Computation Charts for Linear Increase of Velocity With Depth

Abstract

Computation charts are presented which reduceor eliminatecalculationsof correlation and wavefront depth charts. A series of depth charts are made for particular values of the velocity increment solving the time-depth relation for all possible initial velocities of the equation y= (Vo/k)(P-I). From these charts, the average velocity-depth curves are obtained, and also the velocity function to be used on a prolect determined from velocity shooting by comparison to the theoretical average velocity-depth curves. For wave-front depth charts! a series of families of curves are plotted for the full range of velocity increments and all initial velocltles for the equations of the instantaneous center of the wave front, z= (I/o/k) (co& kt/2-r),and the radius of the wave front, r= (l' o/k) (sin/z kt/zj. The relation between k and &' i' J for a range of times is plotted, and therefrom the value of ekrjz obtained for the particuiarvelocity~ increment-fr,r~ th~~solutiorr of-the equatjon t-an 8/z=tan ho/2 &it: Finally, curves for a series of tan e/n against initial velocity curves are plotted for a series of step out times, and therefrom the value of tan O/n = tan &/2. e hi/*, or the angle of dip, 0, is obtained. This latter family of curves can be used to determine the variation of dip with variation in initial velocity in highly folded areas. The latter set of curves is useful for the construction of a time-step-out timedip-depth-offset chart which is used for direct plotting of offset-depth-dip positions of reflecting horizons, or as a trace-analysis underlay chart. Ih-TRODUCTIONThe majority of reflection seismograph depth calculations are based on the linear increase of velocity with depth. The velocity function which is to be used is usually determined from the refraction interval velocity-depth curve, or the average velocity-depth curve by least squares calculation. The interval velocitydepth and the average velocity-depth curves are obt.ained from well, reflection velocity, or refraction velocity shooting. The correlation depth charts based on the chosen velocity function are calculated, but if the survey is in an area of dips greater than so, the necessary calculations are made for time-depth-offset charts.In order to limit calculations to the minimum, charts have been designed from which the average velocity-depth, the time-depth, center point and radius for wave front charts, and the angle-offset-depth for step out times may be obtained for the condition of linear increase of velocity with depth. The equations used have not been derived since they are standard and may be found in current literature and geophysical texts. THEORYThe initial condition for the linear increase of velocity with depth is that I' , = I/o + ky.(1) * Manuscript received by the Editor December 5, 1949. 7 Formerly with Venezuelan Atlantic Refining Company, currently independent consultant. Downloaded 08/11/15 to 128.112.200.107. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

Structural Effect on Hydrocarbon Trapping, North Western Nile Delta, Egypt

“…where: V y is the velocity to a depth y, V 0 is the initial velocity and K y is the slope of the instantaneous velocity-depth line given by the equation of [16]. The average velocity is used for the time to depth conversion.…”