Cliff Frohlich

Teleseismic b values; Or, much ado about 1.0

In this paper we investigate the value of b in the Gutenberg-Richter relation for four teleseismic catalogs of earthquakes: Abes historical catalog, the Harvard Centroid Moment Tensor (CMT) catalog, the catalog of the International Seismological Centre (ISC), and the Blacknest catalog. An unfortunate result is that b differs by 30% or more when determined in different magnitude ranges, in different catalogs, or using different methods. For global catalogs separated into shallow, intermediate, and deep earthquake groups, all values determined for b lie between 0.72 and 1.34. We can identify no systematic global variation of b with depth. For teleseismic catalogs it is difficult to believe measured geographic variations in b because systematic errors cause problems of earthquake detection, earthquake location, aftershock identification, and magnitude determination. However, some variations in b are so persistent and large that they must be real. For deep earthquakes in Tonga-Fiji, for example, various measurements of b He between 1.06 and 1.57, comparable to b for shallow earthquakes, whereas measurements of b for deep earthquakes in the rest of the world are much lower, between 0.53 and 0.96. For shallow earthquakes in the Harvard CMT catalog, earthquakes with thrust and strike slip focal mechanisms have significantly lower b values (0.86 and 0.77) than earthquakes with normal faulting mechanisms (1.06). When we separate the ISC catalog into primary events (mainshocks and earthquakes with no aftershocks or foreshocks) and secondary events (aftershocks and foreshocks), we observe that b for secondary events is nearly always significantly higher than b for mainshocks. However, we show that the difference has no physical significance, as it arises simply from the act of choosing mainshocks as the largest earthquake in a foreshock-mainshock-aftershock sequence. When we correct for this systematic effect by comparing the real catalogs to identical catalogs with randomly reassigned magnitudes, we find that b for secondary events in the real catalog is actually lower than expected. Thus among aftershocks large earthquakes are relatively more common than expected, perhaps because the mainshock rupture loads asperities in adjacent regions.

Triangle diagrams: ternary graphs to display similarity and diversity of earthquake focal mechanisms

Abstract This paper presents a new method for displaying focal mechanisms — plotting them on a ternary graph or ‘triangle diagram’ where the vertices represent normal, thrust, and strike-slip focal mechanisms. This method also provides a natural way for determining the relative proportions of thrust, normal, and strike-slip motion for any particular earthquake focal mechanism.

Earthquake focal mechanisms, moment tensors, and the consistency of seismic activity near plate boundaries

Catalogs of moment tensors for more than 8000 earthquakes provide a more objective and complete description of the earthquake source than do focal mechanisms derived from first motions, and therefore moment-tensors provide a valuable resource for tectonic analysis. We here present background information about the properties of moment tensors and examples of moment tensor analysis. We also introduce a new statistic, the seismic consistency Cs, which measures the similarity of earthquakes within a group. Cs is 1.0 if earthquakes are all alike and 0.0 if they cancel one another. Triangle diagrams provide a practical method for defining the fraction of normal, strike-slip, and thrust fault components for an earthquake and are a new graphical method for displaying source properties of groups of earthquakes. We apply these methods to the Harvard centroid moment tensor catalog to study the characteristics of shallow earthquakes (<50 km depth) within 200 km of typical ridge-transform and subduction zone plate boundaries. In this way, we have reached four major conclusions. First, even along relatively simple plate boundaries, there is considerable variation in the type and orientation of earthquake mechanisms. Second, along individual plate boundaries, groups of thrust, normal, or strike-slip earthquakes generally have Cs equal to 0.8 or higher. Thus for many types of tectonic analyses it is unnecessary to add moment tensors to study seismic deformation; rather, it is sufficient to add scalar earthquake moments of the individual events. Third, moment tensors for some individual earthquakes are quite different from those produced by slip along a planar fault. However, summing up moment tensors shows that the deformation pattern produced by groups of earthquakes is generally more like fault slip than the pattern of typical earthquakes within the group. Fourth, by dividing the sum of moments by the velocity of plate motion and the length of the boundary, we calculate Rmom, the efficiency of seismic moment produced along individual plate boundaries. For the 12.75 years of data available, normal fault earthquakes along spreading ridges produce moment less efficiently than strike-slip earthquakes along transforms. These in turn produce moment less efficiently than thrust earthquakes along subduction zones. For ridge-transform earthquakes, boundaries with fast plate velocities produce seismic moment less efficiently than do boundaries with slow velocities.

Two-year survey comparing earthquake activity and injection-well locations in the Barnett Shale, Texas

Between November 2009 and September 2011, temporary seismographs deployed under the EarthScope USArray program were situated on a 70-km grid covering the Barnett Shale in Texas, recording data that allowed sensing and locating regional earthquakes with magnitudes 1.5 and larger. I analyzed these data and located 67 earthquakes, more than eight times as many as reported by the National Earthquake Information Center. All 24 of the most reliably located epicenters occurred in eight groups within 3.2 km of one or more injection wells. These included wells near Dallas–Fort Worth and Cleburne, Texas, where earthquakes near injection wells were reported by the media in 2008 and 2009, as well as wells in six other locations, including several where no earthquakes have been reported previously. This suggests injection-triggered earthquakes are more common than is generally recognized. All the wells nearest to the earthquake groups reported maximum monthly injection rates exceeding 150,000 barrels of water per month (24,000 m3/mo) since October 2006. However, while 9 of 27 such wells in Johnson County were near earthquakes, elsewhere no earthquakes occurred near wells with similar injection rates. A plausible hypothesis to explain these observations is that injection only triggers earthquakes if injected fluids reach and relieve friction on a suitably oriented, nearby fault that is experiencing regional tectonic stress. Testing this hypothesis would require identifying geographic regions where there is interpreted subsurface structure information available to determine whether there are faults near seismically active and seismically quiescent injection wells.

The Natural Selection of Sexual Cannibalism

Sexual cannibalism, in which a male is eaten by his mate following copulation, is expected to convey a selective advantage to the male under certain conditions. As shown quantitatively in our model the phenomenon is expected when (1) a male can mate only a few times in his lifetime and (2) the cannibalism significantly increases the number and/or viability of eggs fertilized by his own sperm. The expected number of male matings appears to be the more important of these two conditions. The few available observations of sexual cannibalism in several species of arthropods agree qualitatively with the predictions of our model. The same parameters of the model also explain why sexual cannibalism is generally rare among vertebrates. Phenomena selecting for sexual cannibalism appear more closely related to paternal investment strategies than to ecological factors associated with other forms of cannibalism. Because few field studies of invertebrates have followed the mating history of marked males, we cannot test our model quantitatively with existing data. We suggest specific field observations which would provide quantitative estimates of the expected number of male matings. In addition we describe possible laboratory experiments which would give more precise measurements of the increase in fecundity of the cannibalized male.

Earthquakes with Non—Double-Couple Mechanisms

Seismological observations confirm that the pattern of seismic waves from some earthquakes cannot be produced by slip along a planar fault surface. More than one physical mechanism is required to explain the observed varieties of these non—double-couple earthquakes. The simplest explanation is that some earthquakes are complex, with stress released on two or more suitably oriented, nonparallel fault surfaces. However, some shallow earthquakes in volcanic and geothermal areas require other explanations. Current research focuses on whether fault complexity explains most observed non—double-couple earthquakes and to what extent ordinary earthquakes have non—double-couple components.

How well constrained are well-constrained T, B, and P axes in moment tensor catalogs?

The T, B and P axes of earthquake moment tensors (MT) are often used to evaluate regional stress directions and other tectonic parameters; we here undertake three comparisons to assess the uncertainty in the orientations of these axes. These are (1) a direct comparison of common MT in the Harvard, U.S. Geological Survey, or Earthquake Research Institute (ERI) catalogs; (2) a comparison of MT slip vectors and plate motion vectors in several tectonically straightforward regions; and (3) an analysis of the axial variability in the Harvard and ERI catalogs implied by the reported uncertainties in individual MT components. All three comparisons indicate that there is considerable variability within the catalog concerning the axial orientation of MT, but all suggest that axis orientations of the majority of Harvard MT have uncertainties of 15° or less. For compensated linear vector dipole (CLVD) components among the three catalogs, the correlation is very low. For the Harvard catalog, three statistics are especially useful for selecting better constrained MT; these are (1) the relative error Erel, which is the ratio of the scalar moments of the reported error tensor and of the MT itself; (2)ƒCLVD, a measure of the strength of the CLVD component; and (3) nfree, the number of MT elements not fixed at zero in the inversion. For selecting better constrained MT, the appropriate statistical cutoffs chosen depend on the problem of interest, the data available, arid personal preference. However, for analysis of shallow earthquakes we have used Erel ≤ 0.15, ƒCLVD ≤ 0.20, and nfree = 6. While this eliminates 53% of the catalog, our calculations suggest that nearly all the remaining events have T, B, and P axes with azimuth and inclination angle uncertainties of 5°–10° or less.

Causal factors for seismicity near Azle, Texas

In November 2013, a series of earthquakes began along a mapped ancient fault system near Azle, Texas. Here we assess whether it is plausible that human activity caused these earthquakes. Analysis of both lake and groundwater variations near Azle shows that no significant stress changes were associated with the shallow water table before or during the earthquake sequence. In contrast, pore-pressure models demonstrate that a combination of brine production and wastewater injection near the fault generated subsurface pressures sufficient to induce earthquakes on near-critically stressed faults. On the basis of modelling results and the absence of historical earthquakes near Azle, brine production combined with wastewater disposal represent the most likely cause of recent seismicity near Azle. For assessing the earthquake cause, our research underscores the necessity of monitoring subsurface wastewater formation pressures and monitoring earthquakes having magnitudes of ∼M2 and greater. Currently, monitoring at these levels is not standard across Texas or the United States.

Detailed Seismicity of the Alpine Fault Zone and Fiordland Region, New Zealand

A study of the Alpine fault zone and the Fiordland region of the South Island of New Zealand from February through April 1972 indicates high but diffuse microearthquake activity. Composite focal mechanism solutions show that a regional northwest-southeast compression dominates the tectonic pattern. This direction is nearly normal to the Alpine fault, indicating that the Alpine fault is now undergoing a large component of thrust faulting. This agrees with geologic data for uplift of the Southern Alps along the Alpine fault beginning in mid-Miocene time and accelerating in the Pliocene, the time of the Kaikoura orogeny. Before the Kaikoura orogeny, the Alpine fault apparently was a transcurrent fault. This major change in the New Zealand tectonic pattern could have been produced by a relatively minor migration of the nearby Indian-Pacific pole of rotation. Incipient underthrusting of the Tasman Sea appears to be occurring off the Fiordland coast, terminating at the point where the Lord Howe Rise intersects the coast. To the north is a zone of oblique continental convergence, with the Southern Alps being rapidly uplifted along the Alpine fault. North of the Alps, much of the motion is transferred to several faults that have more easterly strike; these formed in the Kaikoura orogeny and constitute a new transform fault system.

An efficient method for joint hypocenter determination for large groups of earthquakes

Abstract The number of seismic events that can be located simultaneously by the Joint Hypocenter Determination method is limited generally by the amount of computer time and computer memory available. To find directly the hypocenters of M earthquatkes and the station corrections to N stations requires solving a system of 4M + N equations in 4M + N unknowns. This paper presents a method of solving this system of equations which is considerably more efficient than Guassian elimination.