Wavefield tomography using extended images

Estimating an accurate velocity model is crucial for seismic imaging to obtain a good understanding of the subsurface structure. The objective of this thesis is to investigate methods of velocity analysis by optimizing seismic images. A conventional seismic image is obtained by zero-lag crosscorrelation of wavefields extrapolated from a source wavelet and recorded data on the surface using a velocity model. The velocity model provides the kinematic information needed by the imaging algorithm to position the reflectors at correct locations and to focus the image. In complex geology, wave-equation migration is a powerful tool for accurately imaging the earth’s interior; the quality of the output image, however, depends on the accuracy of the velocity model. Given such a dependency between the image and model, analyzing the velocity information from the image is still not intuitive and often ambiguous. If the nonzero spaceand time-lags information are preserved in the crosscorrelation, the output are image hypercube defined as extended images. Compared to the conventional image, the extended images provide a straightforward way to analyze the image quality and to characterize the velocity model accuracy. Understanding the reflection moveout is the key to developing velocity model building methods using extended images. In the extended image space, reflections form coherent objects which depend on space (lags) and time (lags). These objects resemble cones which ideally have their apex at zero space and time lags. The symmetry axis of the cone lies along the time-lag axis. The apex of the cone is located at zero lags only if the velocity model is accurate. This corresponds to the situation when reflection energy focuses at origin in both the spaceand time-lag common-image gathers (the slices at zero time and space lags, respectively). When the velocity model is inaccurate, the cone shifts along the time-lag axis. This results in residual moveout in space-lag gathers (zero time-lag slice) and defocusing in