A mathematical analysis to determine component requirements,: and probable error of an analog computer for seismic record evaluation



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The basic desigh of an analog computograph has been worked out to help evaluate reflection seismograms, by simultaneously calculating and plotting points on a seismic profile map, these points corresponding to the reflections detected on the seismic record. The computer is designed for the more common assumptions made in computing that subsurface wave velocities may be approximated by a linear increase of velocity with depth. This thesis has a description of the planned computer following a short section on seismograph theory. In order to make possible an analysis to find component tolerances, it was necessary to establish a relationship between the equation variables and the machine variables. The maximum possible error in output due to an error in any one of the components was then calculated. Equations have been derived in this thesis for quickly calculating the minimum requirements of a computer as described herein, and from these, an analysis has been made of the computer described. In event the general equations thus derived do not apply, a special analysis was made for the problem at hand. The computer was analyzed for (1) minimum dead zone of the position servos, (2) linearity and resolution of potentiometers, (3) conformity to function of function generators, (4) minimum load resistance of potentiometers, (5) phase shifts, (6) changes of gain of amplifiers, and (7) temperature effects in resistances. From the equations developed in the thesis, component requirements and the probable error of a plotted point were calculated for some given conditions. The final section includes some recommendations for improvements in the computer design. It is estimated that with following these recommendations, and using commercially available components, a probable error of as little as 0.02% of the maximum may be possible.