paper.tex

国外免费地震资料处理软件包

or one shot follows the next so soon
that it covers up late arriving echos.
The geophone spacing $\Delta g$ is fixed
when the marine \bx{streamer} is designed.
Modern streamers are designed for more powerful
computers and they usually have smaller $\Delta g$.
Much marine seismic data is recorded with
$\Delta s = \Delta g$
and much is recorded with
$\Delta s = \Delta g/2$.
There are unexpected differences in what happens in the processing.
Figure~\ref{fig:geqs} shows
$\Delta s = \Delta g$,
and
Figure~\ref{fig:geq2s} shows
$\Delta s = \Delta g/2$. %
\sideplot{geqs}{width=2.5in}{
        $\Delta g = \Delta s$.
        The zero-offset section lies under the zeros.
        Observe the common midpoint gathers.
        Notice that even numbered receivers
        have a different geometry than odd numbers.
        Thus there are two kinds of CMP gathers
        with different values of the \bx{lead-in} $x_0$ = {\tt x0}
        }%
When $\Delta s = \Delta g$ there are some irritating complications
that we do not have for $\Delta s = \Delta g/2$.
When $\Delta s = \Delta g$, even-numbered traces
have a different midpoint than odd-numbered traces.
For a common-midpoint analysis,
the evens and odds require different processing.
The words ``\bx{lead-in}'' describe the distance ($x_0$ = {\tt x0})
from the ship to the nearest trace.
When $\Delta s = \Delta g$ the lead-in of a CMP gather
depends on whether it is made from the even or the odd traces.
In practice the lead-in is about $3\Delta s$.
Theoretically we would prefer no lead in,
but it is noisy near the ship,
the tension on the cable pulls it out of the water near the ship,
and the practical gains
of a smaller lead-in are evidently not convincing.

\sideplot{geq2s}{width=2.5in}{
        $\Delta g = 2\Delta s$.
        This is like Figure~\protect\ref{fig:geqs}
        with odd valued receivers omitted.
        Notice that each common-midpoint gather has the same geometry.
        }

\section{TEXTURE}

\par
Gravity is a strong force for the stratification of rocks,
and many places in the world rocks are laid down
in horizontal beds.
Yet even in the most ideal environment the bedding is
not mirror smooth; it has some
{\em \bx{texture}.}
We begin with synthetic data that mimics the most ideal environment.
Such an environment is almost certainly marine,
where sedimentary deposition can be slow and uniform.
The wave velocity will be taken to be constant,
and all rays will reflect as from horizontally lying mirrors.
Mathematically,
{\em texture}
is introduced by allowing the reflection coefficients
of the beds to be laterally variable.
The lateral variation is presumed to be a random function,
though not necessarily with a white spectrum.
Let us examine the appearance of the resulting field data.

\subsection{Texture of horizontal bedding, marine data}
\inputdir{synmarine}
Randomness is introduced into the earth with
a random function of midpoint  $y$  and depth  $z$.
This randomness is impressed on
some geological ``layer cake'' function of depth $z$.
This is done in the first half of program \texttt{Msynmarine} \vpageref{/prog:Msynmarine}. %
\moddex{Msynmarine}{synthetic marine}{52}{74}{user/gee}
The second half of program \texttt{Msynmarine} \vpageref{/prog:Msynmarine}
scans all shot and geophone locations and depths
and finds the midpoint,
and the reflection coefficient for that midpoint,
and adds it into the data at the proper travel time.

\par
There are two confusing aspects of subroutine \texttt{synmarine()} \vpageref{/prog:synmarine}.
First, refer to figure~\ref{fig:sg} and notice that since the ship
drags the long cable containing the receivers,
the ship must be moving to the left, so data is recorded
for sequentially {\em decreasing} values of $s$.
Second, to make a continuous \bx{movie}
from a small number of frames,
it is necessary only to make the midpoint axis periodic,
i.e.~when a value of {\tt iy} is computed beyond the end of the axis
{\tt ny}, then it must be moved back an integer multiple of {\tt ny}.

\par
What does the final data space look like?
This question has little meaning until we decide how the three-dimensional
data volume will be presented to the eye.
Let us view the data much as it is recorded in the field.
For each shot point we see a frame 
in which the vertical axis is the travel time
and the horizontal axis is the distance from the ship down the towed
hydrophone cable.
The next shot point gives us another frame.
Repetition gives us the accompanying program
that produces a cube of data, hence a \bx{movie}.
This cube is synthetic data for the ideal marine environment.
And what does the \bx{movie} show?

\sideplot{synmarine}{width=3in}{
        Output from {\tt synmarine()} subroutine
        (with temporal filtering on the $t$-axis).
%        Press button for \bx{movie}.
        }

\inputdir{shotmovie}

\par
A single frame shows hyperbolas with imposed texture.
The \bx{movie} shows the texture
moving along each hyperbola to increasing offsets.
(I find that no sequence of still pictures can
give the impression that the \bx{movie} gives).
Really the ship is moving; the texture of
the earth is remaining stationary under it.
This is truly what most marine data looks like,
and the computer program simulates it.
Comparing the simulated data to real marine-data \bx{movie}s,
I am impressed by the large amount of random lateral variation required
in the simulated data to achieve resemblance to field data.
The randomness seems too great to represent lithologic variation.
Apparently it is the result of something not modeled.
Perhaps it results from our incomplete understanding of the
mechanism of reflection from the quasi-random earth.
Or perhaps it is an effect of the 
partial focusing of waves sometime after they
reflect from minor topographic irregularities.
A full explanation awaits more research.

\sideplot{shotmovie}{width=3in}{
        Press button for field data \bx{movie}.
        }

\subsection{Texture of land data: near-surface problems}
\par
Reflection seismic data recorded on land frequently displays randomness
because of the irregularity of the soil layer.
Often it is so disruptive that the seismic energy sources are
deeply buried (at much cost).
The geophones are too many for burial.
For most land reflection data, the texture caused by these near-surface
irregularities exceeds the texture resulting from the reflecting layers.
\par
To clarify our thinking, an ideal mathematical model will be proposed.
Let the reflecting layers be flat with no texture.
Let the geophones suffer random time delays of several time points.
Time delays of this type are called
{\em statics.}
Let the shots have random strengths.
For this \bx{movie}, let the data frames be
{\em 
common-midpoint gathers,
}
that is, let each frame show data in  $(h,t)$
-space at a fixed midpoint  $y$.
Successive frames will show successive midpoints.
The study of Figure~\ref{fig:sg} should convince you that the
traveltime irregularities associated with the geophones should
move leftward, while the amplitude irregularities associated with
the shots  should move rightward (or vice versa).
In real life, both amplitude and time anomalies are associated
with both shots and geophones.

\begin{exer}
\inputdir{XFig}

\item
Modify the program of Figure~\ref{fig:cube} to produce a movie
of synthetic %
{\em midpoint %
} gathers
with random shot amplitudes and random geophone time delays.
\sideplot{wirecube}{height=1.0in}{
        }
Observing this \bx{movie} you will note the perceptual problem of being
able to see the leftward motion along with the rightward motion.
Try to adjust anomaly strengths so that both left-moving
and right-moving patterns are visible.
Your mind will often see only one,
blocking out the other,
similar to the way you perceive a 3-D cube,
from a 2-D projection of its edges.
\item
Define recursive dip filters to pass and reject the
various textures of shot, geophone, and midpoint.
\end{exer}
%3.1.textemp