Background Human-induced earthquakes have become an important topic of political and scientific discussion, owing to the concern that these events may be responsible for widespread damage and an overall increase in seismicity. It has long been known that impoundment of reservoirs, surface and underground mining, withdrawal of fluids and gas from the subsurface, and injection of fluids into underground formations are capable of inducing earthquakes. In particular, earthquakes caused by injection have become a focal point, as new drilling and well-completion technologies enable the extraction of oil and gas from previously unproductive formations. Earthquakes with magnitude (M) ≥ 3 in the U.S. midcontinent, 1967–2012. After decades of a steady earthquake rate (average of 21 events/year), activity increased starting in 2001 and peaked at 188 earthquakes in 2011. Human-induced earthquakes are suspected to be partially responsible for the increase. Advances Microearthquakes (that is, those with magnitudes below 2) are routinely produced as part of the hydraulic fracturing (or “fracking”) process used to stimulate the production of oil, but the process as currently practiced appears to pose a low risk of inducing destructive earthquakes. More than 100,000 wells have been subjected to fracking in recent years, and the largest induced earthquake was magnitude 3.6, which is too small to pose a serious risk. Yet, wastewater disposal by injection into deep wells poses a higher risk, because this practice can induce larger earthquakes. For example, several of the largest earthquakes in the U.S. midcontinent in 2011 and 2012 may have been triggered by nearby disposal wells. The largest of these was a magnitude 5.6 event in central Oklahoma that destroyed 14 homes and injured two people. The mechanism responsible for inducing these events appears to be the well-understood process of weakening a preexisting fault by elevating the fluid pressure. However, only a small fraction of the more than 30,000 wastewater disposal wells appears to be problematic—typically those that dispose of very large volumes of water and/or communicate pressure perturbations directly into basement faults. Outlook Injection-induced earthquakes, such as those that struck in 2011, clearly contribute to the seismic hazard. Quantifying their contribution presents difficult challenges that will require new research into the physics of induced earthquakes and the potential for inducing large-magnitude events. The petroleum industry needs clear requirements for operation, regulators must have a solid scientific basis for those requirements, and the public needs assurance that the regulations are sufficient and are being followed. The current regulatory frameworks for wastewater disposal wells were designed to protect potable water sources from contamination and do not address seismic safety. One consequence is that both the quantity and timeliness of information on injection volumes and pressures reported to regulatory agencies are far from ideal for managing earthquake risk from injection activities. In addition, seismic monitoring capabilities in many of the areas in which wastewater injection activities have increased are not capable of detecting small earthquake activity that may presage larger seismic events.

http://science.sciencemag.org/content/sci/341/6142/1225942.full.pdf

Injection-Induced Earthquakes

We mapped the minimum magnitude of complete reporting, M c , for Alaska, the western United States, and for the JUNEC earthquake catalog of Japan. Mc was estimated based on its departure from the linear frequency-magnitude relation of the 250 closest earthquakes to grid nodes, spaced 10 km apart. In all catalogs studied, Mc was strongly heterogeneous. In offshore areas the Mc was typically one unit of magnitude higher than onshore. On land also, Mc can vary by one order of magnitude over distance less than 50 km. We recommend that seismicity studies that depend on complete sets of small earthquakes should be limited to areas with similar Mc, or the minimum magnitude for the analysis has to be raised to the highest com- mon value of Mc. We believe that the data quality, as reflected by the Mc level, should be used to define the spatial extent of seismicity studies where Mc plays a role. The method we use calculates the goodness of fit between a power law fit to the data and the observed frequency-magnitude distribution as a function of a lower cutoff of the magnitude data. Mc is defined as the magnitude at which 90% of the data can be modeled by a power law fit. Mc in the 1990s is approximately 1.2 0.4 in most parts of California, 1.8 0.4 in most of Alaska (Aleutians and Panhandle excluded), and at a higher level in the JUNEC catalog for Japan. Various sources, such as ex- plosions and earthquake families beneath volcanoes, can lead to distributions that cannot be fit well by power laws. For the Hokkaido region we demonstrate how neglecting the spatial variability of M c can lead to erroneous assumptions about deviations from self-similarity of earthquake scaling.

http://basin.earth.ncu.edu.tw/download/courses/seminar_MSc/2009/0225-2_Minimum%20Magnitude%20of%20Completeness%20in%20Earthquake%20Catalogs-%20Examples%20from%20Alaska,%20the%20Western%20United%20States,%20and%20Japan.pdf

Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan

The Omori formula n(t)=K(t+c)-1 and its modified form n(t)=K(t+c)-P have been successfully applied to many aftershock sequences since the former was proposed just 100 years ago. This paper summarizes studies using these formulae. The problems of fitting these formulae and related point process models to observational data are discussed mainly. Studies published during the last 1/3 century confirmed that the modified Omori formula generally provides an appropriate representation of the temporal variation of aftershock activity. Although no systematic dependence of the index p has been found on the magnitude of the main shock and on the lowest limit of magnitude above which aftershocks are counted, this index (usually p = 0.9-1.5) differs from sequence to. sequence. This variability may be related to the tectonic condition of the region such as structural heterogeneity, stress, and temperature, but it is not clear which factor is most significant in controlling the p value. The constant c is a controversial quantity. It is strongly influenced by incomplete detection of small aftershocks in the early stage of sequence. Careful analyses indicate that c is positive at least for some sequences. Point process models for the temporal pattern of shallow seismicity must include the existence of aftershocks, most suitably expressed by the modified Omori law. Among such models, the ETAS model seems to best represent the main features of seismicity with only five parameters. An anomalous decrease in aftershock activity below the level predicted by the modified Omori formula sometimes precedes a large aftershock. An anomalous decrease in seismic activity of a region below the level predicted by the ETAS model is sometimes followed by a large earthquake in the same or in a neighboring region.

The Centenary of the Omori Formula for a Decay Law of Aftershock Activity

The role of acoustic emission in the study of rock fracture

We introduce a new method to determine the magnitude of complete- ness Mc and its uncertainty. Our method models the entire magnitude range (EMR method) consisting of the self-similar complete part of the frequency-magnitude dis- tribution and the incomplete portion, thus providing a comprehensive seismicity model. We compare the EMR method with three existing techniques, finding that EMR shows a superior performance when applied to synthetic test cases or real data from regional and global earthquake catalogues. This method, however, is also the most computationally intensive. Accurate knowledge of Mc is essential for many seismicity-based studies, and particularly for mapping out seismicity parameters such as the b-value of the Gutenberg-Richter relationship. By explicitly computing the uncertainties in Mc using a bootstrap approach, we show that uncertainties inb-values are larger than traditionally assumed, especially when considering small sample sizes. As examples, we investigated temporal variations of Mc for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping Mc on a global scale, Mc reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 Mc 6.0) and the International Seismological Centre (ISC) catalogue (4.3 Mc 5.0).

Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty

In this paper we investigate the value of b in the Gutenberg-Richter relation for four teleseismic catalogs of earthquakes: Abe's 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.

Teleseismic b values; Or, much ado about 1.0

SUMMARY

Single-link cluster analysis is a straightforward method to quantitatively measure the degree of clustering or isolation of groups of elements in a set, such as a catalogue of earthquakes. to apply single-link cluster analysis to a set of N earthquakes, individual earthquakes are first linked to their nearest neighbours to form event sub-groups. the process is then repeated and each sub-group linked to its nearest neighbour, recursively, until N-1 links are found to join all the earthquakes. This paper shows how knowledge of these links can be used to divide a group of earthquakes into any number of spatial clusters. With various modifications this analysis can identify earthquake nests, isolated events, aftershock sequences, and zones of seismic quiescence. to illustrate this method we apply it to; (i) a global data set of 2178 earthquakes having mb of 5.8 or greater reported by the International Seismological Centre (ISC) between 1964 and February 1986, and (ii) sets of earthquakes having mb of 4.9 and greater as reported by the ISC, occurring in Central America and in the Aleutians. to facilitate comparison with real data, this study also investigates the distribution of link lengths for synthetic events placed randomly on 1-D (circular line), 2-D (circular area) and 3-D (spherical volume) geometries. If we remove links between nuclear explosions from the ISC data, the resulting link distribution is quite similar to that for synthetic events placed along a 1-D fault. For the shortest links, the similarity improves markedly if the synthetic fault has a finite width, or if relative location errors cause events to be located away from the fault trace, with a standard deviation of about 15 km.

/pdf/single-link-cluster-analysis-as-a-method-to-evaluate-spatial-1cqh35gh41.pdf

Single‐Link Cluster Analysis As A Method to Evaluate Spatial and Temporal Properties of Earthquake Catalogues

Occasionally, the injection of fluids into deep wells causes or triggers earthquake activity. We propose two lists of yes-or-no questions to assess 1) whether an ongoing injection project has induced an earthquake that has already occurred; or 2) whether a proposed injection project is likely to induce a nearby earthquake. The answers to these questions form a descriptive profile of the injection project that facilitates comparison with other projects. To illustrate the application of these questions, we describe the answers in detail for the first set of questions at two sites: 1) the Rocky Mountain Arsenal near Denver, Colorado, where three significant earthquakes occurred in 1967; and 2) an injection site near Painesville, Ohio, near the epicenter of an earthquake that occurred 31 January, 1986. We also present a table of answers to these questions for several additional sites, and review other factors that may affect the potential for induced, seismic activity. The profiles of injection sites presented herein provide a convenient tool for deciding whether an injection site more closely resembles other sites where injection does, or does not induce earthquakes.

Did (Or Will) Fluid Injection Cause Earthquakes? - Criteria for a Rational Assessment

SUMMARY

This paper investigates several aspects of synthetic catalogue generation and aftershock identification schemes. First, we introduce a method for generating synthetic catalogues of earthquakes. This method produces a catalogue which has the geographic appearance of an actual catalogue when the hypocentres are plotted in map view, but allows us to vary the spatial and temporal relationships between pairs of close events. Second, we discuss six statistics to measure certain characteristics of synthetic and actual catalogues. These include four new statistics So, Bo, S1 and B1 which evaluate the distributions of link lengths between events in space and space-time as computed by single-link cluster analysis (SLC). Third, we develop a new scheme for identifying aftershocks in which a group of events forms an aftershock sequence if each event is within a space-time distance D of at least one other event in the group. We define the space-time separation of events by dst=√(d2+C2τ2), where d is the spatial separation of events, τ is the time separation, and C= 1km day-1. Our experience with several synthetic catalogues suggests that an appropriate trial value for D is 9.4 km1/2 (√S1) - 25.2 km. Here, S1, is the median link length using SLC with the metric dsT. Fourth, we generate synthetic catalogues resembling both teleseismic and local network catalogues to evaluate the validity and reliability of this aftershock identification scheme, as well as other schemes proposed by Gardner & Knopoff (1974), Shlien & Toksoz (1974), Knopoff, Kagan & Knopoff (1982), and Reasenberg (1985). Using a simple scoring method, we find that the SLC method compares favourably with other aftershock identification algorithms described in the literature.

/pdf/single-link-cluster-analysis-synthetic-earthquake-catalogues-3myvsy34n6.pdf

Single-link cluster analysis, synthetic earthquake catalogues, and aftershock identification

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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JB900071

Scott D. Davis

Papers

Teleseismic b values; Or, much ado about 1.0

Single‐Link Cluster Analysis As A Method to Evaluate Spatial and Temporal Properties of Earthquake Catalogues

Did (Or Will) Fluid Injection Cause Earthquakes? - Criteria for a Rational Assessment

Single-link cluster analysis, synthetic earthquake catalogues, and aftershock identification

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