A VELOCITY FUNCTION INCLUDING LITHOLOGIC VARIATION

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 271-288 ◽  
Author(s):  
L. Y. Faust
Keyword(s):  
Travel Time ◽  
Direct Measurement ◽  
General Knowledge ◽  
Velocity Function ◽  
Geologic Time ◽  
True Resistivity ◽  
Resistivity Log ◽  
Vertical Travel ◽  
Water Resistivity

Assuming velocity (V) a function of depth (Z), geologic time (T), and lithology (L) the resistivity log is an approach to the determination of L. Since general knowledge of water resistivity values [Formula: see text] is lacking, the values of true resistivity [Formula: see text] against [Formula: see text] were compared for 670,000 feet of section widely distributed geographically. Variations in [Formula: see text] were presumably averaged out thereby, and the results indicate that statistically [Formula: see text] and [Formula: see text] This formula was applied to an additional 270,000 feet of section more localized geographically to observe its accuracy in predicting vertical travel time. If a correction map for [Formula: see text] variations is applied the results are encouraging but less accurate than good velocity surveys. Examination of an inconclusively small amount of data with more careful measurements of [Formula: see text] suggests that accuracy comparable to direct measurement may be attainable. The cooperation of other investigators and of the electric‐logging specialists is desired.

Hydrogeological applications of the empirical approach to water resistivity - salinity relationships

1971 ◽  
Vol 2 (4) ◽  
pp. 35
Author(s):  
B.M. Haines ◽  
D.W. Emerson ◽  
M.J. Smith
Keyword(s):  
Direct Measurement ◽  
Empirical Relationship ◽  
Approximate Solutions ◽  
Difficult Problem ◽  
Well Logs ◽  
Quantitative Interpretation ◽  
Satisfactory Solution ◽  
Subsequent Determination ◽  
Water Resistivity

Hydrogeological evaluation of subsurface aquifers involves measurement of electrolyte resistivity and subsequent determination of solution salinity. Resistivity of the water may be evaluated by quantitative interpretation of electrical well logs or by direct measurement on recovered samples. Determination of a reliable relationship between electrolyte resistivity and salinity presents a more difficult problem. Approximate solutions have been attempted frequently on theoretical and experimental bases. An empirical relationship derived from previously collected data provides the most satisfactory solution for any particular situation (be it region, valley, basin or aquifer).

VELOCITY FUNCTIONS IN SEISMIC PROSPECTING

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 289-297 ◽  
Author(s):  
H. Kaufman
Keyword(s):  
Travel Time ◽  
Average Velocity ◽  
Time Function ◽  
Instantaneous Velocity ◽  
Geophysical Prospecting ◽  
Velocity Function ◽  
Mathematical Properties ◽  
Basic Equations ◽  
Vertical Travel ◽  
Quantities Of Interest

An account of the mathematical properties of velocity functions used in the seismic method of geophysical prospecting is presented. Basic equations are given for deriving various quantities of interest associated with a particular velocity function, such as average velocity as a function of depth, average velocity as a function of vertical travel time, parametric equations for displacement, depth, travel time, etc. In Part I the relations are based on a given instantaneous‐velocity—depth function. Part II contains a similar analysis based on a given instantaneous‐velocity—vertical‐time function. The results are incorporated in Tables I and II.

Intensities and travel times of seismic rays in a sphere with a linear velocity function

1977 ◽  
Vol 67 (1) ◽  
pp. 33-42
Author(s):  
Mark E. Odegard ◽  
Gerard J. Fryer
Keyword(s):  
Velocity Profile ◽  
Travel Time ◽  
Upper Mantle ◽  
Intensity Ratio ◽  
Computation Time ◽  
Spherical Body ◽  
Travel Times ◽  
Velocity Function ◽  
Intensity Ratios ◽  
Distance Travel

Abstract Equations are presented which permit the calculation of distances, travel times and intensity ratios of seismic rays propagating through a spherical body with concentric layers having velocities which vary linearly with radius. In addition, a method is described which removes the infinite singularities in amplitude generated by second-order discontinuities in the velocity profile. Numerical calculations involving a reasonable upper mantle model show that the standard deviations of the errors for distance, travel time and intensity ratio are 0.0046°, 0.057 sec, and 0.04 dB, respectively. Computation time is short.

Near earthquakes in Central California*

1939 ◽  
Vol 29 (3) ◽  
pp. 427-462 ◽  
Author(s):  
Perry Byerly
Keyword(s):  
Least Squares ◽  
Travel Time ◽  
Sierra Nevada ◽  
Accurate Determination ◽  
Depth Of Focus ◽  
Surface Layers ◽  
P Waves ◽  
Central California ◽  
The Waves

Summary Least-squares adjustments of observations of waves of the P groups at central and southern California stations are used to obtain the speeds of various waves. Only observations made to tenths of a second are used. It is assumed that the waves have a common velocity for all earthquakes. But the time intercepts of the travel-time curves are allowed to be different for different shocks. The speed of P̄ is found to be 5.61 km/sec.±0.05. The speed for S̄ (founded on fewer data) is 3.26 km/sec. ± 0.09. There are slight differences in the epicenters located by the use of P̄ and S̄ which may or may not be significant. It is suggested that P̄ and S̄ may be released from different foci. The speed of Pn, the wave in the top of the mantle, is 8.02 km/sec. ± 0.05. Intermediate P waves of speeds 6.72 km/sec. ± 0.02 and 7.24 km/sec. ± 0.04 are observed. Only the former has a time intercept which allows a consistent computation of structure when considered a layer wave. For the Berkeley earthquake of March 8, 1937, the accurate determination of depth of focus was possible. This enabled a determination of layering of the earth's crust. The result was about 9 km. of granite over 23 km. of a medium of speed 6.72 km/sec. Underneath these two layers is the mantle of speed 8.02 km/sec. The data from other shocks centering south of Berkeley would not fit this structure, but an assumption of the thickening of the granite southerly brought all into agreement. The earthquakes discussed show a lag of Pn as it passes under the Sierra Nevada. This has been observed before. A reconsideration of the Pn data of the Nevada earthquake of December 20, 1932, together with the data mentioned above, leads to the conclusion that the root of the mountain mass projects into the mantle beneath the surface layers by an amount between 6 and 41 km.

A NOTE ON THE DETERMINATION OF THE VISCOSITY OF SHALE FROM THE MEASUREMENT OF WAVELET BREADTH

Geophysics ◽  
1941 ◽  
Vol 6 (3) ◽  
pp. 254-258 ◽  
Author(s):  
Norman Ricker
Keyword(s):  
Travel Time ◽  
Mean Value

From the breadth of a wavelet for a given travel time, it is possible to calculate the viscosity of the formation through which the seismic disturbance has passed. This calculation has been carried out for the Cretaceous Shale of Eastern Colorado, and the value thus found ranges from [Formula: see text] to [Formula: see text], with a mean value of [Formula: see text] grams per cm. per second.

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