Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude ( M ), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement

In this paper we summarize our recently-published work on estimating horizontal response spectra and peak acceleration for shallow earthquakes in western North America. Although none of the sets of coefficients given here for the equations are new, for the convenience of the reader and in keeping with the style of this special issue, we provide tables for estimating random horizontal-component peak acceleration and 5 percent damped pseudo-acceleration response spectra in terms of the natural, rather than common, logarithm of the ground-motion parameter. The equations give ground motion in terms of moment magnitude, distance, and site conditions for strike-slip, reverse-slip, or unspecified faulting mechanisms. Site conditions are represented by the shear velocity averaged over the upper 30 m, and recommended values of average shear velocity are given for typical rock and soil sites and for site categories used in the National Earthquake Hazards Reduction Program's recommended seismic code provisions. In addition, we stipulate more restrictive ranges of magnitude and distance for the use of our equations than in our previous publications. Finally, we provide tables of input parameters that include a few corrections to site classifications and earthquake magnitude (the corrections made a small enough difference in the ground-motion predictions that we chose not to change the coefficients of the prediction equations).

Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work

We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. This new analysis uses a magnitude-independent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. An innovation in technique is introduced that decouples the determination of the distance dependence of the data from the magnitude dependence. The resulting equations are log A = − 1.02 + 0.249 M − log r − 0.00255 r + 0.26 P r = ( d 2 + 7.3 2 ) 1 / 2 5.0 ≦ M ≦ 7.7 log V = − 0.67 + 0.489 M − log r − 0.00256 r + 0.17 S + 0.22 P r = ( d 2 + 4.0 2 ) 1 / 2 5.3 ≦ M ≦ 7.4 
where A is peak horizontal acceleration in g , V is peak horizontal velocity in cm/ sec, M is moment magnitude, d is the closest distance to the surface projection of the fault rupture in km, S takes on the value of zero at rock sites and one at soil sites, and P is zero for 50 percentile values and one for 84 percentile values. 

We considered a magnitude-dependent shape, but we find no basis for it in the data; we have adopted the magnitude-independent shape because it requires fewer parameters.

Peak horizontal acceleration and velocity from strong motion records including records from the 1979 Imperial Valley, California, earthquake

Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 imperial valley, California, earthquake

New observations of the internal structure of the San Gabriel fault (SGF) are combined with previous characterizations of the Punchbowl fault (PF) to evaluate possible explanations for the low frictional strength and seismic characteristics of the San Andreas fault (SAF). The SGF and PF are ancient, large-displacement faults of the SAF system exhumed to depths of 2 to 5 km. These fault zones are internally zoned; the majority of slip was confined to the cores of principal faults, which typically consist of a narrow layer (less than tens of centimeters) of ultracataclasite within a zone of foliated cataclasite several meters thick. Each fault core is bounded by a zone of damaged host rock of the order of 100 m thick. Orientations of subsidiary faults and other fabric elements imply that (1) the maximum principal stress was oriented at large angles to principal fault planes, (2) strain was partitioned between simple shear in the fault cores and nearly fault-normal contraction in the damaged zones and surrounding host rock, and (3) the principal faults were weak. Microstructures and particle size distributions in the damaged zone of the SGF imply deformation was almost entirely cataclastic and can be modeled as constrained comminution. In contrast, cataclastic and fluid-assisted processes were significant in the cores of the faults as shown by pervasive syntectonic alteration of the host rock minerals to zeolites and clays and by folded, sheared, and attenuated cross-cutting veins of laumontite, albite, quartz, and calcite. Total volume of veins and neocrystallized material reaches 50% in the fault core, and vein structure implies episodic fracture and sealing with time-varying and anisotropic permeability in the fault zone. The structure of the ultracataclasite layer reflects extreme slip localization and probably repeated reworking by particulate flow at low effective stresses. The extreme slip localization reflects a mature internal fault structure resulting from a positive feedback between comminution and transformation weakening. The structural, mechanical, and hydrologic characteristics of the Punchbowl and San Gabriel faults support the model for a weak San Andreas based on inhomogeneous stress and elevated pore fluid pressures contained within the core of a seismogenic fault. Elevated fluid pressures could be repeatedly generated in the core of the fault by a combination of processes including coseismic dilatancy and creation of fracture permeability, fault-valve behavior to recharge the fault with fluid, post-seismic self-sealing of fracture networks to reduce permeability and trap fluids, and time-dependent compaction of the core to generate high pore pressure. The localized slip and fluid-saturated conditions are wholly compatible with additional dynamic weakening by thermal pressurization of fluids during large seismic slip events, which can help explain both the low average strength of the San Andreas and seismogenic characteristics such as large stress relief. In addition, such a dynamic weakening mechanism is expected only in mature fault zones and thus could help explain the apparent difference in strength of large-displacement faults from smaller-displacement, subsidiary seismogenic faults.

Internal structure and weakening mechanisms of the San Andreas Fault

Gravity and seismic measurements collected on granitic plutons cut by the San Andreas, Garlock, and San Jacinto faults of central and southern California show that these faults are bounded by belts of anomalous rock extending 2–5 km on both sides of the surface traces of the faults. Borehole and petrographic studies show that anomalously low densities and seismic velocities in this zone are due to both fracturing and chemical alteration. Fracturing, water circulation, and alteration are inexorably interrelated. High fracture densities are required to provide the permeability that allows water to reach and react with rocks hundreds to thousands of meters below the surface. Alteration products stable to seismogenic depths include montmorillonite (MO). Since the products of this alteration include expansive clays, this process is self-limiting. Formation of MO is facilitated by sparse water, whereas kaolinite and other clays can form if the amount of water exceeds the quantity needed for MO. Earthquakes periodically reopen the blocked fractures, a mechanism necessary in generating the broad, deep zone of pervasive alteration inferred from geophysical measurements. These geophysical and petrological patterns are clues not only to the evolution of these faults but also to the dynamics of mechanisms currently operating within the seismogenic zone. This deep circulation model predicts that the strength of a fault segment varies in time. Timing of major earthquakes may be due as much to temporal strength variations as to stress events in the crust. Significant preseismic changes in the physical properties of the crust are probably confined to the zone of fractured rock immediately adjacent to the faults.

Geophysical and geological evidence for fracturing, water circulation and chemical alteration in granitic rocks adjacent to major strike‐slip faults

Velocities of seismic p-waves are unusually low in the vicinity of a 600-meter deep well drilled into quartz diorite located 1.2 km from the San Andreas fault in central California. These low velocities are attributed to the presence of extensive fracturing of rocks along the fault. Now here in the well does the P-velocity exceed 70% of the velocity measured in samples of core from the well. Analyses of electrical and gravity logs suggest that saturated macrocracks, while producing only 5–10% porosity, are responsible for the 30–50% reduction of in situ seismic wave velocities. These macrocracks fail to close in response to confining stress. We attribute this to dilatancy induced by deviatoric stresses associated with the San Andreas fault, although the possibilities of high pore fluid pressures in the rocks or of an increase in fracturing and gouge formation with depth cannot be ruled out. Serious questions are raised concerning the use of laboratory data to model fault zones. In situ measurements of stress, seismic velocity and fluid pressures are necessary before we can hope to completely understand the distribution and mechanism of shallow focus earthquakes.

An in situ velocity study: The Stone Canyon Well

Mapping hydraulic fractures using a borehole-to-surface electrical resistivity method

Strong-motion recordings at Port Hueneme and Pasadena, at hypocentral distances of 24 and 80 km, respectively, have been fit with a number of commonly used dislocation models. The most satisfactory model is a fault in which rupture spreads circularly from the focal point (Savage, 1966). The derived model shows bilateral rupture with a lower bound on the moment of 1.5 × 10 24 dyne-cm. With an assumed rupture velocity of 3.1 km/sec the stress drops are in the range of 50 to 200 bars. The moment of the initial rupture is well determined, but much uncertainty can exist in the other fault parameters. For example, if the rupture velocity is 1.55 km/sec, an equally good fit to the Port Hueneme record can be achieved, but a stress drop close to 4000 bars is required. The area of the initial rupture is smaller than the area outlined by the aftershock distribution. There is evidence in the Port Hueneme record that the rupture process involved a multiple earthquake, which would help explain the inconsistency between the initial slip area and the area shown by aftershocks. Studies of one-dimensional wave propagation through the sediments beneath the Port Hueneme station suggest that the surface motions have been amplified by a factor of about 2.8 compared with an equivalent bedrock recording, although the wave forms have not been distorted significantly. The observed motions were compensated for the effect of the sediments before the model fitting. A comparison of different dislocation models shows that rupture propagation effects are important in fitting the observed motions and that if the finite extent of the rupture surface is accounted for, the ω −2 high-frequency decay of the displacement spectrum often attributed to the Haskell dislocation model should be closer to ω −3 .

Source parameters of the Pt. Mugu, California, earthquake of February 21, 1973

At the Stringfellow Class I waste-disposal site near Riverside, California, the influence of variations in groundwater chemistry and saturation on electrical measurements made from the surface was tested Spontaneous potential, D C electrical sounding, dipole-dipole resistivity profiles, and mise-a-la-masse measurements were employed to investigate the sub-surface migration of the acidic fluids deposited in this site between 1956 and 1972 Mise-a-la-masse exploration conducted at the downstream edge of the site detected a major anomaly which, on excavation, proved to be the signature of a previously unsuspected leak from the surface disposal ponds on the site Downstream from the site, a dipole-dipole profile and electrical soundings correlate well with electrical conductivity of groundwater obtained from monitoring wells This study demonstrates that geophysical methods may be used to search for and map leaks from toxic chemical waste dumps

Donald J. Stierman

Papers

Geophysical and geological evidence for fracturing, water circulation and chemical alteration in granitic rocks adjacent to major strike‐slip faults

An in situ velocity study: The Stone Canyon Well

Mapping hydraulic fractures using a borehole-to-surface electrical resistivity method

Source parameters of the Pt. Mugu, California, earthquake of February 21, 1973

Electrical methods of detecting contaminated groundwater at the stringfellow waste disposal site, riverside county, California