26 Seismic Imaging The processing classically applied to surface waves is based on spectral analysis and involves two steps. The first step is the construction of a dispersion curve (a plot of phase-velocity against frequency). A large number of techniques are available, which can be classified into two main classes: frequency–wavenumber or spatial auto-correlation. The next step aims to obtain shear wave velocity (i.e. stiffness) profiles as a function of depth and horizontal position along the seismic survey line. The profiles are calculated using one of the two iterative purposes: matching the experimental dispersion curves to a theoretical curve derived from forward analytical modeling or an automatic least-squares approach. A field example of surface waves processing is provided in chapter 6. 1.3 Example of field records A seismic spread is composed of a source spread and a receiver spread. In 2D seismic surveys, the sources and receivers are located on the same line which defines a 2D seismic profile. In 3D seismic surveys, the sources and receivers are usually located on 2 orthogonal lines: a line of sources and a line of receivers. The relative positions of the sources and receivers define the acquisition geometry. A seismic record is a set of seismic traces recorded at different receiver positions. The seismic trace represents the vibrations of the ground due to wave propagation generated by a seismic source. A geophysicist is able to identify the different seismic waves from a field record. For a simple geological model (a single horizontal layer over an infinite substratum), the arrival times T of the different body waves observed at a distance X from the source are given by simple T-X equations (T-X curves). Figure 1.4-a shows, for a line of receivers, different possible locations of source points. The distance between 2 geophones on the seismic line is 2 m. If the source point (green dots) is located at the extremities of the receiver spread, the spread is called an end-on spread and the shot is an in-line shot (2D). If the source point (yellow dots) is located on a line perpendicular to the receiver line, the spread is called a cross-spread and the shot is a cross-line shot (3D). The distance between the source position and the receiver position is called the Offset X. An offset can be decomposed in an in-line offset x, and a cross-line offset y, such that: X2 = x2 + y2 If y = 0, and if x = 0 corresponds to the middle of the line of receivers, the spread is called a split-dip spread, and the shot is a split-dip in-line shot (2D). Body waves can be differentiated by their T-X curves. Figure 1.4-b shows the ray paths and the T-X curves associated to the direct wave, refracted wave and the reflected wave. The arrival times of a surface wave are locally approximated by linear equations. Figure 1.4-c shows an in-line shot obtained with an end-on spread with the identification of the different waves. Figure 1.5 shows a cross-line shot obtained
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