Borehole measurements such as gamma ray, resistivity, sonic and density logs, rock cuttings, core samples, casing points, and biostratigraphic results are all recorded in depth. Conversely, seismic measurements and our interpretations are inherently in seismic travel time.
To convert borehole measurements from depth to time, or to convert the seismic interpretation from time to depth, a time–depth relationship needs to be established. We can use one of many techniques including velocities derived from seismic, a checkshot or VSP, a sonic log, or a combination of any of these. We confirm the time–depth relationship at the borehole location by generating a synthetic seismogram.
To make a synthetic seismogram we need to:
- Generate a reflectivity series.
- Apply a time–depth relationship.
- Convolve with a wavelet and compare to the seismic data.
If the synthetic seismogram is a good match to the seismic we can say that the time–depth relationship is robust and that the borehole data are located accurately on the seismic section and can be confidently extrapolated outwards.
Generating a reflectivity series
Reflectivity is generated by changes of impedance I = ρVP within the earth. Since impedance is the product of velocity (VP) and density (ρ) we can generate a reflectivity series directly from the slowness (DT) and bulk density (RHOB) curves. A full suite of quality velocity and density logs is not always available, so pseudo-curves can be estimated using established relationships like Faust or Gardner, as discussed in Well tie perfection.
Estimating the time–depth relationship
We use all the information available to us to generate the time–depth relationship — remember, it is all about the time–depth relationship. Commonly, we start by integrating the sonic log to estimate time–depth pairs, that is, we sum up all the measurements to get a total travel time to each depth in the bore hole. Because sonic velocities are not the same as seismic velocities, due to the phenomenon called dispersion, and because there are often gaps and spurious measurements in the sonic log, the integrated sonic velocities often leave an incomplete record that provides a poor tie. We can calibrate the sonic velocities with a checkshot survey.
The checkshot survey is a measurement of seismic travel time at a range of depths in the borehole, at least at key stratigraphic boundaries and total depth. With checkshot data, we are saying, in effect, that we know how long it takes for seismic energy to travel to this depth. So the time–depth relationship must include these points.
In a marine setting, another time–depth point is the time and depth of the seabed reflection. The seabed time can be read from seismic and the seabed depth is recorded in the well file.
Pulling it together
We convolve the reflectivity series with a wavelet to give the appearance of the seismic. Using the estimated time–depth relationship, the synthetic seismogram can be compared directly to the seismic. If there is a good set of logs, a wavelet that approximates that of the seismic section, and a good time–depth relationship we should have a good tie between the seismic and the borehole. The synthetic will be a ‘good match’ to the seismic, with similar frequency content, high amplitudes in the same place, transparent zones in the seismic matched by little reflectivity in the synthetic seismogram, and not much dispute from anyone who looks at the tie.
Often we are not so fortunate. I outline some ways to deal with poor ties in Well tie perfection.