Modeling studies, based on geodetic data, can be considered fundamental process science, because these studies attempt to understand the physical processes of earthquakes and volcanic eruptions. Of course, studies of strain accumulation in an active fault zone are relevant to regional tectonics as well as regional earthquake hazard calculations. For a review of interseismic crustal deformation see Larson (this issue). Also in this group are modeling studies of deformation that is related to a relatively rapid natural event. Often, elastic dislocation theory (e.g., Okada, 1985 & 1992) adequately describes deformation associated with tectonic or volcanic events. Recently, several studies have developed new methods for applying this theory to modeling natural events (Arnadottir et al., 1992; Du et al., 1992 & 1994; Matthews and Segall, 1993; Arnadottir and Segall, in press).
Within the time period covered here, the 1992 Landers and Cape Mendocino earthquake sequences and the 1994 Northridge earthquake occurred in California. A variety of geodetic measurements recorded these events well. Because the Northridge earthquake occurred only shortly prior to this writing, studies generally are still in progress, yet a summary of early results has been published (USGS & SCEC Scientists, 1994). In contrast, many recently completed and important works on the Landers sequence exist, so much of the focus here is on the Landers sequence.
The Landers earthquake sequence that culminated in a
large earthquake on June 28, 1992 (Sieh et al., 1993; Special Issue of
Bull. Seismol. Soc. Amer., 1994) was geodetically recorded with
numerous networks and instruments. This event measured Mw=7.3, where
Mw indicates a magnitude estimate based upon the earthquake moment
, and is generally used for moderate to
large events. Geodolite and 2-color trilateration and Global
Positioning System (GPS) survey networks, as well as the continuous
GPS network called the Permanent GPS Geodetic Array (PGGA) and
continuous strain and tilt recordings (primarily from Pinon
Flat Observatory) contributed an impressive set of geodetic
recordings. Furthermore, this was the first earthquake successfully
imaged by Interferometric Synthetic Aperture Radar (ISAR). Many
published articles document the displacement field associated with
this earthquake and pre- and post-seismic deformation, as well as the
stress changes it caused.
Prior to the Landers earthquake, both geologic and geodetic data characterized the style and rates of deformation in the Eastern Mojave Shear Zone (Dokka and Travis, 1990; Sauber et al., 1986; Savage et al., 1990). A study of the background deformation field by Savage et al. (1993) found that strain accumulated uniformly through time in the 19 years prior to the earthquake sequence, and that the epicenter lay within a tectonically unusual area of northwest-southeast oriented extension. The Landers sequence began with events near the San Andreas fault on April 23, 1992 including the Mw=6.1 Joshua Tree earthquake. The Joshua Tree earthquake produced its own displacement field and aftershock sequence. Inversion of geodetic data for this event showed that slip concentrated north of the hypocenter, and that the aftershock sequence occurred essentially in areas where shear stress increases occurred (Bennett et al., in press). Data from the Pinon Flat Observatory laser strainmeters and other instruments, as well as from the two nearest continuous GPS stations at Pinon Flat and Goldstone, may indicate anomalous deformation following the Joshua Tree sequence and preceding the Landers main event (Wyatt et al., 1994; Wdowinski et al., in press). As well, the Joshua Tree aftershock sequence did migrate northwards to the eventual nucleation point of the main event (Hauksson et al., 1993).
Researchers studied the co-seismic ground deformation associated with the earthquake using several geodetic methods; trilateration with GPS (Murray et al., 1993), continuous GPS (Blewitt et al., 1993 and Bock et al., 1993), survey mode GPS measurements (Miller et al., 1993) and a more extensive combination of trilateration and GPS measurements (Hudnut et al., 1994). Several of these studies included models of the slip distribution for the earthquake. In addition, Freymueller et al. (1994), Johnson et al. (1994) and Hudnut & Larsen (Slip distribution of the 1992 Landers, California earthquake sequence, determined from geodetic data, submitted to J. Geophys. Res. , 1994) carried out more detailed modeling of the slip distribution based on geodetic results. Also, Wald and Heaton (1994) studied the temporal and spatial slip distribution by making use of the geodetic data in conjunction with seismological data. These studies together advanced co-seismic slip determination methods, and helped to elucidate the source process of this particularly interesting and well documented earthquake. It is perhaps reassuring that, for the Landers earthquake, geological, seismological and geodetic studies produced generally similar slip distribution estimates.
Another notable advance made in studying co-seismic deformation became possible with a relatively new geodetic tool. SAR interferometry methods imaged the Landers earthquake, making it the first earthquake ever to have its displacement field documented by satellite imaging techniques. To produce the dramatic image of this earthquake that graced the cover of Nature, Massonnet et al. (1993) combined SAR images obtained by the European Space Agency ERS-1 satellite with a United States Geological Survey (USGS) digital elevation model to produce interferograms representing the range component of displacement across the entire region of the earthquake rupture (Figure. 1).
This result announced a new measurement method, with exciting potential capabilities. Scientists had never before been able to produce such a complete picture of an earthquake's displacement field. Subsequent work on the Landers sequence has further advanced ISAR interpretation and methods. Peltzer et al. (1994) showed how ground tilt and rotation signals are expected to appear in ISAR imaging, and interpreted some unusual portions of the Landers interferograms in terms of tilt and buried slip, by using the ISAR results in conjunction with geodetic results and surface faulting data. Zebker et al. (1994) have introduced a different method of constructing high resolution interferograms in their study of Landers, and by doing so have documented motion on secondary faults and shown that in places the ground shattered into ``tiles'' hundreds of meters in scale. Furthermore, work with ISAR has produced the only available displacement gradient information for an aftershock of the Landers earthquake (Massonnet et al., 1994) and for the Eureka Valley earthquake (Peltzer and Rosen, in press). Present limitations are; 1) detection of one motion vector component, 2) decorrelation where high strains occur, 3) application generally to desert areas, 4) spotty ground coverage, and 5) other obligations of the ERS-1 satellite making the measurements. Nevertheless, this new technique clearly holds much promise.
Another aspect of crustal deformation research that is important for understanding fundamental processes is the study of postseismic deformation. Recent study of the postseismic deformation associated with the Loma Prieta earthquake of 1989 has shown an inward collapse of the coseismic rupture zone. Also, nearly as much postseismic fault slip as coseismic slip occurred, the main postseismic slip occurred down-dip of coseismic slip area, and the postseismic signal had a time constant of about 1.5 years (Savage et al., 1994). Other explanations of the Loma Prieta postseismic signals are plausible (e.g., Linker and Rice, in press; Burgmann et al., in press). Complementary geodetic studies on the preseismic, coseismic and postseismic deformation associated with the Loma Prieta earthquake are being published as chapters of a USGS Professional Paper (USGS Prof. Paper 1550), in addition to articles published in the Bulletin of the Seismological Society of America (BSSA) special issue on the Loma Prieta earthquake (1991). Other recent postseismic studies include work on the 1857 Fort Tejon earthquake (Pollitz and Sacks, 1992), the 1906 San Francisco earthquake (Gilbert et al., 1993), the 1944 and 1946 Nankai Trough earthquakes (Savage and Thatcher, 1992), the 1959 Hebgen Lake earthquake sequence (Savage et al., 1993), the 1964 Alaskan earthquake (Savage and Plafker, 1991), and the Landers sequence (Blewitt et al., 1993; Bock et al., 1993; Shen et al., 1994; Wyatt et al., 1994).
Postseismic deformation studies exemplify how geodetic data
can uniquely allow determination of aseismic fault behavior, which
is essential to understanding the process of strain accumulation
and release in a seismogenic region, which is in turn fundamental
to understanding earthquake recurrence processes. For example, Savage
and Plafker (1991) showed that although the relatively rapid
postseismic effects of the 1964 Alaskan earthquake persisted for less
than a decade, the rates of relative uplift (that have been steady
since about 1974) are unlikely to be sustainable for the duration of
the 
1000 year recurrence interval there. On this basis, they postulate
a longer-term relaxation may occur, with a time scale of about 100 years,
to explain their data. This behavior appears to differ from that
observed in a Japanese subduction zone setting, where steady deformation
is evidently re-attained within a decade or so after a large plate
boundary rupture (Savage and Thatcher, 1992). Larson (this issue)
treats other aspects of postseismic and interseismic deformation.
As these studies illustrate, existing methods can determine postseismic phenomena, but typically require special effort to establish a monitoring network following an event, followed by repeated measurements over several years' time. Certainly, some standing questions exist regarding postseismic data, and improved measurements for future earthquakes would be valuable. Perhaps to a greater degree, if geodesy is to be used to search for preseismic phenomena, this challenge demands improved monitoring to resolve associated signals. For many geodetically measurable phenomena, continuous GPS complements continuous strain measurements (e.g., Tralli, 1991). Continuous strainmeters can attain higher resolution and precision, yet the two approaches measure deformation over different spatial and temporal scales. Wyatt et al. (1994) provide an example of how continuous geodetic measurements compare for the Landers earthquake (see Figure. 2). The continuous GPS data indicate a somewhat longer period and much larger amplitude postseismic relaxation than do the laser strainmeter data, which remains enigmatic.
The laser strainmeter data also indicate that anomalous deformation may have occurred between the times of the Joshua Tree earthquake and the Landers mainshock (preseismic to Landers), and between Landers and the Big Bear aftershock (preseismic to Big Bear), although how these signals relate to the earthquake sources is unclear Wyatt et al. (1994). One may also compare the strainmeter data with geodolite and GPS data collected prior to the Loma Prieta earthquake (Gladwin et al., 1993, Johnston and Linde, 1993, and Lisowski et al., 1993). Because the GPS measurements began on the Eagle-Rock to Loma Prieta line only shortly prior to the June 27, 1988 Lake Elsman preshock, and those available GPS data differ from the geodolite data on the same line, it is not clear whether or not the shear strain anomaly detected with strainmeter data represents a regional anomaly. The sparse spatial density of strainmeters and continuous GPS networks (and frequently sampled geodolite lines) has made it impossible to better resolve these intriguing preseismic anomalies associated with the moderate and large earthquakes in recent years. However, other evidence suggests linear accumulation of strain with time over many years prior to substantial earthquakes (e.g., Lisowski et al., 1993; Savage et al., 1993; Savage and Lisowski, 1994).
We are at a stage of having recorded some interesting anomalies prior to significant earthquakes, yet it is difficult to have confidence in these results because too few stations recorded the anomalies. We also have evidence that at the level of accuracy of the geodolite and survey-mode GPS network measurements, temporal fluctuations in strain accumulation over many years' time prior to significant events are not identifiable. Hence, if one presumes for a moment that precursory phenomena exist, we expect that detection of associated deformation signals will require greatly improved geodetic monitoring.
Vastly improved monitoring of crustal deformation with existing continuous GPS, strainmeter, and perhaps even the relatively new ISAR technology is now possible. Such systems would complement the short-period and broad-band seismic networks now in operation, and thereby greatly improve the earthquake monitoring and research program. Clearly, the capabilities exist to implement much better quality seismological and crustal deformation monitoring---this is perhaps especially germane to metropolitan areas where large populations and immense infrastructure face either seismic or volcanic hazards.
For example, in an effort to apply continuous GPS measurements towards improving long-term hazard estimation and providing deformation data through near real-time earthquake information systems, the continuous GPS network in the Los Angeles metropolitan area is being augmented with about 20 new stations in a joint project between Jet Propulsion Lab, Scripps Institution of Oceanography, and the U. S. Geological Survey, coordinated by the Southern California Earthquake Center (SCEC) and funded primarily by NASA, USGS, and NSF. A similar effort, called the Bay Area Regional Deformation array (BARD), is being expanded in the San Francisco metropolitan area.