Introduction

As defined to the author, the purpose of this paper was to provide a history of seismic imaging from its infancy through the digital revolution and into the present. The idea was to have something to both commemorate and celebrate the many achievements of contributing Geophysicists during the seventy-fifth anniversary of the founding of the Society of Exploration Geophysicists. At the time, this seemed to be a good idea. While not being involved in the early days, I felt sufficiently mature (read old enough) to at least survey the remaining giants in the field and provide something better than an overview of what they achieved. The plan was to produce at least a readily understandable analysis of the kinds of technology the practitioners developed, when they developed it and how they applied it. As I progressed it quickly became apparent that I was probably not really up to the task. This was a humbling experience. While geophysicists are frequently heard to remark on the small size of the practitioners of the art, the last seventy-five years are filled with truly brilliant scientists who through dedicated efforts brought forth a remarkable combination of Physics, Mathematics, Engineering, and Computer Science directed at unraveling complex Geologic reflections to make it possible to map subsurface strata and find the hydrocarbons that drove the world's life-style and culture to what it is today. It would have been relatively easy to survey a wide range of papers on the subject, but making it human requires knowledge not only of those who published, but of those who achieved much while working in relative obscurity. Its this latter group that will probably not be recognized sufficiently. These are the people to whom we owe much of the practical aspects of technology utilization. I hope I do them justice.

Where the word migration came from is not completely clear, but the reigning wisdom suggests that it came from the Geologic conception of how oil "migrates" updip. It is fairly well known that when Geologists discovered that drilling the "highs" was the right thing to do, it became clear that finding the "trap" meant finding the high into which the oil "migrated." Technically, in its simplest form, migration (map-migration) is fully explained by Figure 1. One need only measure relative dip in each of two perpendicular directions, calculate and for a reasonable velocity and then use these values to find $x^\prime$ and $y^\prime$ . These latter values determine the position of both the output vector and $\tau$ the migrated time $\tau$ . Figures 2 and 3 illustrate the migration of a prospective unmigrated-time contour map. First, the unmigrated map in 2 is gridded. At each grid point the local apparent dip is measured and the equations of Figure 1 are used to calculate the migration vector endpoints. These new values together with the migrated time are then re-countoured to produce a migrated map. Figure 3 shows the resulting vectors along with the migrated position in black of a two-dimensional line in red. In these figures the construction is based on a constant velocity, but with a suitable "raychart" early doodlebuggers were able to find corresponding values for vertically varying velocities . Understanding Figure 1 provides a simple but realistic explanation of every migration algorithm to be discussed below. All seismic migrations move events from apparent positions to close-to-correct imaged positions and then shift events to migrated time or depth. In the early days, all final maps were depth maps. When depth errors occurred they were corrected through a suitable change in velocity. While all modern migration algorithms, in fact, do precisely what this map-migration approach does, they are mostly based more on Huygens' principle as envisioned in Figure 4 and 5 than they are on vector computations. The diffraction-stack method of figure 4 provides the basic rough principle. Points from the recorded data are swept out over circles in this constant velocity case. The envelop of these curves then reconstructs the dipping event at its proper subsurface location. As is evident in the second, Figure 5, Huygens' principle also easily reconstructs more complex migrated images from the unmigrated data. This "swing arm" approach achieves the same result as the map migration method described above, but can be made to work for all arrival times in a seismic recording and consequently can produce a close to a full image of the reflective horizons in the recorded data.

The basic principles briefly outlined above should serve as a foundation for understanding what follows. Beginning with Rieber in 1936 and finishing with the so-called high-tech algorithms of today, seismic migration is the search for sound speed (velocity) and dips. Sound speed is required to move events with measured apparent dip to their true spatial and subsurface position. As will be seen, the solution to this simple but basic problem is what has driven seismic research since the beginning of the method in the 1920s. Less knowledgeable readers are advise to keep this in mind as they progresses through subsequent paragraphs.

MapMig

Figure 1. Map Migration in 3D. The vector in this figure defines the direction and length of movement. The lateral repositioning defined by the vector followed by the shift to shorter "migrated" time is what all migrations do. The shift to shorter time is basically equivalent to a normal moveout (NMO) correction.

Unmigmapscale

Figure 2. An unmigrated time map. This map was made in the late 1970's at Amerada Hess Corporation from a grid of 2D marine lines. It was hand contoured and then gridded with a ruler. Each point on the grid provides apparent dip in both the and directions.

MapMigMap

Figure 3. The vectors as computed from the gridded version of the map in Figure 2. Some of these vectors are over two miles long.

Diffstack

Figure 4. A schematic for a "swing arm" method for migration. Although as illustrated, this method is based on a constant velocity it is easily extended to local vertically varying functions. This method clearly invokes Huygens' principle.

Huygens

Figure 5. Schematically applying the swing arm technique to data from a syncline. The top part of this figure is synthetic data from a single reflector with two synclines. The classic bow-ties are clearly evident. The bottom part show how, even without proper amplitudes, Huygen's principle reconstructs the reflector as the envelope of a set of velocity dependent curves. I am indebted to Norm Bleistein for this figure.