Hampson russell velocity model krigging seismic velocities
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Physical seismic modelling generates a seismic response using a laboratory-scale geological model (Edwards, 1992). The physical model data yielded several unexpected high-amplitude events raypaths for these events were identified by comparing the numerical and physical model datasets, as well as by numerical analysis and graphical raytracing. In addition, similar numerical wedge models were produced using a finite-difference technique. We furthered the study of wedge reflections by analysing 2D seismic data recorded over simple wedge models in the physical modelling laboratory at the University of Calgary. Tuning occurs at a separation of τ d/2, (half the dominant period of the wavelet). b) Maximum amplitude of the reflection as a function of time separation.
![hampson russell velocity model krigging seismic velocities hampson russell velocity model krigging seismic velocities](https://i1.rgstatic.net/publication/319168649_Semiautomatic_seismic_well_ties_and_log_data_interpolation/links/59a06a4aaca2726b90114b76/largepreview.png)
a) Model seismic traces for the reflection from the top and base of a thinning bed (indicated by spikes). It shows the constructive interference resulting in tuning at a separation of half the dominant period of the wavelet and the approximately linear amplitude relationship for small separations or, equivalently, small bed thicknesses. In Figure 1b) the amplitude of the composite reflection event as a function of time separation of the reflections is displayed. Also shown are the traces corresponding to the associated reflection events from the two interfaces. The spikes in Figure 1a) indicate the reflection coefficients for the top and base of the bed, positioned in time as they become closer together. Widess found that as the bed thickness decreases further, below one eighth of a wavelength, the amplitude is, to a first-order approximation, linearly related to the thickness of the bed (Figure 1). When they are separated by half a period (two-way time), or a quarter wavelength (one-way distance), amplitude tuning, or maximum constructive interference, occurs.
![hampson russell velocity model krigging seismic velocities hampson russell velocity model krigging seismic velocities](https://www.researchgate.net/profile/Tom-Brocher/publication/250074855/figure/tbl3/AS:668689745575939@1536439467087/D-Velocity-Model-for-Pump-Station-10-Depth-km-V-p-km-sec-V-s-km-sec.png)
As the bed thickness decreases, the two events become closer together in time and start to interfere, forming a composite reflection event. When the bed thickness is large, the top-wedge and base-wedge reflections are separate. The wedge model considered by Widess involves two equal but opposite reflection coefficients, from the top and base of a thinning bed. Widess (1973, 1982) provided a foundation for understanding how the amplitude of reflection events changes as the thickness of a bed decreases below the dominant wavelength of the seismic data. Wedge models are important in seismic imaging they are analogous, for example, to wedges of carbonate rocks carried in thrust faults in the Rocky Mountain Foothills, edges of thin salt pillows, and irregular permafrost or basalt encountered in Canadian frontier basins. This study suggests that puremode and converted-wave multiples can be significant, high-amplitude events in data recorded in the presence of high-velocity rocks with a wedge-like geometry. Migration of the physical model data was accomplished using 2D poststack Kirchhoff time and depth migration. Amplitudes of the top-wedge and base-wedge reflections show additional complexities not observed in simple acoustic seismic models of the wedges. Finite-difference exploding reflector models, using numerical versions of the same wedge velocity models, were generated to assist in the identification of these events. Rather than producing simple tuning associated with thin beds, 2D zero-offset seismic surveys over these physical models showed a surprising number of high-amplitude dipping events corresponding to pure-mode, mixed-mode, and doubly-converted multiples within the wedge. Several physical seismic models of simple wedges were built to assess amplitude effects commonly associated with the classic ‘Widess’ wedge.