Seismic Reflection Processing Illustrations

The Stacking Chart and Normal Moveout

Creating a seismic reflection section or profile requires merging the ``pure profiling'' aspects of the survey with its ``pure sounding'' aspects. This involves geometric corrections to the data to re-organize the common-shot records into a large number of common-midpoint records (the pure sounding data for one midpoint), for a large number of midpoints. At left is a synthetic cross-section that will yield 50 shot records from shots spaced at an X-axis distance of 0 to 100 m. It contains a shallow and a deep flat reflector, and a dipping reflector.

Each shot was recorded by 50 receiver groups extending between 0 and 100 m further from the shot. So to get the receiver coordinate add the shot coordinate to the receiver offset. The stacking chart at left allows you to find two receivers in the data volume that have the same midpoint, and thus define parallel lines of constant midpoint. The midpoint X-coordinate is given along an axis perpendicular to the lines of constant midpoint. The width of the data volume along a midpoint-line gives the fold, or the number of traces that will be stacked together into a stacked trace at the midpoint.

The pure profiling part of the reflection experiment is represented by the zero-offset time section at left. Here the colors represent trace amplitudes, with cool colors for negative amplitudes and warm colors for positive. Green is zero amplitude. This is the section that would result from towing a source and receiver together behind a boat, with no noise. The section simply uses the trace from each shot record with zero source-receiver offset, or distance. By comparing with the model cross section above you can see (in time order) the shallow flat reflector, its surface multiple (note the surface reflection coefficient of -1), the dipping reflector, a second multiple of the shallow reflector, a surface multiple of the dipping reflector, and the deep flat reflector.

Unfortunately, in land reflection work the zero-offset traces are the most contaminated by source4 generated noise like air waves and surface waves, and the zero-offset section is useless. The process of NMO correction, or stretching the seismograms in a CMP gather to flatten the hyperbolic reflection, together with stacking will emulate the zero-offset section and take advantage of the signal/noise enhancement provided by summing multiple traces over the fold. Note the slight broadening of stacked pulses (NMO stretch), and the enhancement of flat reflections over multiples and dipping reflections.

The data collected by a large number of pure sounding experiments along a profile forms a volume with 3 independent variables (x_s, X_g, t), and the trace amplitude as the dependent variable. Here large positive amplitudes are visualized as solids in warm colors, while small and negative amplitudes are made transparent. The stacking chart above is on the top of the volume, and you can think of each seismogram as hanging from a point (x_s, X_g) on the stacking chart.

On the right front face of this volume is a shot record in offset and time (X_g, t), showing the typical hyperbolic moveouts, and the direct arrival at the top. Note that the dipping reflector actually has a negative moveout, from shooting it updip. Of course this is just one shot record of many along parallel slices in the volume. This one is at (x_s=100 m, X_g, t) with x_s fixed at 100 m and X_g and t variable.

It is easy to figure our where each reflection is coming from by looking at the left front face of the volume. This perpendicular slice has variable shot location, offset fixed at zero, and variable time (x_s, X_g=0, t). It is thus exactly the zero-offset section described above.

Now, using our analysis of where the common midpoints lie on the stacking chart, we can simply slice the volume at the correct oblique angle (30 degrees for this survey) to obtain CMP gathers. The number of traces along each slice is its fold. Note that all reflections have hyperbolic normal moveout in the CMP gather, with their apexes at zero offset. This is true as well for the dipping reflector that had negative moveout in the shot record. The dipping reflector does show a higher apparent asymptotic velocity.

This slice is a CMP gather for a midpoint further to the right along the x axis. It is narrower and thus has a lower fold, and note that all contributions will be from longer-offset traces; there are no zero-offset traces for this midpoint.

Here is the same CMP slice as immediately above, but we have replaced the data volume with one in which the NMO-correction process has been carried out. This should work well, as the model section has constant and known velocity. The hyperbolic moveouts have been removed, and all reflections have taken the time t₀ of their hyperbolic apex. This is also the time of a flat reflector in the zero-offset section.

Note that after NMO correction even the dipping reflector is flat across all traces, although only in the CMP slices. Note also the NMO stretch of the upper reflector at the farther offsets.

Taking the NMO-corrected volume and viewing it level in the direction of stacking across the CMP fold shows what will happen in the stacked section. This view is similar to the stack above.

We look for structure in the zero-offset plane, and velocity in the shot gather. As you look at the animation of the volume (QuickTime or MPEG format), try to trace the reflection surfaces and their geometry through the volume between the shot gather and zero-offset planes.

The purpose of the NMO correction is to subtract the additional time to a reflector due to increasing source-to-receiver offset, and bring the hyperbolic asymptotes level. After flattening, the volume can then be summed horizontally into the zero-offset plane, called stacking. With real data this is the only way to see reflections on that plane, and why we have to perform profiling and sounding experiments concurrently in a real reflection survey.

The reflection volume data are accessible in Sun's VFF format by clicking on the cvmod.vff file here. You can display it on a Sun workstation by starting the SunVision application and selecting the SunVoxel tool. On a Mac you can acquire the MacCubeView application for viewing the same data.

Velocity Analysis from Constant-Velocity Stacks

In the view at left of a survey from near the Amargosa River in eastern California, the right face is a CV stack, with a midpoint axis across and the time axis extending down. The left face is called a velocity spectrum, with a stacking velocity axis across and the time axis down. Since the right face is from the maximum stacking velocity, you may note in the spectrum for the midpoint shown that velocity increases with time (actually depth) between the two major reflections.

By slicing through the volume with CV stacks, you can examine an individual reflection at a range of velocities, and pick the velocity for which it is strongest and most laterally-continuous. Alternatively, you can examine the velocity spectra of a selection of midpoints, and try drawing the velocity versus time curve on each one. Velocity inversions are usually (but not always) caused by noise or multiple reflections that should not be included.

The CV stack volume data are accessible in Sun's VFF format by clicking on the smavwTV3cvstack.vff file here.

Reflection Lab Exercise