VI. TOPOGRAPHY, TECTONICS, AND EROSION

SAR Interferometry and Surface Change Detection

Perhaps the most basic question we need to answer is "Why does landscape take the form it does?" Global digital elevation data are vital for addressing this fundamental scientific issue. We actually know much less about the surface topography of the Earth than of Venus, due to the recent success of the Magellan mission and the fact that two-thirds of the Earth is covered with water. Surprisingly, though, even the Earth's continents are less well surveyed than Venus. The need for global digital topographic data has been nicely summarized in previous reports (Dixon and Burke, 1988; Mueller and Zerbini 1989; Rundle, 1990), although little has been said about the need to use these data to study erosional processes. Accordingly, this is the focus of this chapter.

The Earth's topography ultimately reflects a balance between two competing mecha-nisms, tectonics and erosion (see discussion in Harrison, 1994). Continental denudation rates are controlled primarily by topographic relief or slope, precipitation, climate, vegetation, and rock type. Obviously, there are many interrelationships between these factors. For instance, topography can produce microclimates that vary spatially over relatively short distances and have an indirect effect on erosion rates through its control of climate. Likewise, topography can control vegetation, with similar indirect effects on the erosion rate.

Denudation rates from individual river drainage basins can vary by orders of magnitude, but we are far from understanding the reason for this large variation. Currently, the only published explanation for the variation in 45 major river drainage basins (Milliman and Meade, 1983) involves the use of average elevation as a proxy for the topographic control of denudation rate (Pinet and Souriau, 1988). Obviously, this does not explain very much of the natural variation in denudation rate. The classical model for erosion supposes that the erosion rate is dependent on average elevation with a denudation rate of 0.1 every million years (0.1/My). This model gives an exponential decay of elevation with a time constant of about 50 My. A better job can be done by assuming that the denudation rate is dependent on average elevation and precipitation, but even this is a very simple-minded model of the immense complexity with which topography controls the erosion rate. Even after allowing for both precipitation and average elevation, there remains considerable variation in the 45 drainage basins' erosion rates that is not explained in this simple model. Much of this variation can be attributed to the fact that average elevation is only a poor proxy for the way topography controls the erosion rate.

Erosion tends to be catastrophic and localized. Local erosional events such as land-slides decorrelate the topography sufficiently to prohibit the use of differential radar interfero-metry to study topographic change. On the other hand, local changes may be large and observable by simple differencing of "before" and "after" DEMs.

The first priority is to obtain an accurate, high-resolution global DEM that can produce an accurate slope map. These data allow us to assess how topographic erosion control actually works. Previous study groups have suggested that 1- to 3-m vertical accuracy and 25- to 30-m horizontal resolution is appropriate for many studies, although a 10-m horizontal resolution data set would yield important new information. For example, 10-m horizontal resolution and 1-m accuracy for the primary DEM model would better describe the surface spacing and size of important geomorphologic features, especially hill slope variations in arid and temperate regions and river terraces. It would also have new commercial and engineering applications, as well as geologic applications, e.g., potential identification of buried active faults.

Differential interferometry may not be able to detect major or minor erosional events because of the previously mentioned decorrelation problem. However, there are several oppor-tunities for studying the balance between erosion and uplift by investigating fold-and-thrust belts formed by subduction. Belts in Taiwan, Zagros, the Himalayas, and Papua, New Guinea are possible targets. Determining the net uplift rates in these tectonically active areas would provide a better idea of the time scales involved in mountain building.

Models have been proposed in which there is a balance between denudation and uplift. If uplift does not occur, erosion will cause the topography to decay after a few hundred million years. This model was first proposed by Wise (1974). A modern example of the denudation/ uplift balance is the island of Taiwan, as described by Dahlen and Barr (1989) and Barr and Dahlen (1989). Taiwan is very active seismically and has a high average elevation. Its mechanical erosion rate is huge, more than six times the highest rate in the world's other 45 river drainage basins. Its chemical denudation rate is also exceedingly high. Taiwan's average erosion rate is about 3.9 mm/yr, with higher rates over the central mountain belt--an average of about 5.5 mm/yr. Uplift rates have been measured at several spots around the coast, and they cluster close to 5 mm/yr. Thus, Taiwan is an excellent place to study the denudation/uplift balance because the uplift rates are in the correct measurement range for differential radar interferometry. One model of the denudation/uplift balance makes the erosion rate linearly dependent on elevation; if this is the case, the uplift rate along the ridge of the central mountain belt would be considerably greater than the 5.5 mm/yr average quoted above.

Taiwan is a natural laboratory for the study of erosion and uplift. For SAR interferometry, the only drawback is that much of the island is vegetated, which could preclude direct uplift measurement due to temporal decorrelation. However, radar corner cube reflectors could be used at selected locations to give a series of point measurements. While areas such as Zagros and the Himalayas are drier and less vegetated, their uplift rates are lower and measurable amounts of uplift would take longer to occur. And although the uplift rates in Papua, New Guinea on the Huon peninsula may be even faster than in Taiwan, they also suffer from the problem of vegetation.

Because of isostasy (the general equilibrium of the Earth's crust maintained by a yielding flow of rock material beneath the surface under gravitational stress), high erosion rates over significant horizontal areas (i.e., distances comparable to or greater than the regional isostatic compensation distance) can effectively suck up material from the lower crust and/or upper mantle. This signal could easily be studied in Taiwan since the erosion rates are high and detailed erosion rates have been calculated for various parts of the island.

Although earthquakes were already treated in an earlier section, we note here that detailed geomorphic studies using primarily topographic data have yielded significant advances, including the location of active faults, especially where these faults are buried. While geodetic methods may indicate that a region is deforming, detailed geomorphic studies help to determine which fault is active and point to promising sites for paleoseismic studies, a critical technique for determining recurrence intervals. In addition, detailed geomorphic data, when combined with geochronology, can give a very accurate picture of long-term slip rates.

These data are important because current topography is a direct reflection of both tectonic (mainly constructional) and erosive (mainly destructive) processes. In areas where erosion rates are low and/or rates of tectonic processes are high, it is possible to more quantitatively relate the observed surface topography to the tectonics (e.g., Isacks, 1988). One of the more exciting prospects for high-resolution, high-accurancy digital topographic data is that they can be inverted--either by themselves or with other geophysical data--to constrain unknown tectonic processes of interest. This application would extend the use of digital topographic data far beyond its traditional uses of comparing combined data sets or using statistics to quantify land forms.

The basic idea is to pose a tectonic model in a form that predicts the topography numerically, then test the model and constrain its parameters by numerical comparison with the data. The technique's power has been illustrated by recent work on analogous marine data, namely sea-floor tectonic fabric digitally imaged by acoustic systems like Gloria, Seabeam, or Seamarc (Shoberg et al., 1991; Shoberg and Stein, 1994). Obvious targets for land studies include continental fold-and-thrust belts, such as the eastern Andes (Isacks, 1988), and continental extension zones, such as Afar (e.g., Acton et al., 1991).