Seismic Duck requires a PowerPC Macintosh with at least 256 colors. It works best with 16-bit color ("thousands of colors"), and also works with 8-bit color.
2. For Short Attention Spans
If instructions bore you, press the space bar and see what happens. Read on to understand what happened.
3. Preface
The goals of Seismic Duck is to demonstrate some physics and be interesting as a game. These goals require balance. At one extreme is accurate physics, which typically happens at time and distance scales that are too small or large to be interesting. At the other extreme, most games employ cartoon physics suitable only for Wiley Coyote. The author attempts balance with the rule ``Be qualitatively accurate, but quantitatively interesting.'' Thus Seismic Duck's time and space scales are quite distorted. The sound waves are too slow, and the horizontal scale covers an extremely large lateral distance in proportion to the vertical scale. Nonetheless, many of the qualitative aspects are accurate, at least as much as a 2-dimensional finite-difference world allows. Waves propagate, interfere, spread, and reflect as they should.
4. Where Oil Hides
The game of Seismic Duck involves applying geophysics to find oil. This section explains where oil hides, and the next section explains how to find it. For an oil reservoir to form, there has to be porous rock which stores the oil and cap rock which stops the oil from leaving. A classic trap is shown below:
An underground hill like this is called an anticline. The opposite sort of valley is called a syncline.
Hydrocarbons (gas, oil, asphalt, coal) come from natural chemical transformation of old dead plants buried in rock. Over a long time, gas and oil migrate upwards through porous rock until they reach a layer of non-porous cap rock. They collect at the high point. Below is a diagram showing gas, oil, and water trapped under a cap rock.
Another common structural trap for gas and oil is where the porous rock is terminated by a fault. Traps in the current version of Seismic Duck are always anticlines.
It should be understood that despite the fact that oil reservoirs are also called pools, the reservoir is not like a pool of water, but mostly rock. You should think of it as a dirty hard sponge. When great pressure is applied to the sponge, some of the the gas and oil come flowing out. The weight of the overlying rock provides most of the pressure necessary to extract oil. Sometimes the pressure is so great that the oil flow out by itself, and in extreme cases blowing out of the well. Though wells always have spectacular blowouts in the movies, modern drilling in fact goes to great pains to avoid blowouts.
Asphalt and coal do not flow. You have to dig for those.
5. How To Find Oil
Some anticlines show as bulges at the surface. Such obvious structures were drained in the early days of the oil industry. To find oil these days, geophysicists look miles underground by sending sound waves into the ground. Waves partially reflect from underground boundaries, and thus provide information about subsurface structures.
More precisely, reflection occurs when the acoustical impedance changes. The acoustical impedance of a rock is the density of the rock multiplied by the velocity of sound in the rock. For example, cap rock and porous rock have difference acoustical impedances. The boundary between the cap rock and porous rock partially reflects incident sound waves. Thus the depth of an underground structure can be found by creating a sound at the surface, and timing how long it takes to receive a reflection. The time it takes for the sound to reach the boundary and come back is called the (two-way) travel time. The depth of a boundary can be estimated from the travel time and velocity of sound in the rock. For instance, if the speed of sound is 3 km/sec in the rock and takes 12 seconds to make it from the surface to the boundary and back, then the boundary must be 2 km deep.
Of course, in reality there are multiple reflection paths and varying rock velocities to consider. In modern oil exploration, high-performance computers compute the subsurface structure from the reflected waves. But in the old days, there were no computers and geologists examined raw seismic data. Seismic Duck brings back these old days, and makes you an old-fashioned prospector for oil.
If all this sounds like a lot difficult calculations, do not despair. Though careful quantitative calculations are necessary in practice, you won't need them in Seismic Duck. The key in Seismic Duck will be interpreting patterns in seismograms (recordings of waves). Even a bright preschooler can learn to play it with some coaching on what patterns are important.
6. Running Seismic Duck
When Seismic Duck starts up, the main display looks like this:
The horizontal green line divides the display into two halves. The bottom half shows three simultaneous views: geology, reservoir, and seismic. The section below on the View menu explains these in more detail. The top half shows the surface position of the duck and platform, and a seismogram. The seismogram records the wave pressure at the surface and scrolls upwards.
At the bottom there are various meters. The ones on the left measure gas, oil, and water. The ones on the right show the seismogram gain and air gun charge. The rest of this section explains the various keys, menus, and dialogs that control the program.
Keyboard
Below is a diagram of the keys that control motion of the duck and drilling platform.
Platform Control: The cursor keys control the platform, which moves left or right. The drill moves up or down. The platform cannot be moved if the drill is in rock. In game mode, drilling downwards into fresh rock costs money, and too many dry wells will bankrupt you.
Duck Control: The keys < and > control the duck's motion, left or right.
Air Gun Control: The space bar shoots the duck's air gun. The air gun takes time to recharge. In game mode, the duck carries the air gun. When not in game mode, you can also shoot the air gun anywhere underground. Just move the cursor to the shot position and click the mouse button. This is handy for studying various seismic effects.
File Menu
The File menu lets you start a game and start surveying new areas. You may survey and extract oil from as many areas as you want during a game. You may also end a game early before the clock runs out.
View Menu
The View menu lets you turn each view on or off separately, and lets you control how data is displayed in colors. When playing the game, all three views are turned off, as the point of the game is to deduce the view from seismic data. Below is a summary of the three views and the color dialog
Geology: Shows the underground layers of rock, and (if present) ocean above the rock.
Reservoir: Shows the contents of the reservoir. The color code is red/green/blue for gas/oil/water as in the earlier picture, and black for empty. The colors get dimmer as you drain the reservoir.
Seismic: Shows seismic pressure waves. These are the waves created when the duck creates an shot by shooting its air gun. The pressure shown is relative to the static pressure within the rock.
Color: The color dialog lets you choose how data is displayed as colors. The color popup menu chooses the general color scheme. The style popup menu controls how wave pressure is mapped onto the general color scheme. The linear style varies color smoothly with relative pressure. The dark and linear scheme is shown below.
If the geology view is enabled, then zero becomes the color of the rock instead of black. The other style is sign only, which varies the color according to the sign only. Somewhat surprisingly, you can usually deduce the underground structure by knowing the sign only. In real life, computers can often construct a quite accurate image of underground structure from sign-only seismic data.
Model Menu
The Model menu lets you change the following parameters in the game.
Auto Gain Control: When automatic gain control is disabled, the seismogram gain is fixed at 1 and the signal is recorded as received. When enabled, the seismogram gain is amplified (or attenuated) to make the recorded root-mean-squawk constant. The gain is limited to 8x. The advantage of automatic gain control is that it lets you see weak reflections. The disadvantage is that it introduces artifacts. Most noticeably, automatic gain control causes the initial signal from a shot to not look triangular, because the gain is rapidly changing. Therefore, I recommend that you keep it off until you have mastered the basics.
Geology: The geology dialog lets you change various parameters of the geological model. The water popup lets you do off-shore exploration. Adding water makes it much more challenging, because there is a strong reflection off the water bottom. Notice that waves travel much more slowly in the water than in the cap rock. The dip popup selects how steep the anticlines are. The folding popup selects the complexity of the anticlines. Simple folding creates a single anticline. Moderate folding creates up to three anticlines. Complex folding creates up to five anticlines. No folding results in no anticlines, and hence nowhere for hydrocarbons to collect!
Shot: The shot dialog lets you change the characteristics of a shot from the air gun, which creates the seismic waves. The signature is the shape of the wave created by the shot. The frequency is how fast the shot occurs. The amplitude is how strong the shot is. More about the signature is said in the next section (Exploration Geophysics). In real life, buried explosives are usually used to create shots on land, and air guns on water. But ducks, being aquatic creatures, have evolved purely air-gun technology. In real life, air guns sound like a low-pitched loud thump.
7. Exploration Geophysics
The best way to learn about exploration seismology is to experiment with the geology and seismic views enabled. Try taking shooting the air gun at various locations and see how the waves bounce off structures. Observe how waves reflect and interfere, and how underground structure affects the recorded seismogram. Below are some basic principles in geophysics.
P waves vs. S waves: There are really two major kinds of seismic waves: pressure waves (P) and shear waves (S). Pressure waves are also called acoustic waves. Oddly enough, the P and S symbols do not stand for Pressure and Shear, but Primary (P) and Secondary (S), but because pressure waves are inherently faster than shear waves and arrive at the receiver first. Shear waves never travel through liquid because liquids does not shear. (But there is an aquatic bird called a Shearwater. Go figure!) That's how physicists know that parts of the inner earth are liquid -- P waves go through and S waves do not. There are also other kinds of waves peculiar to the surface or boundaries. For instance, the damaging waves from an earthquake are a special form of wave (called ground roll) that travels only the surface of the earth. Because they are limited to the surface, their intensity falls of much more slowly than P or S waves do. Seismic Duck does not model shear waves and ground roll for sake of simplicity and speed. The other kinds of waves travel at different speeds, and if simulated, would greatly slow down the animation and make the seismograms much harder to interpret.
Phase of Reflection: A reflection can have the same or opposite phase as the incident wave. The phase of a reflection depends upon whether the acoustical impedance goes up or down when a boundary is crossed. Taking note of the reflection phase can yield a valuable hint about whether a reflection is from the top or the bottom of the sandstone. The reflection from the top of the sandstone has the opposite phase; the reflection from the bottom of the sandstone has ame phase. To see this, use the Geology dialog to set the water to none and the folding to none. Then shoot the air gun and observe the reflections. Turning on automatic gain control from the Model menu may help you compare the reflections, because it amplifies the weaker ones from the bottom of the sandstone that have to travel farther. Reversal of phase shows up as a change in the order of colors. For instance, if the incident wave has blue (positive pressure) traveling in front of red (negative pressure), a reflected wave with reversed phase will have red traveling in front of blue.
Free Surface Boundary Condition: The top boundary is treated as a ``free boundary condition'', which means that there is no resistance to motion at the boundary. No resistance means no pressure, and this requires it reflect a wave with opposite phase so that the reflection cancel the incident wave. Use the mouse to shoot the air gun about an inch below the surface. Examine the reflection and you will see that it indeed has opposite phase.
Slope of Seismogram: The initial seismogram for a shot looks like a a cone. The slope of the sides is inverse to the velocity of the waves. That is, the slower the medium, the steeper the sides of the cone, as shown below:
First Break: Everyone knows that the fastest path between two points is not always a straight line. Sometimes it's faster to take a detour to get on an expressway. Below is a diagram of such a situation, where the water on top has a much slower velocity than the rock on the bottom:
A wave can travel from shot point S to receiver point R by traveling along the surface, or diving down to the faster rock below. Parts of the wave take each path (and all paths in between). In the diagram shown, the longer path shown is faster. This phenomena is called the first break on a seismogram, where the slope of the outer ``cone'' becomes less steep. To see the first break effect, set the water depth to shallow and folding to none. Set the air gun frequency to low and shoot the air gun. Watch as the part of the wave in the rock overtakes that in the water. When that overtaking part of the wave reaches the surface, the first break shows up on the seismogram as a change in the slope of the outer edge of the seismogram. On real seismograms, there can be second breaks, third breaks, etc. The position of breaks is one way to determine the depth of a boundary. Below is a snapshot with the leading edge of the seismogram and first break marked.
Head Wave: Corresponding to the first break in the example above is another kind of wave in the water with a strange property -- it moves through the slower medium (water) at the velocity of the faster medium! This kind of wave occurs at a boundary, and is called a head wave. In the Seismic Duck water and rock model, the head waves are fairly weak. To see them, it may help to use the Color dialog to set the style to Sign Only.
Waveguide: A slow layer of rock between two fast layers of rock can trap waves and guide them along the layer. This is the same sort of waveguide effect that guides light through fiber optics. To see the effect, turn off the Reservoir view and turn on the Geology and Seismic Views. Use the mouse to shoot the air gun inside the sandstone, near the left edge. If you shoot too close to the left edge, the damping will quash the shot, so be sure to shoot at least a centimeter in from the left edge. Immediately after the shot, much of the wave will escape the guide, because it struck the boundaries at too steep an angle to be reflected back into the waveguide. These escaped waves will race ahead. However, after a while you will see some ``blips'' that travel trapped inside the sandstone layer. These blips are waves being guided by the sandstone layer. If the layer makes a sharp turn, you will see some of the wave escape the waveguide.
Air Gun Signature: The signature of an air gun is the shape of it's pulse. The Shot dialog lets you choose one of the four signatures shown below.
You will see that the waves caused by the Gaussian signature looks more like the Rickert wavelet. This is because after being pushed by the air gun's impulse, the rock snaps back the other way. This is called ringing. Similarly, the waves caused by the Rickert and Zero Phase signatures all have an extra bump. The Rectangular signature is not normally used, because it is not band limited and severe aliasing occurs. Aliasing also occurs with the other signatures if the frequency is set too high. Aliasing is explained in the next section (Exaggerations, Approximations, and Artifacts).
Band Limited: You may be wondering about the choice of airgun signatures. Why these signatures? The reason is that except for the rectangular pulse, these signatures are almost finite in time but exponentially band limited, meaning their frequency content falls off exponentially with increasing frequency. That is, if played on an audio system most of the sound would come from the woofers, not the tweeters. Signatures such as the rectangular pulse, which is not (duck)band-limited, would cause problems. Try the rectangular pulse and see what happens.
Hyperbolic Moveout: The reflection from a flat horizontal reflector shows up on the seismogram as a hyperbola. The reason is that as the receiver point moves out away from the shot point, the waves have to travel a longer path.The deeper the reflector, the more the hyperbola is flattened out. Thus one way to estimate the depth of a reflector is to observe the flatness of its recorded hyperbola. To see this effect, use the Geology dialog to set the water depth to shallow and the folding to none. Then shoot the air gun at the surface and examine the resulting hyperbolas on the seismogram. The hyperbola for the reflection from the water will have sharper curvature than the hyperbolas for reflections from the deeper boundaries.
Cable Feathering: In real oil exploration over water, a boat pulls a long cable behind it. Along the cable are receivers that pick up the seismic signal. Ideally, the cable becomes straight as it is pulled and the receivers line up. However, water currents can push the receivers out of alignment. This is called cable feathering. Ducks are experts on cable feathering.
Coning: As oil is extracted, the gas above and water below may form cones that intrude into the layer of oil. This is a nuisance in real oil wells too.
Edwin Drake: First person to drill for oil (1861). He did not use any seismic methods. Ducks are proud of famous Drakes.
Ultrasound: A common method of imaging fetuses in the womb is ultrasound. The physics of ultrasound are essentially the same as for seismic imaging. The difference is one of scale: kilometers vs. centimeters. The resolution of the reconstructed image is limited by the wavelength, which is inverse to frequency. Thus ultrasound uses much higher frequencies than seismic imaging.
8. Playing the Game
In the game, all major underground views are hidden. All you see underground is where you drill. There is a fixed time limit in which to extract all the gas and oil that you can. You may survey more than one area. Your score is shown on the gauge that looks like the gage on an old-fashioned gasoline pump. By old-fashioned, I mean the kind that did not read your credit card. Really old fashioned would be the kind that showed you the actual gasoline in a big glass graduated cylinder!
Gas vs. Oil: The total dollar value of all gas and oil is the same in all geological models. In other words, the scarcer they are, the higher the price. Oil is worth much more than gas. In real life, gas is not worth drilling for unless there is also oil. Even the industry's standard symbols for wells shown below imply this fact -- the symbol for a gas well looks almost like the symbol for a dry well!
Costs: Air gun shots are free. Drilling costs money. This is a slight exaggeration, but emphasizes the point that seismic data is relatively cheap compared to drilling. Your initial bankroll is enough to drill three or four dry wells.
Where to drill: Since gas usually collects at the center of an anticline structure and is worth less than the surrounding oil, it usually pays to aim for oil by drilling off to the side of the structure. Practice interpreting the seismogram with the reservoir view turned on before tackling the game. Study how the top of the seismogram hyperbolas and bright spots correlate to underground structure.
Stratigraphic Information: Drilling a dry well is not a complete loss, because you can see the layers drilled into. Thus drilling gives you information about the depth and angle of layers (strata) at the drill site, just as in real life.
9. Exaggerations, Approximations, and Artifacts
As mentioned in the preface, Seismic Duck exaggerates certain quantities for sake of visual interest. Furthermore, certain approximations are used that result in artifacts that are not real physics. Many of these approximations show up in real numerical simulations too, so they are worth understanding. Interestingly enough, artifacts also show up in the pictures that computers generate from seismic data. In unlucky instances, the artifacts look like real structures and companies drill for them!
Aliasing and Numerical Anisotropy: Seismic Duck solves the wave equations using a finite grid to approximate a continuous medium. If the wavelengths are too short relative to the grid spacing, the simulation becomes inaccurate. Furthermore, the grid is rectangular, which breaks circular isotropy. To see both artifacts, use the Shot dialog to select a high frequency Gaussian pulse. Use the mouse to shoot in the middle of the shale. See how the wave degenerates into a bunch of blinking dots (which is the aliasing problem), and how some of the wavefronts that should be circular look like overstuffed square pillows instead (the anisotropy problem).
Anticline: The anticline structures in Seismic Duck have grossly exaggerated vertical scale in order to make their affect on reflections visually obvious. They are also greatly simplified by having a single porous layer. Real structures are flatter and usually contain many alternating layers of porous and non-porous rock, which makes for many reflections in real life. Oil companies use high-speed computers to convert all those reflections into pictures of the layers.
Auto Gain Control: An artifact of automatic gain control is that the initial seismogram does not have a simple triangular form, but rather looks like it is wearing an arrowhead as a hat. The reason is that the initial portion of the air gun pulse is a weak signal, which causes the gain to be raised to its upper limit. When the air gun pulse reaches maximum strength, the gain becomes quite low. This rapid change in gain is why the initial seismogram does not look triangular. You can see this rapid change by watching the gain meter during a shot.
Damping: Real waves propagate over the entire earth. Seismic Duck models a finite area, so approximations must be used at the boundaries to fake a larger world beyond. The approximation used is to damp the waves on the bottom and side boundaries. If you look closely with automatic gain control turned on, you can see some reflection from these boundaries.
Ducks: Real collection of seismic data over water involves boats, not ducks. Receivers (geophones) record the seismic data and are attached to long cables that the boats pull behind them.
Full Traps: At best, seismic data reveals structures, but not oil. In Seismic Duck, the structures always have oil. In real life, you have to drill to find out if there is gas, oil, or water only. Read Yergin's The Prize [Yer] for an account of Mukluk, a place in the Artic Ocean where $2 billion was spent drilling into a structure that turned out to have only salt water.
Interpolation: Seismic Duck solves the wave equation on a grid with two-pixel spacing between grid points, both horizontally and vertically. There are 4x as many pixels as grid points, thus most of the pixels are interpolated from neighboring grid points. The artifact of this approximation is that some zero-crossing boundaries of waves take on a stair-step appearance.
Poisson Solver: The reservoir model uses a crude Poisson solver that presumes that water and oil are compressible gases. This approximation seems to be good enough and fast enough for game purposes. Supporting the widely used IMplicit Pressure Explicit Saturation (IMPES) models at video frame rates seems impractical with current personal computers.
Spreading: The real world is three dimensional, and wave intensity falls off inverse-square with distance traveled from a point source. This is because a wave emitted by a point source in three dimensions becomes an expanding spherical shell. Seismic Duck models only two dimensions, so wave intensity falls off inversely to distance traveled.
Supersonic Duck: The duck can waddle or swim faster than the waves. Considering that the velocity of sound in rock is about 6 times that for air, this means the duck exceeds Mach 6!
Velocity: Seismic Duck sets the velocities of water, sandstone, and shale to 1.5, 2.1, and 3.0 km/sec. respectively. The values for water and shale are about right, but in the real world, the velocity of sound in sandstone would be much closer to the velocity of sound in shale. The exaggeration is necessary to force reflections that are strong enough to be visually obvious. A related exaggeration is that the densities of water, sandstone, and shale are treated as equal in order to make the calculations fast enough for animation. Real rocks are about 2.4 times denser than water.
10. About the Programming
Mathematics: Seismic Duck uses the classic staggered-grid finite difference method of Virieux[Vir], with some ad-hoc damping added.
Code: Seismic Duck generates optimized code on the fly. Optimizations include pipelining, unroll-and-jam, and skewing of data sets. This is essential to obtaining maximum speed from the PowerPC chip. Some quacks pontificate that self-modifying code is a fowl programming practice that should be banned. However, the author is a professional compiler writer and thus carries diplomatic immunity in this matter.
Known Idiosyncrasies:
* Window does not interact with other windows gracefully.
* Seems to ignore some suspend events.
To Reach The Author
The author welcomes comments, and can be reached at:
1406 Country Lake Dr.
Champaign IL 61821
robison@kai.com
11. Acknowledgements
Greg Ferrar pointed out the finer points Mac programming. Scott Morton advised me on the necessity of band-limiting the air gun. Mark Stockwell discovered that the early version used parts of the keyboard that are not on lap-top Macs. Former employment at Shell's Bellaire Research Center (Houston) taught me everything I know about geophysics. Any geophysical errors in Seismic Duck are my own.
12. Legal
Distribution:
Seismic Duck 1.4 is freeware. This software may be freely distributed as long as it is not modified and this file "Seismic Duck 1.4 READ ME" accompanies it.
Disclaimer:
No warrantee expressed or implied. Use this software at your own risk.
All versions of Seismic Duck use finite-difference equations that do not duplicate the real world, but merely approximate it with arbitrarily large error, including but not limited to aliasing, numerical anisotropy, and numerical dispersion. Seismic Duck does not model 3D or non-linear effects. Seismic Duck is not suitable for serious oil exploration.
13. Bibliography
[Pet] Peterson, Roger Tory, Birds of Texas, 1988.
[SG] Sheriff, R. E., and Geldart, L. P., Exploration seismology Volume 1, History, theory and data acquisition.
[She] Sheriff, Robert E., Encyclopedic Dictionary of Exploration Geophysics, 3rd edition.
