, thus efficient, solutions to FWI. Nowadays, new developments follow this approach and try to establish the above stated inversion strategies within integrated systems or toolboxes providing flexibility in choosing inversion methods and in general follow modularized approaches to solving the seismic inverse problem [12–16]. As one variety of Gauss–Newton FWI, the scattering-integral (SI) method [9,17] is particularly suitable for modularization, but is not considered by one of the above stated modular approaches. The fundamental steps of solving the forward problem and deriving a model update can be naturally decoupled, since the computation of the involved derivatives of waveform data with respect to the model parameters (called waveform kernels) is done by combination of the wavefield originating from the seismic source with Green’s functions originating from the receiver positions that are independent of actual measured seismograms. Green’s functions can be re-used in different source–receiver combinations serving as generalized backpropagations. This motivates to pre-compute the required wavefields and store them to hard disk before computing the waveform kernels. As a consequence, it becomes possible to solve the forward problem independently using established wave propagation codes, which are connected to the inversion algorithm by a suitable interface. Hence, this approach allows to independently develop inversion concepts and regularization methods on one hand, and to develop the in general demanding forward codes, e.g. with the objective of computational performance, on the other hand.