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How to evaluate data space and model space

What is a good observed data space? What is a good estimated model space? It is difficult to answer these two questions, because the answers depend on the practical applications. Up to now, the acquisition systems basically can be divided into three classes: Case $\textbf{d}_{1}$: Full-area acquisition system. A 3D survey area is discretized into a regular grid, and each grid point has a receiver point and a shot point. This is an ideal case, in which a data set has an even azimuth interval, offset interval and CMP interval. Such a data set is a complete one. In practice, to minimize acquisition costs, a receiver is put at each grid point, and the shot points are arranged depending on the on-site situations. Case $\textbf{d}_{2}$: Wide-azimuth acquisition system with partial sacrifice of cross-line aperture. The land acquisition system belongs to this category. It is difficult to maintain even azimuth intervals and even offset intervals because of complex variations of the surface and near-surface, and the consideration of acquisition efficiency and costs. Commonly, we have to move the shot point to an advantageous location, sacrificing spatial regularization. Case $\textbf{d}_{3}$: Narrow-azimuth acquisition system with complete sacrifice of cross-line aperture. The present marine acquisition system belongs in this category. It is easy to achieve an even azimuth and even offset, but the data set is incomplete because it lacks the cross-line aperture. This acquisition system is not suitable in cases of complex structure variance along the cross-line direction. Similarly, we can divide the model space into three categories: Case $\textbf{m}_{1}$, with a flat surface and some flat subsurfaces; Case $\textbf{m}_{2}$, with a flat surface and some complex subsurfaces; and Case $\textbf{m}_{3}$, with a rough topography and some complex subsurfaces. Table 1 gives the relationship between the data space and model space in different cases.
  d_1 d_2 d_3
m_1 even azimuth interval, even offset interval and even CRP illumination; a complete data set uneven azimuth interval, uneven offset interval and basically even CRP illumination; even azimuth interval, even offset interval and even CRP illumination
m_2 even azimuth interval, even offset interval and uneven CRP illumination uneven azimuth interval, uneven offset interval and uneven CRP illumination even azimuth interval, even offset interval and uneven CRP illumination
m_3 even azimuth interval, uneven offset interval and uneven CRP illumination uneven azimuth interval, uneven offset interval and uneven CRP illumination even azimuth interval, uneven offset interval and uneven CRP illumination
From the table, we know that wide-azimuth acquisition gives wider aperture in the cross-line direction. However, this also causes an uneven azimuth interval and uneven offset interval, which will result in a noisy image. Narrow-azimuth acquisition can give an even azimuth interval and even offset interval but sacrifices the cross-line aperture. Our conclusion can be summarized with following statements: In Case $\textbf{m}_{1}$, the regularization of the data space yields an even sampling of the model space. In a geologically symple medium, a good data set is one with an even azimuth interval, an even offset interval and an even CMP interval. In Cases $\textbf{m}_{2}$ and $\textbf{m}_{3}$, a good data set is one with an even azimuth interval, an even offset interval and an even CRP illumination. In practice, even CRP illumination commonly means that a data set is irregular. There exists a trade-off between the even illumination and the regular data set. Since an irregular acquisition configuration generally yields a noisy image, a field data set should be preprocessed to be regular. On the other hand, bad illumination causes a vague image or no image, or yields false amplitude; therefore, the illumination deficiency should be compensated with other information from well-logging, rock physics or geology data. From the perspective of prestack imaging, assuming the macro-velocity model is accurate enough, a good model space can be defined as one which has an amplitude-preserving angle gather on each point of a reflector at each azimuth, which is the main goal of seismic-wave imaging (, ).
next up previous print clean
Next: relationship between data space Up: Expression of Data space Previous: Expression of Data space
Stanford Exploration Project
5/3/2005