Robust cluster analysis for attribute-property calibration and classification


Seismic attributes may be useful for estimation of rock properties and for classification of stratigraphical components.

The following figures illustrate an example.

The general idea is to estimate rock properties from seismic attributes

Cross sections that show the promise of using Acoustic Impedance to guide porosity estimation.

Note the high porosity layer that coincides with a zero crossing on the Seismic Reflectivity section (after residual phase correction based on VSP)

and with a low Impedance layer on the Acoustic Impedance section

The basemap shows the location of the (segmented) sections

A layer is defined by two horizons

On the the single well display,

note the similarity between the impedance log to both the porosity log and the impedance well trace (right track). This is significant as the acoustic impedance well trace was generated WITHOUT well data.

A cross plot of the acoustic impedance estimated from surface seismic versus the acoustic impedance measured in the well.

There is a very reasonable fit considering the vast difference in the two methods of estimating acoustic impedance; surface seismic with 30 Hz waves versus KHz sonic and electrical resistivity.

It is reassuring that both methods have good agreement, because while the borehole data are more reliable, it measures only a very small volume of the reservoir; the immediate vicinity of the wells. Only seismic data contains information on the volume away from the logged boreholes.

A `Quality Matrix' can be built from various attributes and borehole measurements (based on Kendall Tau statistics)

Porosity-Impedance relations almost like rock physics lab results.
High porosity means the rock is less stiff and this means Low Acoustic Impedance

A calibration function can be estimated on the wells,

and used to estimate properties away from the wells

This way we use Acoustic Impedance to guide Porosity estimation.

Compared to Porosity estimated by interpolating well measurements

the seismic guided estimate has higher resolution. The estimates are the same near the wells, but are very different are away from the wells

The depth is indicative to water saturation
for the simple reason that water is heavier than oil. This way we use Depth to guide Water Saturation estimation.

Compared to water saturation mapped by interpolation of well measurements without seismic guidance
Again the differences are mainly away from the wells.


Reflection Heterogeneity and Instantaneous frequency are sometimes indicative for petrophysical heterogeneity. Specifically for volume of clay and dolomite.

Heterogeneity might indicate volume of clay

Sometimes, reflection amplitude is indicative to Thickness. This is due to destructive and constructive interference of the reflection from the top and the one from the bottom.

It's nice to see that, more or less, the estimations of dip and azimuth agree. (We don't see a line because on these 4 wells the dip and the azimuth are about the same)

Controlled study

The wells in yellow are the control wells

To summarize

Robust cluster analysis

One of the key steps in the method above is the analysis on the multidimensional scatter of attributes and properties. This analysis is behind the quality matrix, provides seismic classification, and is an important step in calculating the calibration function. Above, we used K-means cluster analysis which is roughly based on the following algorithm:

  1. Arbitrarily divide the points in the scatter to clusters. Where the number of clusters is a user parameter. For each cluster, calculate it's center of gravity and the standard deviation which is the sum of the squares of the distances of each point from the center of gravity of its cluster.
  2. Loop over the scatter points. For each point try to move it to another cluster. Recalculate the standard deviation. If it is reduced accept the move, if the standard deviation increases reject the move.
  3. Re-loop until convergence.

This algorithm can be improved.