The simulation of a zero-offset stack section from multicoverage seismic reflection data for 2-D media is a widely used seismic reflection imaging method that reduces the amount of data and enhances the signal-to-noise ratio. The aim of the common-reflection-surface stack is not only to provide a well-simulated zero-offset stack section but also to determine certain attributes of hypothetical wavefronts at the surface useful for a subsequent inversion. The main advantage of the common-reflection-surface stack is the use of analytical formulae that describe the kinematic reflection moveout response for inhomogeneous media with curved interfaces. These moveout formulae are valid for arbitrary shotreceiver pairs with respect to a common reference point and do not depend on the macro velocity model. An analytic reflection response that fits best to an actual reflection event in the multicoverage data set is determined by coherency analysis. We applied the common-reflection-surface stack to various synthetic and real data sets. For synthetic data sets, i. e. for a given model, data-derived as well as model-derived (forward calculated) wavefront attributes were computed. This enables us to verify the wavefront attributes determined by the commonreflection-surface stack exposing a wide agreement with the expected results. For real data sets we compare conventional stacking results and the common-reflection-surface stack.
S U M M A R YFinite difference (FD) simulation of elastic wave propagation is an important tool in geophysical research. As large-scale 3-D simulations are only feasible on supercomputers or clusters, and even then the simulations are limited to long periods compared to the model size, 2-D FD simulations are widespread. Whereas in generally 3-D heterogeneous structures it is not possible to infer the correct amplitude and waveform from 2-D simulations, in 2.5-D heterogeneous structures some inferences are possible. In particular, Vidale & Helmberger developed an approach that simulates 3-D waveforms using 2-D FD experiments only. However, their method requires a special FD source implementation technique that is based on a source definition which is not any longer used in nowadays FD codes. In this paper, we derive a conversion between 2-D and 3-D Green tensors that allows us to simulate 3-D displacement seismograms using 2-D FD simulations and the actual ray path determined in the geometrical optic limit. We give the conversion for a source of a certain seismic moment that is implemented by incrementing the components of the stress tensor.Therefore, we present a hybrid modelling procedure involving 2-D FD and kinematic raytracing techniques. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity.
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