Marchenko methods in a 3-D world. Issue 1 (10th October 2019) - Lomas, A; Curtis, A
SUMMARY: Marchenko methods are a suite of geophysical techniques that convert seismograms of energy created by surface sources and measured by surface receivers into seismograms that would have been recorded by a virtual receiver at an arbitrary point inside the subsurface—an operation called redatuming. In principle these redatumed seismograms contain all contributions from direct, primary (singly-reflected) and multiply-reflected waves that would have been recorded by a real subsurface receiver, without requiring prior information about interfaces that generated the reflections. The potential of these methods for seismic imaging and redatuming has been demonstrated extensively in previous literature, but only using 1-D and 2-D Marchenko methods. There remain aspects of the methods that are poorly understood when applied in a 3-D world, so we investigate the application of Marchenko methods to 3-D data, subsurface structures and wavefields. We first show that for waves propagating in three dimensions, Marchenko methods can be applied to seismic data collected using both linear (so-called 2-D seismic) and areal (3-D seismic) acquisition arrays. However, for 2-D acquisition arrays the Marchenko workflow requires additional dimensionality correction factors to obtain accurate solutions, even in a subsurface that only varies with depth. Without these correction factors phase errors occur in redatumed Marchenko estimates; these errors propagate through the Marchenko algorithm and create depth errors in the Marchenko images. Furthermore, applying Marchenko methods to fully 3-D seismic wavefields recorded by linear (2-D seismic) arrays that contain out-of-plane reflections deteriorates surface-to-subsurface Green's function estimates with spurious energy and resulting images are less accurate than those created using 'conventional' imaging methods. The application of fully 3-D Marchenko methods using data recorded on areal arrays solves both of the above problems, creating accurately redatumed wavefields and images with reduced artefact contamination. However, it appears that source–receiver spacing at most of $λ _A /4$ is required for accurate results using existing Marchenko methods, where λ A is the dominant wavelength and in many real 3-D seismic acquisition scenarios this is impractical.