Integrating the Sonic Log
The reflection coefficient set that is calculated from sonic and density log data could be a string of numbers versus depth. This is because logs are recorded versus depth. However, we need a string of reflection coefficients versus two way seismic time in order to make a synthetic seismogram. To translate depth to two way time, we use a time versus depth plot made from an edited, integrated sonic log, or a computer representation of such a plot.

Integration is a summation of the sonic log readings taken at equal depth increments. This is often adjusted to a datum depth or time horizon, not necessarily the surface. Because the sonic log depth is measured relative to the surface but cannot often be recorded all the way to the surface, we also have to estimate or tie the sonic integrated time to a known horizon below the surface casing. The checkshot survey plays an important role in tying the sonic to surface or some other datum.

The formula is:
      1: T2way = Tsurf - Tdatum + 2 * Sum (DELTcor * INCR)

Where:
__Tsurf = Two way time from surface to start of sonic log (ms)
__Tdatum = Two way time from surface to desired datum (ms)
__DELTcor = Edited sonic log reading adjusted to SRS or VSP (us/m or us/ft)
__INCR = Digitizing increment (meters or feet)

Once the integration is finished, a depth and acoustic impedance can be calculated for each two way time, by interpolating linearly between two digitized data samples. For more precision, a spline interpolation can be used. The reflection coefficient string is then calculated from the interpolated data. The sonic and density data should always be edited before integration.

The depth digitizing increment should be fine enough to allow reasonable interpolation between the time sample points. The time sample rate is chosen to include the highest frequency (thinnest) events desired on the synthetic. Sample rates from 0.25 to 8 ms are used, with 1 ms the most common. Depth sample rate to match the time sample rate depends on the rock velocity. Too fine a depth sample rate wastes computer time and storage space; too coarse gives poor results.

Some sonic logs have integrated travel time indicated by tick marks along one margin of the log. These are ONE WAY travel times. Hole volume integration may also be indicated by tick marks, and can be confused with sonic integration ticks. These ticks were made before editing, so they are seldom used directly in making a synthetic seismogram. Some integration ticks are recorded incorrectly, and each case should be checked against the actual log data to verify the validity of the integration.

A computed log analysis on two-way time scale with VSP or synthetic seismogram traces allows accurate horizon picks and correlation of attributes to lithology or fluid content.

A sonic log with integration tick marks along the right edge of the depth track

The integration tick marks are very hard to see on many logs. This example has them along the right edge of the depth track. Many tick marks fall on or near depth lines. Every tenth tick is larger than the others to make it easier to count. The ticks can appear on any margin of the log and are generally easier to see on modern digital logs.

Remember to re-integrate after any edits.