The Vertical Seismic Profile: A Bridge Between Velocity Logs And Surface Seismograms
Authors: Omnes Gildas 
Published: December 2007

Abstract
The determination of the velocity of seismic waves as a function of depth at a well is generally based on the sonic log often complemented by well shooting. Thus, sonic logs in addition to their contribution to the study of the porosity of geological formations contribute to the improvement of surface seismic data and their interpretation. However, events recorded on surface seismograms are reflections while sonic logs and well surveys record arrivals of direct transmitted waves. Thus, identifications of seismic mirrors are inferred on the basis of velocity contrasts and travel times without direct experimental evidence linking the sonic log and the surface seismogram. The roles of multiple reflections and mode conversion remain hypothetical. Reflection coefficients can merely be estimated.
The Vertical Seismic Profile (VSP) corresponding to a well is the seismogram which would be obtained when shooting near a well and recording the input from seismic traces regularly spaced inside the well.
A VSP provides the missing direct experimental link between surface seismograms on one side and sonic logs and checks shot results on the other side. Actually, for a relatively modest additional effort invested in field operations and processing, a VSP can produce all the information contained in a normal well velocity survey and much more. VSPs may be used for the delineation of reservoirs, the identification and analysis of seismic events and thorough velocity studies where anisotropy is considered. While logs are influenced by a relatively small volume of geological formations around the well, VSPs allow studies where considered dimensions are at least those of the Fresnel Zone.

Introduction
A sonic log or continuous velocity log of a well indicates the transit time for acoustic waves in microseconds per foot or per meter as a function of depth.
It is a very valuable document for porosity determination, moreover it reflects in great detail the stratigraphy of a sedimentary series. The quality of correlations between sonic logs obtained in wells several tens of miles apart is frequently surprisingly good.
Actually, it may be said that the ultimate wish of users of seismic sections is to have them transformed into a continuous series of sonic logs. This will most probably remain a wish. Although interesting attempts are being made. Figure 1 is an example of a section where relative isovelocities are contoured. It is the result of a so-called inversion of a seismic reflection section. The well velocity log has been filtered through a band pass filter in order to remove the high and the very low frequencies which cannot be recorded through seismic channels. Thus, what is left is a plot of "relative velocities" as a function of time. Both the thin velocity anomalies and the general increase of velocities with depth are absent There is obviously a strong similarity between the filtered sonic log and the relative velocity curves deduced from the seismic traces.
Strictly speaking, these curves should be considered as representing relative acoustic impedances (products of velocities by densities). Actually where density contrasts are strong and both a sonic and a density log are available, an acoustic impedance log is calculated and used. In many cases, density logs are not available and, moreover, the variations of velocities reflect accurately enough the variations of acoustic impedances.