Question 9 of 10: Acoustic Impedance and the Role of Sonic Logs in Reflection Seismic

Question 9: Acoustic Impedance and the Role of Sonic Logs in Reflection Seismic (16.66% of paper)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Acoustic impedance. Acoustic impedance is defined as the product of a medium's bulk density and its compressional-wave velocity, $Z=\rho V_p$. It is important because a seismic reflection is generated at any interface where impedance changes — the normal-incidence reflection coefficient is $R=(Z_2-Z_1)/(Z_2+Z_1)$ — so reflection strength depends jointly on BOTH density and velocity contrast, and a boundary with a large velocity change but negligible density change (or vice versa) can still produce a weak reflection if the two effects happen to offset one another. Critically, no reflection is produced across a boundary with no impedance contrast, however geologically important that boundary may be, which is the fundamental reason the seismic reflection method images impedance discontinuities rather than geological units directly.

Sonic log. A sonic (acoustic) log is a wireline logging tool that measures the compressional-wave interval transit time ($\Delta t$, in µs/ft or µs/m) of the formation immediately around a borehole: a transmitter emits an acoustic pulse and two or more receivers at fixed spacing time its first arrival, giving $\Delta t=1/V_p$ directly at each depth sampled. Because it is run alongside a density log (or density can be estimated from a standard velocity-density relation) at the SAME borehole, the sonic log directly yields $Z=\rho V_p$ as a continuous function of depth.

Use in processing and interpretation. The sonic (and density) log's continuous impedance profile is used to build a SYNTHETIC SEISMOGRAM: the reflection coefficient series computed from the logs is convolved with an estimate of the seismic source wavelet to predict what the surface reflection survey should record at that well location. This synthetic is then TIED to the actual surface seismic section, which serves two essential purposes: it converts the seismic section from travel TIME into DEPTH using the well's own accurately known depth-vs-time relationship (a velocity/checkshot survey), and it identifies exactly which reflection event on the seismic section corresponds to which known stratigraphic marker in the well, resolving what would otherwise be an ambiguous time-domain interpretation. The sonic log's high vertical resolution (cm-scale) compared to the seismic section's own resolution (tens of metres, set by the dominant wavelength) also lets an interpreter recognize that a single "seismic reflector" may in fact represent the composite response of several closely spaced thin-bed interfaces, informing how confidently a specific bed can be picked on the seismic data alone away from well control.