Imaging the total wavefields by reflectivity estimation using amplitude-normalized wavefield decomposition: Field data example

Abstract

To combine imaging information of up- and downgoing wavefields using primaries and multiples, we have developed an imaging framework based on the subsurface impulse response. The latter is expressed at every depth level by a Fredholm integral equation defined in terms of the amplitude-normalized upgoing pressure and downgoing vertical velocity wavefields. The subsurface impulse response can be obtained by inverting the matrix form of the integral equation. By performing a multidimensional deconvolution (MDD) of the upgoing components by the downgoing components, this procedure gives the reflectivity matrix. By assuming locally reacting media or lateral shift invariance, we can describe how the MDD can reduce to simpler deconvolution imaging conditions. Based on an example acquired with dual-sensor towed streamers and simultaneous sources, we have developed a real data application of imaging the total up- and downgoing wavefields by reflectivity inversion. The total upgoing wavefield used in the imaging scheme is composed of the scattered energy from primaries and multiples. The primary reflected wavefield is generated by a direct downgoing source wavefield, which is mostly passing the acquisition surface at offsets smaller than the nearest data channel. Hence, the most relevant part of the direct wavefield is not measured in the studied example. From near-field pressure measurements, we predict the missing direct arrivals needed to image the primary reflected wavefield; we then synthesize the total downgoing wavefield by adding the downgoing scattered energy. By downward extrapolating the total up- and downgoing wavefields, a structural image is obtained by extracting the zero-spatial and temporal lags of the reflectivity matrix (computed by MDD of the decomposed wavefields). The obtained image is compared with the results computed from deconvolution imaging conditions. Furthermore, calculating the reflectivity matrix naturally allows for extracting the angle-dependent information of the subsurface.