- This segment is the beginning of a series on the basic physics of seismology. We will approach the topic with a minimum of mathmatics, striving to develop some intuition and some simple mental models that can be used in many common situations. We start out imagining that we generate a loud sound pulse at our near the surface and then listen to the echoes that come back to us. We want to understand what those echoes mean, what causes them to occur and what they can tell us about the rocks in the subsurface. In this segment, we will examine the simple case of waves propagating vertically. A restriction we will relax in a later segment. We will discuss acoustic impedance and how to calculate the reflection strength of a subsurface layer, the reflection coefficient. And finally, we will look briefly at a real world example. The simplest model for seismic reflections is to consider a plane wave traveling straight down producing relflections as it crosses interfaces between different types of rocks. Acoustic impedance is defined as a rocks density times it's velocity and changes in acoustic impedance are what generate seismic reflections. We often most speak of hard rocks which have a high acoustic impedance. Typically things like carbonates and cemented sands and soft rocks which have a low acoustic impedance. Typically un-cemented sands and shales. But the boundary between two different rock types, a sand a shale for example, often times a reflection is produced. The strength of that reflection is represented by the quantity we call, the reflection coefficient, usually abbreviated R-F-C. The reflection coefficient is simply the normalized change in acoustic impedance. We subtract the upper layer impedance from the lower layer impedance and divide by the sum of the two. It takes on values between plus one and minus one. Zero means no reflection. What could cause there to be no reflection at a sand-shale interface? If you had a higher velocity low-density porous sand sitting on a high-density lower velocity shale, the product of density times velocity could end up being the same for both cases. This can and has happened. Not seeing the seismic reflection does not always mean that there is no change in the type of rocks. Since the reflection coefficient maybe either positive or negative. We can see distinctly different behaviors. But the acoustic impedance increases across the interface, then a compression reflects back as a compression. Whereas if the acoustic impedance decreases, then the sense of the reflected wave is reversed. As shown in the illustration. Let's consider a real world example from the Gulf of Mexico. These are young unconsolidated rocks, primarily a sand-shale system. At a depth of about 12,000 feet or 3,600 meters, typical values for a wet reservoir sand might be a velocity of 12,500 feet per second or about 3,800 meters per second and a density of 2.6 grams per cc. A typical shale at that depth might have a velocity of 10,000 feet per second or about 3,000 meters per second and a density of about 2.4 grams per cc. These numbers give acoustic impedance values of the sand and shale of 9,880 and 7,200 respectively. The reflection coefficient is then .157. It is useful to note that the actual energy reflected is the square of the reflection coefficient. So the reflected energy is .0246 or about two and a half percent. The Earth is nearly transparent to sound. When we conduct seismic surveys, we are listening to very faint echoes representing a small fraction of the energy we put into the Earth. So to review, vertical incidence reflection strengths are governed simply by the normalized change in acoustic impedance called reflection coefficients. Acoustic impedance is defined as velocity times density. In the next knowledgette, we will discuss the convolution and how we can create synthetic seismic traces.