Joe Dellinger and Lev Vernik
Presented at the 62nd annual SEG meeting under the title "Do core-sample measurements record group or phase velocity?", pages 662-665. Appeared in the November 1994 GEOPHYSICS, pages 1774-1779.
© 1994 Joe Dellinger, Lev Vernik, and the SEG
Read just the INTRODUCTION, or see the entire text of the paper in postscript form.
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Figure 1: (GIF) (PS) Shale cores cut at 0, 90, and 45 degrees (perpendicular, parallel, and at a 45-degree angle to the layering respectively). The disks at the top and bottom of each core show the relative width of the P-wave transducers.
Figure 2: (GIF) (PS) The shapes of qP (outer curve), qSV (inner solid curve), and SH (dotted) wavefronts for the medium used in our numerical model. The 90, 45, and 0-degree labels show the direction of vertical for the corresponding shale-core orientations.
Figure 3: (GIF) (PS) Snapshots demonstrating two "ideal" core-sample experiments. The positions and sizes of the source and receiver transducers are indicated respectively by thick (red) horizontal lines at the bottom and top of the model. Top: a wide-source experiment for measuring vertical phase velocity. Bottom: a point-source to point-receiver experiment for measuring vertical group velocity.
Figure 4: (GIF) (PS) Snapshots showing the behavior of qP-waves in our 90 (top) and 45 (bottom) degree core-sample simulations. The dashed lines show the width of Vernik and Nur's cores; the thick (red) solid lines at the bottom and top show the size and positions of the P-wave source and receiver transducers.
Figure 5: (GIF) (PS) How the recorded signal in the 45-degree P-wave case depends on experimental geometry. In the left subplot the transducer width is fixed at 12 mm while the transducer offset is varied; in the right subplot the transducer offset is fixed at 0 mm while the transducer width is varied. Short horizontal lines mark first-break times.
Figure 6: (GIF) (PS) Snapshots showing the behavior of SH (top) and qSV (bottom) waves in our 45-degree simulation.