Introduction - Chapter 1
The whispering waves were half asleep, The clouds were gone to play. And on the bosom of the deep The smile of Heaven lay. - Percy Bysshe Shelley
The first offshore drilling for oil in Texas occurred along Goose Creek, 21 miles southeast of Houston on Galveston Bay. In 1903, John I. Gaillard noticed bubbles coming to the surface of the water. With a match, he confirmed that the bubbles were natural gas, a strong indication of oil deposits. The discovery well was drilled and hit oil on 2 June 1908, at 1600 ft. In 1916, a well at Goose Creek hit a 10,000-barrels-per-day (bbl/day) gusher at a depth of 2017 ft (Figure 1). Initially, that well produced 8000 bbl/day. The community changed overnight as men rushed to obtain leases, to build derricks, and to drill wells. Within two months, the well leveled off to 300 bbl/day. The largest well of the field was Sweet 16, which came in on 4 August 1917, gushing 35,000 bbl/day from a depth of 3050 ft. This well stayed out of control for three days before the crew could close it.
The Goose Creek field is on a deep-seated salt dome with slightly arched overlying beds. When a hurricane hit in 1919, the Goose Creek oil field suffered tremendous property damage. The hurricane’s relatively mild 39-mph winds destroyed more than 1450 oil derricks.
At the time of the Goose Creek discoveries, the proper equipment for finding new oil fields included a Brunton compass, a K&E stadia handbook with Jacob’s staff, a 7-ft stadia rod, a small bricklayer’s hammer, and of course a couple of matches.
In contrast, this book gives the basis of the geophysical imaging processing methods used today for discovering and extending oil fields. Digital signal processing is the fundamental tool used. A signal can be analog (with continuous time) or digital (with discrete time). A seismic wave traveling in the earth is an analog signal, but it is recorded as a digital signal. A water clock (of ancient days) is a timekeeper operated by means of a regulated flow of water into a vessel. An hourglass is a timekeeper operated by means of a regulated flow of sand into a vessel. Both of these clocks depend on a medium flowing downward through a hole. According to human senses, water is continuous and sand is discrete. Accordingly, a water clock is analog, and an hourglass is digital. Each speck in water represents an instant in continuous time. Each grain of sand represents an instant of discrete time.
There are two general ways by which mechanical energy can be transferred from one place to another: (1) the passage of matter from one place to another and (2) the passage of energy though a material medium in such a way that the medium is left essentially unchanged after the transfer. The first way can be achieved by actions such as kicking a football. The second way is achieved by a mechanical traveling wave, such as a seismic wave. For such a wave to exist, there must be a source of disturbance, a medium that can be disturbed, and some physical connection through which adjacent particles in the medium can influence one another.
Seismic waves travel through the rock layers of the earth. A source of energy makes an initial rock particle oscillate around its equilibrium position. This oscillation begins to push and pull on the second particle so that it oscillates about its equilibrium position. In this way, the energy is transferred from the first particle to the second particle. In turn, the oscillation of the second particle causes the third rock particle to oscillate around its equilibrium position. Again, the energy transfer occurs. This process continues consecutively. Each individual particle acts to displace the adjacent particle so that it too begins to oscillate. In this sequential manner, a disturbance travels through the medium and thereby transports kinetic energy.
Two basic types of waves are longitudinal waves and transverse waves. Longitudinal waves also are referred to as compressional waves or primary (P) waves. Transverse waves also are referred to as shear waves or secondary (S) waves. In a longitudinal wave, the oscillating particles of the medium are displaced parallel to the direction of propagation (i.e., the direction of energy transmission) of the wave. In a transverse wave, the particles are displaced in a direction perpendicular to the propagation direction. Seismic waves fall under two broad categories: (1) body waves, which travel through the body of the medium, and (2) surface waves, which travel near the surface.
Seismic waves can be either longitudinal or transverse. Transverse mechanical waves require a rigid medium (such as rock) to transmit their energy. A fluid (either liquid or gas) lacks the required rigidity. Hence, airborne sound waves and waterborne ocean waves are longitudinal waves. In addition to mechanical waves, there are electromagnetic waves. Such waves can travel though a material medium, such as glass, but they also can travel though a vacuum, such as in outer space. Sunlight is the most familiar type of electromagnetic wave. All electromagnetic waves are transverse.
The phenomena perceived by our eyes as light and by our ears as sound are propagated as wave motion. That motion occurs not on a 2D surface such as the plane formed by the top of a still pond but in 3D space. Many of the properties of wave motion can be understood by studying the familiar waves traveling in a body of water. Water waves produced by a dropped stone move out in circular rings at a constant speed. That wave speed is called the velocity of propagation and is denoted by v. The waves themselves have crests and troughs - points at which the water level is elevated and points at which the level is depressed. The water surface undulates rhythmically between crests and troughs. The distance between successive crests or between successive troughs is called the wavelength and usually is denoted by the Greek letter . As the waves travel past a fixed point on the surface of water, they cause a vertical up-and-down motion of the water at that given point. Such up-and-down motion repeats itself in time in a periodic manner. The number of times per second that the up-and-down motion repeats itself is called the frequency of the wave and is denoted by f. In what follows, we shall examine in mathematical detail three fundamental aspects of wave motion:
1) the velocity v with which the wave travels, or propagates
2) the distance between crests (or between troughs) - that is, the wavelength
3) the frequency f with which the medium pulsates to and fro
The period T is the time that two successive wave crests (or troughs) take to pass a fixed point. For a sinusoidal wave, the following relationship holds:
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Also in this chapter
- Wavefronts and raypaths
- d’Alembert’s solution
- One-dimensional waves
- Sinusoidal waves
- Phase velocity
- Wave pulses
- Geometric seismology
- The speed of light
- Huygens’ principle
- Reflection and refraction
- Ray theory
- Fermat’s principle
- Fermat’s principle and reflection and refraction
- Appendix A: Exercise