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Phase-shift migration of approximate zero-offset teleseismic data

Jeff Shragge


A hybrid of traditional survey-sinking migration is derived that is applicable to teleseismic wavefields. To reconfigure teleseismic data to an approximate equivalent of zero-offset, an adjoint linear moveout shift is applied. This transformation enables the straightforward development of phase-shift operators to downward continue the modified teleseismic data. This method also affords an opportunity for imaging earth structure with a variety of forward- and backscattered modes through appropriate choices of wavefield velocities. This method is applied to a synthetic teleseismic data set, and several migration results are presented to demonstrate its effectiveness.

The use of idealized plane-wave sources in exploration seismic imaging is well documented Claerbout (2001). One situation where plane-wave sources are often realized is in imaging with earthquake waves recorded at large epicentral distances (i.e. teleseismic distances). Many advances in teleseismic imaging have stemmed from adapting existing seismic exploration techniques to the teleseismic context. In particular, much recent effort has been centered on reconfiguring multi-dimensional Kirchhoff-based migration/inversion formulations for teleseismic plane-wave sources and acquisition geometry Bostock et al. (2001).

Multi-dimensional wave-equation migration methods are not applied widely in teleseismic imaging. Although the advantages of wave equation-based methods over their Kirchhoff counterparts are known to explorationists, two issues persistently hinder their use in the teleseismic community. One problem is that Fourier-based methods are difficult to apply to data of non-uniform spacing. In practice, this is often observed because of practical limitations in acquisition. A second issue is that the geometry of teleseismic sources and data needs to be reconciled with the geometry of traditional pre- and post-stack migration formulations. Hence, both of these issues must be addressed before wave-equation migration algorithms are applied.

The aim of this paper is to show that, with only minor adjustments, traditional wave-equation migration is readily applicable to teleseismic wavefields (i.e. by accounting for the effects of upward propagating plane-wave sources). This paper specifically addresses the second issue by demonstrating that the application of an adjoint linear moveout (LMO) operator successfully reconfigures teleseismic data to an approximate equivalent of traditional zero-offset data. Consequently, migration of data with a hybrid of traditional survey-sinking methodology becomes possible. The method can use different source and receiver wavefield velocities, which permits imaging with converted waves present in most three-component earthquake records. Although this paper does not address the first issue directly, there is at least one method to successfully re-grid irregularly spaced teleseismic data to a regular mesh Curry (2003).

I begin with a general discussion of what source and receiver wavefields mean in the context of teleseismic imaging. I develop modified double square root operators appropriate for downward continuing teleseismic data, and discuss the choice of velocities required to image different converted modes. The method is then applied to a synthetic data set generated by finite differencing plane wave sources through a simplified lithospheric subduction zone model.

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