Acquisition aperture correction in the angle domain toward true-reflection reverse time migration

Abstract

Due to incomplete aperture coverage and complex overburden structures, the migration process cannot provide a trueamplitude image even though a true-amplitude propagator is used. Amplitude compensation based on source-side illumination ignores the aperture effects on the receiver side, and it may fail to recover the true-reflection/scattering strength of a geologic structure from the image. The structural dip largely controls if the wave incident on the structure can be reflected back and received by the acquisition aperture, so it should be taken into account in removing the acquisition effects from the migration image. We derived a dip-angle domain amplitude correctionfrom the resolution theory. The stacked migration image created by reverse time migration was decomposed into common dip images, which were compensated individually by the corresponding amplitude correction factor. Then, we summed up the corrected images to form a final image. To construct the amplitude correction factor, we generated a monofrequency Green's function at the shot/geophone location and further decomposed it into incident/ scattered plane waves. They were combined based on Snell's law to construct correction factors for different dips. The final amplitude correction factor was formed by visiting all the shotgeophone pairs in the observation system. We devised efficient algorithms to make the amplitude correction more practical. We evaluated two numerical experiments, a five-layer model and the SEG/EAGE salt model, in which the amplitude correction led to a scalar/pressure image with an amplitude better matching the true impedance contrasts of subsurface structures, especially in areas with steep dips and in subsalt regions.

Full-wave seismic illumination and resolution analyses: A Poynting-vector-based method

“…Substituting equation 1 into equation 2, the depth image can be expressed as (e.g., Xie et al, 2005;Yan et al, 2014) Iðx;…”

“…For a timedomain method such as the finite difference, theoretically, one can use Fourier transform to convert the entire time-space wavefield into frequency domain. Then, the wavefield can be decomposed into its wavenumber component by using the local slant stacking or local fast Fourier transform (FFT), followed by calculating the PSF using equations 7 and 8 (Yan et al 2014). However, such a procedure often involves intensive calculations, huge input/output, and storage and is computationally inefficient.…”

“…Xie and Yang (2008) propose the illumination and resolution analysis method based on the time-domain local slowness analysis. Cao and Wu (2009a), Yan and Xie (2012), and Yan et al (2014) propose the illumination method based on the frequency-domain angle decomposition. An alternative method, which first calculates the point spreading function (PSF) by directly imaging a point scatter, followed by converting the PSF into the wavenumber domain for illumination analysis, was also proposed (Fletcher et al, 2012;Cao, 2013;Chen and Xie, 2015;Valenciano et al, 2015).…”

“…Yang et al (2013) use an illumination compensation strategy for wavefield tomography in the image domain. Cao (2013) and Yan et al (2014) test image correction for the full-wave RTM image.…”

The imaging resolution analysis for complex models applied in seismic survey design

“…There are several ways to get seismic illumination based on full-wave equation (Xie and Yang, 2008;Yang et al, 2008;Cao and Wu, 2009;Yan, et al, 2014), but the computation are unbearable. Xie, et al (2005Xie, et al ( , 2006, Wu, et al (2006); and Mao and Wu (2011) calculated the relationship among the PSFs, the pre-stack depth migration and the PSDM resolution based on the one way propagator, and thus the seismic wave equation illumination, the seismic migration imaging and the imaging resolution analysis are connected.…”