Gravity is one of the most basic forces in nature. The gravitational force of the Sun keeps the Earth in its orbit around the Sun. The Earth also exerts a gravitational force due to its mass; on Earth, gravity is the force that pulls us towards the center of the Earth and, thus, helps to define "up" and "down". Sir Isaac Newton, in 1766, described gravity mathematically as that of the mutual attraction or force between two bodies that is a function of their masses and the distance between them. The strength or magnitude of gravity depends directly on the mass of the two bodies and inversely on the square of the distance between them. Newton proposed that the gravitational force, F, between two masses, m1 and m2, could be written as
where d is the distance between the two masses and g is the universal gravitational constant, a number that is the same everywhere. Mass is a fundamental property of the substance making up a particle or object. Your weight, on the other hand, is the force that you experience as a result of the gravitational attraction between your mass and that of the Earth (or the Moon or wherever you happen to be at the time). You weigh more on the Earth than on the Moon, but your mass is the same in both places. The greater your mass and/or the greater the mass of the other body, the greater the attraction and the more you weigh. You also weigh more if you are closer to the other body (smaller d).
What geophysicists measure is the gravitational acceleration, g, due to the mass of the Earth. Galileo Galilei, in 1592, showed that the velocity of all objects increases or accelerates at the same rate if dropped from the same starting point with no air resistance. If you drop a rock down a well, the rock falls, accelerating at a rate of about 980 cm/s2 (centimeter per second per second) or 980 Gal (1 cm/s2 equals 1 Gal, named in honor of Galileo) or 1 G. This means that during each second of free fall, the velocity or speed of the rock increases by 980 cm/s. Often scientists and engineers talk about "G's" when referring to the accelerations that one experiences in an elevator or a roller coaster or that buildings experience during an earthquake. Geophysicists measure g in units of milliGals (1 milliGal or mGal equals 1/1000 Gal) because they are looking for very small changes in g due to the changes from place to place in the density of the rocks in the crust of the Earth (to depths of 30 km or more). How do geophysicists measure gravity?
How does density relate to mass? Density is directly proportional to mass, m, since density, r, is defined as
where V is volume. The higher the density of an object, the more mass it contains within its volume. For example, a liter of water weighs far less than the same volume of mercury. Rocks can have different densities and geophysicists can isolate the small changes in g caused by the density distribution of rocks below the Earth's surface with very precise measurements of g. Table 1 is a list of typical densities of rocks exposed in the San Francisco Bay area.
The value of gravitational acceleration, g, is not constant everywhere on the surface of the Earth, but depends on several factors including:
(1) the distance to the center of the Earth (the Earth is not a perfect sphere, being flattened at the poles, and the distance to its center is also affected by the elevation of the Earth's surface),
(2) the Earth's rotation,
(3) the irregular distribution of land above (or water below) sea-level (topography),
(4) the time-varying attraction between the Earth and the sun and moon (and the tides in the oceans and even in the solid Earth that are caused by this attraction), and
(5) the irregular distribution of different rocks with different densities inside the Earth.
For any place on the Earth's surface at any specific time, we can predict quite accurately the effects on g of all the factors listed above, except for the effects of the different rock types because, in most places, we do not know very much about the types or locations of rocks beneath the ground surface. This information is exactly what earth scientists seek. The theoretical value of g corrected for factors 1-4 listed above can be subtracted from the actual, measured value to infer the distribution of different rocks inside the Earth. The difference between the actual and theoretical value is called a Bouguer gravity anomaly (Pierre Bouguer was a French geophysicist who laboriously measured a degree of latitude in the Andes in the 1700s; it took seven years!). On map GP-1006, the gravity measurements are also corrected for the broad, gentle effects of isostasy (thus the term isostatic residual gravity; see box 2.2) so that the anomalies predominantly reflect density changes in the upper and middle crust (approximately the upper 15 km). After the effects of factors 1-4 and isostasy have been subtracted, the remaining (or residual) gravity values reflect the density of the underlying rocks and can be used to help determine what kinds of rocks are located below the surface.
Higher residual gravity values are found over rocks that are more dense (in other words, they have more mass) and lower gravity values are found over rocks that are less dense. Look at Table 1. Do you see any patterns to the densities according to age or composition? In general, younger rocks are less dense than older rocks, and sedimentary rocks are less dense than metamorphic or igneous rocks. Why do younger rocks tend to be less dense than older rocks? As sediments are laid down, older layers are buried by younger layers. The older layers become more compressed by the weight of younger and younger layers of sediments, squeezing out water or air from the pores or spaces between the sediment grains and increasing the rock's density. Why are sedimentary rocks generally less dense than igneous or metamorphic rocks? Rock density is also a function of composition. Compare the densities of the rocks of units cg and ci. Both of these geologic units consist of igneous rocks, but are characterized by different compositions. Granitic rocks are composed of minerals rich in silicon and aluminum (felsic), whereas the igneous rocks grouped under unit ci tend to be rich in iron and magnesium (mafic). Minerals that contain a lot of silicon and aluminum weigh less than minerals containing iron and magnesium. Many types of sedimentary rocks tend to be enriched in felsic minerals and, therefore, tend not to be very dense. In addition, because of the way metamorphic and igneous rocks form, they tend to have very little pore space and, thus , they usually are fairly dense rocks.
Shaded areas on Figure 3 on GP-1006 show some of the prominent gravity highs in the Bay area. After comparing this map with the simplified geologic map, with what kinds of rocks do these gravity highs coincide? The gravity highs tend to occur over outcrops of what geologists have named the Franciscan Complex (unit KJf on the geologic map) and over outcrops of plutonic rocks (units ci and cg). Plutonic rocks are rocks that solidified from molten rock beneath the surface of the Earth. Geologists believe that the Franciscan Complex is part of former oceanic crust and overlying sedimentary rocks that were scraped up onto North America in a subduction zone ( box 2.3) many millions of years ago and then were smeared laterally along the edge of the continent by faulting along the San Andreas and other faults. Over what kinds of rocks do gravity lows occur (hachured areas)? Are these rocks young or old compared to the rocks that coincide with gravity highs? Most of the gravity lows occur over Cenozoic sedimentary rocks that have formed in valleys and former seas that once covered parts of the San Francisco Bay area. The magnitude of the gravity low is proportional to the thickness of the low-density sedimentary rocks. If you were an oil-company geologist, how would you use the gravity map to drill for oil or gas in the Bay area bearing in mind that the major oil and gas fields of the world occur within thick accumulations of sedimentary rocks? Where would you drill for oil or gas?
Do clusters of earthquakes (yellow circles) tend to occur over gravity highs or lows? Do earthquakes parallel the gravity contours or cut across them? In many cases, the earthquakes tend to follow closely spaced contour lines. This close spacing of the contours means that the gravity values change abruptly over a short distance (a steep gravity gradient). Because the gravity values reflect rock densities, this means that the density of the rocks varies spatially. Why do the rock densities change spatially? One possible cause for this change is that a fault has juxtaposed rocks of different densities (see Fig. 2 on GP-1006). In areas where geologists cannot map or observe faults at the surface because they are covered by buildings or unconsolidated sediments or where seismologists cannot map the faults because of the lack of earthquakes, one can sometimes use gravity gradients to locate faults. Do you see any gravity gradients within the valleys covered by young sedimentary deposits? Many of the gradients are located along the sides of the larger, flat-bottomed valleys. Furthermore, the way the gravity values change across the fault can tell you if the fault is vertical or sloping (dipping). Figure 2 on GP-1006 shows cross sections across vertical and dipping faults and the corresponding changes in gravity that these fault geometries produce. The geometry of the fault is important for predicting the kind of motion produced by faulting. Vertical faults tend to slip horizontally or laterally, whereas dipping faults tend to move up and down. Engineers need to know what kind of motion buildings and bridges would be subjected to during an earthquake so that they can design them to withstand the shaking.
Gravity data also may shed light on geologic structures controlling where and why earthquakes occur along faults in the Bay area. Using a road atlas, locate the San Mateo Bridge in the southern part of the Bay area. You can see the bridge on GP-1006 meeting the East Bay shoreline at the -18 mGal contour line where the Bay is about 10 km wide. Do you see any clusters of seismicity along the Hayward fault north of the San Mateo Bridge? The biggest cluster of seismicity occurs over an isolated gravity high that tops the 0-mGal contour line. The gravity high tells us that dense rocks underlie this part of the fault. These dense rocks could be acting to concentrate seismicity in this area. Think of water flowing in a stream. If the stream is clear of debris, the water flows without interruption. If you place a log or stone in the stream, the water builds up around the object as it tries to continue along its course. Seismologists believe that when a fault ruptures, the rupture often starts and ends at rough points (asperities ) along the fault where the rocks are harder to deform. A block of dense rocks in the fault zone may act similarly to a knot in wood or a log in a stream. Earthquakes will cluster at and around the stronger material.
Gravity and GP-1006 Map Exercises
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