

\title{Cross-hole seismology at SEP}
\lefthead{Muir}
\righthead{Crosshole seismology}
\footer{SEP--67}
\author{Francis Muir}

\INT

Although surface-to-surface geometry is still pre-eminent in seismic
exploration, the increasing use of the seismic method in oil field
exploitation applications such as reservoir delineation has led to the
development of new downhole tools, and with these tools the need for
new data processing techniques. To this end, the SEP conducted a weekly
seminar/workshop throughout the Summer Quarter on cross-hole data 
processing.

\mhead{THE DATA}

The idea for the workshop sprang from two datasets that were presented
in seminars. The first was a remarkable (reversed) profile of crosshole
data that Jon Claerbout had got from Western Geophysical. Both the 
vertical and inline horizontal components were available, and they both
showed very clean compressional and shear direct arrivals.

The second set of data was shown by Reinaldo Michelena who had sufficiently
processed the data under an isotropic assumption that it had become 
clear that it was, in fact, anisotropic. That is, that slanting rays were
traveling faster than horizontal rays.

\mhead{PROCESSING PROCEDURES}

The idea was to get a dataset and use it as the basis for a workshop. 
A single 3-component profile would fit quite easily into anyone's 
workstation, and yet would contain enough information to end up with
an estimate of the elastic moduli (to an unknown density factor) of
the earth between the two boreholes. 

A benefit of working with crosshole data is that it was expected that
we would come across unexpected problems, and that many of our
techniques would need to be developed from first principles, rather
than available processing package solutions.

\shead{Preprocessing}

The data we chiefly used was a single 3-component reversed profile.
That is, there was a single 3-component receiver fixed in one borehole,
and a source which was moved and shot every 50 feet over a span of the
other borehole.

At first the data was processed without benefit of precise location
information, and there were some traces which had gains that were
substantially different to others. In the end, we were able to
disentangle the headers and come up with a reasonable idea of the
borehole geometries.

\shead{Rotating the receiver}

Since the source is a variable pressure source, it was taken to have a
vertical symmetry axis. The same receiver was used throughout the data
recording process, so it seemed reasonable to assume that it did not
move up and down, or rotate during the experiment. This proved to be a
good assumption. There were two rotations involved, one about a
vertical axis to point the receiver at the other borehole, and the
other in the vertical plane joining the two boreholes. This was likely
to be more complicated, since it would depend on both the wave type and
the vertical angle between the receiver and the various source
locations..

\shead{Source waveform estimation}

Western were using a source extended both in time and along the
borehole for this work. As received, the raw data had been correlated
so that the wavelets were somewhat collapsed. Nevertheless, the direct
arriving compressional waves had well developed precursive energy, and
the normal minimum phase deconvolution was clearly inappropriate.

The compressional waves were quite clean and similar in character, and
the first plan called for picking, shifting, and stacking to form the
estimate.

\shead{Source wavelet deconvolution}

Since kinematic inversion based on picked events was to be the heart of
the planned processing suite, Dwork's Result (1950) for maximizing signal
peak amplitude to rms background noise was chosen as the first thing to try.

\shead{Velocities estimation}

There are two important qualities that distinguish crosshole from
conventional surface datasets.

\begin{itemize}

\item Source to receiver distances as well as travel-times are known.

\item Both time/distance and NMO velocities are avaiable

\end{itemize}

Our intention, then, was to estimate these velocity pairs for at least
the two plainly visible direct arrivals, P and SV, and, maybe, for the
hidden SH arrival.

\shead{Velocities to elastic moduli}

If these velocity pairs can be established for all three wavetypes of a
transverse isotropic model, then the five elastic moduli of the TI
model, C11, C33, C13, C44 and C66, can be estimated to an unknown
density factor. If the SH event could not be identified, then we would
still have four of the five, missing only C66.

\shead{A tomographic scheme}

Since we had a single profile of data, we would not be able to do more
than estimate the mean elastic properties of the material between the
two boreholes. However, Reinaldo Michelena had been working on a
1-component, multiple profile dataset, and this would be useful for
testing out ideas on anisotropic tomographic inversion methods.

This work is incomplete, but we have developed some ideas for a
practical scheme:

\begin{itemize}

\item Replace the conventional isotropic scheme with one based on
elliptic dispersion relations with vertical symmetry axes. This only
doubles the degrees of freedom for each wavetype, but is sufficient to
arrive at reasonable estimates of the elastic moduli of the material.

\item Begin by estimating the best homogeneous model, and then, by a
divide-and-conquer technique, arrive at increasingly finely layered
models.

\item If it proves necessary, use the final, finely layered output as
the input to a vertical divide-and-conquer scheme.

\end{itemize}

\mhead{CONCLUDING REMARKS}

I have presented the original intentions of the workshop. The
actual results are in the papers and short notes that follow. The
format of the seminar/workshop seemed to work well, and maybe chiefly
because we were doing what SEP does best---we worked with real data.

\REF

\reference{Dwork, B. M., 1950, Detection of a pulse superimposed on
fluctuation noise: Proc. IRE, {\bf 38}, 771--774.}
