22 Seismic Imaging Box 1.1 Snell’s law. Angular relationships between incident, reflected and transmitted rays for the various wave types in the case of an incident compressional wave with a wave-front perpendicular to the plane of the diagram. Particle motion is represented schematically (after Lavergne, 1989). When a P or SV-wave strikes an interface at an angle of incidence not equal to zero, four waves are generated: two transmitted (one P and one SV-wave) and two reflected (again, one P and one SV-wave). The angular relationships between the propagation directions of each of these waves are given by Snell’s law (Box 1.1). The creation of an S-wave from a P-wave, or vice versa, is a phenomenon called mode conversion. For cylindrical structures, SH-waves propagate without mode conversion. Box 1.2 gives the wave equations associated with particle displacements (u, v, w) observed in the (x, y, z) directions for a seismic profile oriented in the x-direction and perpendicular to the axis of a cylindrical structure on the y-axis. Particle movements in the y-direction, associated with SH-waves, are governed by a simple equation involving only the displacement v along y and the velocity VS, hence there can be no mode conversion (Box 1.2, Eq. (2)). Equations are more complex for the u and v displacements associated with the propagation of P and SV-waves (Box 1.2, Eq. (1)). The wave equation may be used to calculate synthetic seismograms that are the response of the subsurface to an excitation. For a distribution of velocities (VP and VS) and densities ρ, a synthetic seismogram can be calculated for a given acquisition geometry. The synthetic seismogram can be compared with an actual field record registered with the same geometric parameters (source and receiver positions). The distribution of velocities and densities can be updated so that an
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