A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms representing deformations in an infinite medium, a term related to surface deformation and that is multiplied by the depth of observation point. Several practical suggestions to avoid mathematical singularities and computational instabilities are also presented. The expressions derived here represent powerful tools both for the observational and theoretical analyses of static field changes associated with earthquake and volcanic phenomena.

http://arrowsmith510.asu.edu/TheLectures/Lecture18/Okada_1992.pdf

Internal deformation due to shear and tensile faults in a half-space

Geophysical applications of radar interferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (∼100 pixels km−2), a competitive precision (∼1 cm), and a useful observation cadence (1 pass month−1). They record movements in the crust, perturbations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interferograms from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guidelines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and discriminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volcanoes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environmental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intuition necessary to interpret it.

/pdf/radar-interferometry-and-its-application-to-changes-in-the-2xi2itqotn.pdf

Radar interferometry and its application to changes in the Earth's surface

To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a brittle manner is thought to be a function of both shear and confining stresses, commonly formulated as the Coulomb failure criterion. Here we explore how changes in Coulomb conditions associated with one or more earthquakes may trigger subsequent events. We first consider a Coulomb criterion appropriate for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock. We find that the distribution of aftershocks for the Landers earthquake, as well as for several other moderate events in its vicinity, can be explained by the Coulomb criterion as follows: aftershocks are abundant where the Coulomb stress on optimally orientated faults rose by more than one-half bar, and aftershocks are sparse where the Coulomb stress dropped by a similar amount. Further, we find that several moderate shocks raised the stress at the future Landers epicenter and along much of the Landers rupture zone by about a bar, advancing the Landers shock by 1 to 3 centuries. The Landers rupture, in turn, raised the stress at site of the future M = 6.5 Big Bear aftershock site by 3 bars. The Coulomb stress change on a specified fault is independent of regional stress but depends on the fault geometry, sense of slip, and the coefficient of friction. We use this method to resolve stress changes on the San Andreas and San Jacinto faults imposed by the Landers sequence. Together the Landers and Big Bear earthquakes raised the stress along the San Bernardino segment of the southern San Andreas fault by 2 to 6 bars, hastening the next great earthquake there by about a decade.

/pdf/static-stress-changes-and-the-triggering-of-earthquakes-4r29mmr407.pdf

Static stress changes and the triggering of earthquakes

GEODETIC data, obtained by ground- or space-based techniques, can be used to infer the distribution of slip on a fault that has ruptured in an earthquake. Although most geodetic techniques require a surveyed network to be in place before the earthquake1–3, satellite images, when collected at regular intervals, can capture co-seismic displacements without advance knowledge of the earthquake's location. Synthetic aperture radar (SAR) interferometry, first introduced4 in 1974 for topographic mapping5–8 can also be used to detect changes in the ground surface, by removing the signal from the topography9,10. Here we use SAR interferometry to capture the movements produced by the 1992 earthquake in Landers, California11. We construct an interferogram by combining topographic information with SAR images obtained by the ERS-1 satellite before and after the earthquake. The observed changes in range from the ground surface to the satellite agree well with the slip measured in the field, with the displacements measured by surveying, and with the results of an elastic dislocation model. As a geodetic tool, the SAR interferogram provides a denser spatial sampling (100 m per pixel) than surveying methods1–3 and a better precision (∼3 cm) than previous space imaging techniques12,13.

The displacement field of the Landers earthquake mapped by radar interferometry

[1] The GPS-derived velocity field (1988–2005) for the zone of interaction of the Arabian, African (Nubian, Somalian), and Eurasian plates indicates counterclockwise rotation of a broad area of the Earth's surface including the Arabian plate, adjacent parts of the Zagros and central Iran, Turkey, and the Aegean/Peloponnesus relative to Eurasia at rates in the range of 20–30 mm/yr. This relatively rapid motion occurs within the framework of the slow-moving (∼5 mm/yr relative motions) Eurasian, Nubian, and Somalian plates. The circulatory pattern of motion increases in rate toward the Hellenic trench system. We develop an elastic block model to constrain present-day plate motions (relative Euler vectors), regional deformation within the interplate zone, and slip rates for major faults. Substantial areas of continental lithosphere within the region of plate interaction show coherent motion with internal deformations below ∼1–2 mm/yr, including central and eastern Anatolia (Turkey), the southwestern Aegean/Peloponnesus, the Lesser Caucasus, and Central Iran. Geodetic slip rates for major block-bounding structures are mostly comparable to geologic rates estimated for the most recent geological period (∼3–5 Myr). We find that the convergence of Arabia with Eurasia is accommodated in large part by lateral transport within the interior part of the collision zone and lithospheric shortening along the Caucasus and Zagros mountain belts around the periphery of the collision zone. In addition, we find that the principal boundary between the westerly moving Anatolian plate and Arabia (East Anatolian fault) is presently characterized by pure left-lateral strike slip with no fault-normal convergence. This implies that “extrusion” is not presently inducing westward motion of Anatolia. On the basis of the observed kinematics, we hypothesize that deformation in the Africa-Arabia-Eurasia collision zone is driven in large part by rollback of the subducting African lithosphere beneath the Hellenic and Cyprus trenches aided by slab pull on the southeastern side of the subducting Arabian plate along the Makran subduction zone. We further suggest that the separation of Arabia from Africa is a response to plate motions induced by active subduction.

GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions

A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

/pdf/surface-deformation-due-to-shear-and-tensile-faults-in-a-2vckanzx6g.pdf

Yoshimitsu Okada

Papers

Surface deformation due to shear and tensile faults in a half-space

Internal deformation due to shear and tensile faults in a half-space