Luc Ikelle and Lasse Amundsen have written a major new textbook which aims…'to provide readers with the basic background needed to tackle not only the present challenges of petroleum seismology but also some foreseeable challenges.'

An example of wave propagation through a subsurface model. The source used to generate waves in this example is an explosive source. We can recognize some of the reflections and transmissions at the various interfaces. Another explosive is made later similuating either the so-called "seismic interference" or multishooting acquisition. Alongside the snapshots we also show seismic data recorded by horizontal arrays of sensors. Notice that the various reflections and transmissions of energy in the snapshots are also captured by seismic data.

The source is then moved to another location, where the entire process of generating and recording waves is repeated. The seismic data recorded in this process are then imaged, based on arrival time and the magnitude of the reflection energy, to obtain a model of the subsurface. The time it takes for the wave to travel from the source to the receivers is recorded in the seismic data. From these traveltimes we can reconstruct the depth of the reflector at which the recorded energy has been reflected. Furthermore, the magnitude of the reflected wave allows us to determine the contrast in physical properties that caused the reflection. Thus we can reconstruct the locations of the various discontinuities of our geological model and the contrasts of physical properties which characterize these discontinuities. (see Chapter 7 of Introduction to Petroleum Seismology for more details.)

…the statistics chapter in particular gives probably the best concise description of the use of second-order statistics in geophysics that I have come across.

Let us recall that solutions of wave equations (the building blocks of seismology) involve waves traveling in positive as well negative time, the so-called "retarded" and "advanced" waves. Retarded waves progressively move with increasing time, as visualized in the classical movies of wave propagation (see Introduction to Petroleum Seismology for more details). They are consistent with the way the current seismic data acquisitions are carried out; they arrive at receiver locations at some time after they have left the source location. Advanced waves travel backward in time; that is, they arrive at the hydrophones or geophones before they have left the source point. These waves are really an affront to our common sense and our understanding of how the world operates -our ever-aging bodies being an obvious testimony. So despite the fact that advanced waves are valid solutions to the wave equations, they are generally ignored in most seismology studies, at least in part, because of their counterintuitive nature. One of the key features of the diagrammatica that we have been developing in recent years is that these advanced waves are included in our constructions of the scattering diagrams of seismic events.

In our scattering diagrams, such as the ones in this figure, the process of wave propagation begins on the left and ends on the right. The solid line represents waves traveling forward in time (forward wave propagation), and the dotted line represents waves traveling backward in time (backward wave propagation). In forward wave propagation, the process begins on the left and ends on the right, whereas in backward wave propagation, it is the opposite. The arrows are added in these scattering diagrams to clearly indicate the direction of wave propagation. The point at which the two lines meet is known as the scattering point. Scattering points can occur at the intersection of two solid lines, of two dotted lines, or of a solid line and a dotted line. The time is not explicitly shown in the scattering diagrams in order to avoid an unnecessary complication associated with a third axis. Notice that all events recorded in seismic data (i.e., direct waves, primaries, ghosts, and multiples) have a forward propagation. Therefore, in our diagrammatica, these events will be entirely marked by solid lines and will go from left to right. We will call them "real events." Their noncausal versions, which correspond to backward propagation, will be marked by dotted lines and will go from right to left. We will call them "anticausal events." Events which combine solid and dotted lines in their constructs will appear only in intermediate, unobservable stages of a process for constructing a real event. We will call these events "virtual events," as suggested by Ikelle et al. (GJI, 2006; JSE, 2005; and GP, 2007).

…Ikelle and Amundsen have shown their grasp of the fundamental current issues in seismic data acquisition and processing.

To aid in the understanding of the direction of wave propagation of the last leg (the negative bending leg) of the wave path of virtual events, we have simulated the wave propagation of this leg. Actually, our simulation includes both a virtual event and a real event to facilitate comparison. We can effectively see that the virtual events propagate backward in time, in the opposite direction of real events. Because the two events share the same paths until the upgoing wave hits the interface, it is normal that the forward-propagating event and backward-propagating event arrive at the interface at the same time. The virtual event then ceases to propagate, whereas the real event continues its forward motion.

Notice also the difference in spatial direction between real and virtual events. Actually, the virtual and real events propagate not only in the opposite direction in time but also in the opposite direction in space.