Well-log data processing

The processing of the well-log data requires several steps that need to be automated. First, I will block the well-log curves to keep the low-frequency variations, thereby allowing definition of interfaces between the different facies. This step is the most important for this data type since it conditions the results obtained after further processing of the logs. The sonic logs and the gamma ray logs will be blocked as well. Other curves, such as the density log, may also require blocking.

Once the blocking has been performed, I will derive an interval velocity V_int(i) within each block using either

• the direct summation from ray theory, as follows:

  $$V_{int}(i) \; = \; \frac{\Delta Z_i}{\Delta T_i} \;\;\;\;\;\; \Delta T_i \; = \; \sum_j \delta t_j$$ (4)

  where $\Delta Z_i$ is the thickness of the block i and $\Delta T_i$ is the sum of all the sonic values $\delta_j$ within the block i, or

• the Backus average from effective medium theory:

  $$\frac{1}{M_i} \; = \; \frac{1}{\Delta Z_i} \int \frac{dZ}{\r... ...2} \;\;\;\;\;\; V_{int}(i) \; = \; \sqrt{\frac{M_i}{\rho_i}}$$ (5)

  where $\rho$ is given by the density log, v is given by the sonic log ($v = 1/\delta t$), and $\rho_i$ is the average density, indicated by the blocked density log.

The choice of method depends on the ratio of the seismic data wavelength to the thickness of the block. Ray theory is used when this ratio is less than 10. When it is greater than 10, effective medium theory applies.

Using the Dix equation 1955 I can convert the interval velocity into RMS velocity, which is assumed to be the same as the stacking velocity.