# Spatiotemporal Assessment of Induced Seismicity in Oklahoma: Foreseeable Fewer Earthquakes for Sustainable Oil and Gas Extraction?

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.77. Such a relation could be used to establish “sustainable water injection limits” aiming to minimize seismicity to values comparable with several historically representative averages. Results from these analyses coincide on previously found sustainable limits of 5 to 6 million m

^{3}/month but expand to operations that could attain the same number through differential monthly planning. Findings could potentially be used for model intercomparison and regulation policies.

## 1. Introduction

^{2}of the epicenter. OCC has also taken many other actions in response to recent earthquakes, including a disposal volume reduction plan [12].

## 2. Data Sources

_{L}, M

_{W}, m

_{b}and M

_{d}) are available between 1882 to present. In the interest of revealing spatiotemporal patterns of near-recent seismic activity in Oklahoma, only earthquakes occurred after January 2006 are studied in detail.

## 3. Earthquake Unit Homogenization and Data Completeness

#### 3.1. Magnitude Unit Homogenization

_{L}) also known as Richter magnitude, (2) duration magnitude (M

_{d}), (3) body-wave magnitude (m

_{b}) and (4) moment magnitude (M

_{w}). The number of earthquakes occurred between January 2006 and December 2017 is given in Table 1 with respect to the different used magnitude units. Nonetheless, many earthquakes were simultaneously recorded in different scales which facilitate their unit homogenization. As the majority of seismic events (i.e., 25,956) are reported in M

_{L}scale, all other units are converted to M

_{L}to reduce data uncertainty introduced during this conversion. In order to do so, two empirical magnitude conversion relations are derived for those events with significant number of data pairs (i.e., [M

_{L}, m

_{b}] and [M

_{L}, M

_{w}]). Since [M

_{d}, M

_{L}] had zero pairs, a previously derived expression is applied [23] for such a conversion. Scatterplots with the event magnitude pairs, fitted, and 95% confidence envelopes are shown in Figure 1. The derived and used statistical regressions, sample size, cross-correlation coefficients and author are shown in Table 2.

#### 3.2. Earthquake Magnitude of Completeness

_{L}to 5.9 M

_{L}. In an earthquake catalog, the magnitude of completeness (M

_{C}) is the minimum magnitude above which earthquakes within a certain region are reliably recorded. Defining M

_{C}is necessary due to the complexity, spatial and temporal heterogeneity of seismometer networks and time series records [24,25]. To assess M

_{C}for our earthquake dataset, a frequency-magnitude distribution (FMD) plot was created for the entire dataset (see Figure 2) based on the entire magnitude range (EMR) method proposed by Woessner and Wiemer [25]. Their method estimates the FMD based on the Gutenberg-Richter law [26]. For the data with magnitude below the assumed Mc, EMR uses a normal cumulative distribution function [25]. Woessner and Wiemer [25] compared the EMR method with other three including maximum curvature-method (MAXC; Wiemer and Wyss, 2000), goodness-of-fit test (GFT; [27]), and Mc by b-value stability (MBS; [28]), and they concluded that EMR is the most favorable model to calculate Mc from regional earthquake catalogues [25]. The FMD curve indicates a data-based suggested value [25] of M

_{C}= 2.6 which will be used as minimum trustable M

_{L}to include in the subsequent analyses.

## 4. Interannual Seismicity and Wastewater Injection Activity in Oklahoma

_{L}5.0 (Oklahoma Geological Survey 2017). From 1882 to 2002, (120 years) Oklahoma had a total of 186 earthquakes with M

_{L}≥ M

_{C}, for an average of 1.55 earthquakes per year (Oklahoma Geological Survey 2017). The Figure 3a,b compile the recent history of earthquake events (bars, N(M

_{L})) occurred in Oklahoma from 2000 to 2017 with M

_{L}≥ M

_{C}and discretized by M

_{L}category. Comparatively to its precedent years, the number of seismic events per year with M

_{L}≥ M

_{C}occurred from 2003 to 2008 increased to 4.9 (39 in total; see Figure 3a). However, 2009 appears as a benchmark year that marks a significant increase relative to historic means (see Figure 3b). Between 2009 and 2017, the state had averaged 730 earthquakes per year (6570 total), which is more than four hundred times (i.e., 471) the historic averages up to year 2002. Since “felt earthquakes” usually refer to those with 3 ≤ M

_{W}≤ 5 (National Research Council 2013), Figure 3b also depicts N(M

_{L}) per M

_{L}category with M

_{C}≤ M

_{L}< 3, 3 ≤M

_{L}<4 and 4 ≤ M

_{L}< 5 in Oklahoma from 2000 to 2017. A particular peak in seismicity occurred in 2015 with 2560 events, followed by a steady decrease to 786 in 2017. This bell-shaped trend is replicated by each of the used categories in Figure 3b (e.g., M

_{C}, 3 and 4), except by the M

_{L}≥ 5 whose peak occurred in 2016. The total number of “damaging earthquakes”, which are those with M

_{l}≥ 5, also increased after 2009 as shown in Figure 3b.

^{6}m

^{3}/year) from OCC UIC Class II wells reports that begin in 2006 to near present. From 2006 to 2012 the volume of injected water ranged around 150 × 10

^{6}m

^{3}/year. However, starting in 2012 a rapid increase in IW volumes is observed that peak in 2014 and 2015, followed by a sharp decline in 2016 and 2017 when the IW gets back to a number around the 2006–2012 average of 150 × 10

^{6}m

^{3}/year. A paired time series analysis of the coupled IW and N(M

_{L}) reveals that both variables have shown a similar trend since the start of the unconventional use of injected water to retrieve oil and gas.

_{L}≥ M

_{C}and the corresponding location of wastewater disposal wells operated during the most active year (i.e., 2014) are illustrated in Figure 4a,b. In both figure panels, the different symbol sizes represent different categories of M

_{L}and IW. The spatial distribution of the two variables resembles a spatially correlated structure whose dependency functions need to be determined for different time lags. Further, during this period (2006–2017) most earthquakes occurred in central and northern Oklahoma while the largest magnitude ones occurred in the central region of the state. Accordingly, historically the largest IW volumes occurred mainly in central and northern Oklahoma. In counties like Osage, seismicity appears to be low possibly due to the dense rock bodies that reduce seismogenic potential for basement faults [31,32].

## 5. Regional Migration Pattern of Epicenters and Wastewater Injection Activity

_{T}, Y

_{T}) in any year (T) is the representative geographic location of all epicenters (X

_{i}, Y

_{i}) adjusted for the local magnitude M

_{L}associated with each earthquake (i) acting as weighting factors (w

_{i}) as shown in Equation (1) [33].

_{i}is the M

_{L}for each earthquake event (i) in a particular year T. Following equation (1), weighted mean centers of all earthquakes occurred in a particular year T would be closer to epicenters with the largest M

_{L}during that year. The major and minor axes of these weighted standard deviation ellipses are calculated as the second moment of the x- and y-coordinates distribution from each weighted mean center [34]. This cleaner approach, illustrated by Figure 5a, shows a generalized northwest seismic migration pattern from 2006 through 2017. Correspondingly, Figure 5b illustrates the weighted mean centers and standard deviation ellipses of wastewater disposal wells in each year from 2006 through 2017. Analogously to epicenters, wastewater injection locations are weighted by the volumetric magnitude of the annual injection volumes associated with each well. Thus, the weighted mean center of wastewater disposal wells in a particular year would be geographically closer to wells with larger annual injection volumes, reflecting the regional trend of well activity in that specific year. In summary, both unconventional oil and gas extraction and earthquake count show a northwest migration pattern during 2006 to 2017. To recognize year to year migration patterns, Figure 6 compiles those bivariate trends through vectors whose length is proportional to the average migration distance between consecutive years. The diagram shows some years when both processes migrated similar distances in similar directions, particularly 2007–2008 (~33 to 35 km SE), 2009–2010 (10 to 20 km NNE), 2012–2013 (~43 km SSE), 2014–2015 (~9 to 22 km SE) and 2016–2017 (7 to 15 km W). In other cases, the two vectors keep an angular distance greater than 90 degrees such as 2006–2007, 2010–2011 (N-E quadrant), 2011–2012 (mostly E quadrants), 2015–2016 (mostly S quadrants). The large disparity in distances in 2006–2007, 2011–2012 and 2013, 2014 maybe due to the fact that injection operations moved quickly in the last months of the last year and earthquake count (since it has a lagged response) did not immediately showed the expected pattern of migration. Overall, regional migration patterns seem to correspond to one another evidencing a zonal effect of the unconventional oil and gas industry on the number of regional earthquake count.

## 6. A Parsimonious Model of Seismicity.

_{t}) as a function of IW

_{t − i}for i = 0, 1, 2, etc, months. This time delay (i.e., i) can be physically expressed as the time the pressure increase takes to propagate from the injection wells to critically stressed faults in the crystalline basement [15,18]. The cross-correlogram illustrated in Figure 7a reveals that lags i = 0 through −25 previous to the seismic events appear to mostly contribute to the bivariate co-dependence between IW (predictor) and N (predictand). The Figure 7b quantifies the contribution of each lag i to the total correlation structure above the Pearson correlation coefficient significance threshold. According to the correlations for lags 0 to 25 months, we extract weight coefficients (w

_{i}) for each lagged contribution to express $\widehat{\mathrm{IW}}$ as a function of IW

_{t − i}(i = 0, 1, 2…, 25 months) as shown in Equation (2):

^{3}/month) to N

_{t}for all M

_{L}≥ M

_{C}(see Equation 3). Figure 8 illustrates such a fitted relation applied to the logarithms of the monthly values since 2011 (complete data pairs).

_{t}). The term “sustainable limit” in column 5 of Table 3 refers to potential maximum injection values per month that the Oklahoma state regulation authorities (e.g., OCC and/or EPA) could consider for regulation of the oil and gas industry. This by no means accounts for other influences on environmental issues like water or energy consumption, groundwater, land or air pollution. In this table, it appears that constant and continuous rates (i.e., IW

_{t − i}) of 5.6 million m

^{3}/month (i = 0, 1, 2, 3, etc) could reduce the number of earthquakes to pre- year 2000 conditions to 1.55 earthquakes per year with magnitude M

_{L}>M

_{C}. However, one could also define other limits like the mean water injection during the period 2003–2008 (6.8 million m

^{3}/month) as a sustainable limit, but at the expense of potential additional seismic occurrences (5.1 events/year) similar to the beginning of the 2000 decade or previous to the boom of oil and gas extraction (pre 2009–2015). Also note how, since this law is potential, an increase in 1 × 10

^{6}m

^{3}/month of injected water represents different changes in seismicity across the spectrum of IW values with larger values triggering dramatic increases in seismic events, N

_{t}. As an example, an increase of 1 million m

^{3}/month above 19 million m

^{3}/month (super-boom scenario) would represent more than 1000 additional earthquakes (M

_{L}> M

_{C}) per year.

## 7. Model Output Intercomparison

_{C}= 3.0) and removed (declustered) any instances of foreshocks and aftershocks from the main events, the parsimonious model had to be re-calibrated for this data-based but maintaining the IW

_{t − i}correlation derived in Section 6 of this manuscript. For an M

_{C}= 3 and declustered database, Equation (4) represents the number of expected main shocks as a function of the antecedent 25 months of waste water injection (using Equation 2). Similarly to Equation (3), this model explains 75% of the seismic activity at a monthly time scale.

## 8. Discussion

#### 8.1. Acknowledging Methological Limitations

_{w}to M

_{L}) procedure introduces a maximum uncertainty of 19% (see Section 3.1 and Table 2) the location and size of the weighted mean centers and standard deviation ellipses will have a maximum inherited error of 9.5%. Third, the analyses did not consider other influences on earthquakes’ induction or generation mechanisms such as regional rock fracturing or geologic structures that propagate or moderate seismic waves. Moreover, due to the limiting number of years with data (2006–2017), we do not know how the panoramic would look like in the future in views of higher (or lower) levels of wastewater injection. Further we recommend caution when planning to use of the statistical relationships found here for future years as the rock systems might not behave in a linear fashion anymore since the increasing rock-fracturing processes might propagate across larger regions becoming a network of interconnected faulted systems that might translate in widespread earthquakes swarms. Finally, the results achieved in this study, however, need to be further explored within different subregions to consider particular geological heterogeneities that could result in potentially different behaviors than the ones shown here.

#### 8.2. Contributions to State-of-the-Art

^{3}/month or any combination of values of IW during the antecedent 25 months that allow obtaining around 1.5 earthquakes per year with M

_{L}≥ M

_{C}. A similar number of 5 × 10

^{6}m

^{3}/month was also found by Langenbruch and Zoback [18]. However, these authors propose a steady injection condition per month, but according to Equation (2) there could be other combinations of differential (seasonal) injection that could lead to the same result of minimum earthquakes. Third, possibly the best utility of the results of this manuscript is its use as a tool for model intercomparison with current and future models. For example, Pollyea et al. [20] developed a geospatial analysis of the bivariate occurrence of earthquakes with the location of salt-water disposal wells. We coincide with Pollyea et al. [20] in that there is a general of north-west migration of both processes. However, a difference we find is the fact that instead of circles we obtained the two-axis variability ellipses and weighted the well and epicenter locations by magnitude and injection volumes, providing a more accurate description of their spatially correlated distribution. We also provide year by year direction of migration and distance patterns. Results from the model output intercomparison experiment show comparable capabilities of the Parsimonious (Hong et al, this paper) and Hydromechanical [17] models in the long-term with the Parsimonious representing better the recent decline in seismicity conditions. However, both these models seem to have a weak performance at detecting rapid changes better captured by the seismogenic model [18].

#### 8.3. Contributions to Sustainable Extraction and Decision Making: What are Sustainable Limits?

## 9. Conclusions

^{2}= 0.77. Using such a relation, several sustainable extraction limits are explored and compared with historic means. Results from these analyses coincide and expand on previously sustainable limits of 5 to 6 million m

^{3}/month to potential combinations that could attain the same number within the 25 previous months. A model intercomparison of our parsimonious model, a hydromechanical model, and a seismogenic model reveals a satisfactory performance of the proposed approach and similitude to the hydromechanical model outputs. Nonetheless monthly sharp changes in seismicity could only be more appropriately represented by the seismogenic model. The approach proposed in this manuscript could potentially be regionalized according to the geology of each zone and results could potentially be used as a tool for further model intercomparison experiments and decision making on spatially varied permission distribution and regional industry development to minimize negative consequences of induced earthquakes.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Ellsworth, W.L. Injection-Induced Earthquakes. Science
**2013**, 341, 1225942. [Google Scholar] [CrossRef] [PubMed] - Frohlich, C.; Hayward, C.; Stump, B.; Potter, E. The Dallas–Fort Worth earthquake sequence: October 2008 through May 2009. Bull. Seismol. Soci. Am.
**2011**, 101, 327–340. [Google Scholar] [CrossRef] - Horton, S. Disposal of Hydrofracking Waste Fluid by Injection into Subsurface Aquifers Triggers Earthquake Swarm in Central Arkansas with Potential for Damaging Earthquake. Seismol. Res. Lett.
**2012**, 83, 250–260. [Google Scholar] [CrossRef] - Kim, W.Y. Induced seismicity associated with fluid injection into a deep well in Youngstown, Ohio. J. Geophys. Res. Solid Earth
**2013**, 118, 3506–3518. [Google Scholar] [CrossRef] [Green Version] - Llenos, A.L.; Michael, A.J. Modeling earthquake rate changes in Oklahoma and Arkansas: Possible signatures of induced seismicity. Bull. Seismol. Soci. Am.
**2013**, 103, 2850–2861. [Google Scholar] [CrossRef] - Van der Elst, N.J.; Savage, H.M.; Keranen, K.M.; Abers, G.A. Enhanced remote earthquake triggering at fluid-injection sites in the midwestern United States. Science
**2013**, 341, 164–167. [Google Scholar] [CrossRef] [PubMed] - Keranen, K.M.; Weingarten, M.; Abers, G.A.; Bekins, B.A.; Ge, S. Sharp increase in central Oklahoma seismicity since 2008 induced by massive wastewater injection. Science
**2014**, 345, 448–451. [Google Scholar] [CrossRef] [PubMed] - Weingarten, M.; Ge, S.; Godt, J.W.; Bekins, B.A.; Rubinstein, J.L. High-rate injection is associated with the increase in U.S. mid-continent seismicity. Science
**2015**, 348, 1336–1340. [Google Scholar] [CrossRef] [PubMed] - Keranen, K.M.; Savage, H.M.; Abers, G.A.; Cochran, E.S. Potentially induced earthquakes in Oklahoma, USA: Links between wastewater injection and the 2011 Mw 5.7 earthquake sequence. Geology
**2013**, 41, 699–702. [Google Scholar] [CrossRef] - Barbour, A.J.; Norbeck, J.H.; Rubinstein, J.L. The effects of varying injection rates in Osage County, Oklahoma, on the 2016 M
_{w}5.8 Pawnee earthquake. Seismol. Res. Lett.**2017**, 88, 1040–1053. [Google Scholar] [CrossRef] - Walsh, F.R.; Zoback, M.D. Oklahoma’s recent earthquakes and saltwater disposal. Sci. Adv.
**2015**, 1, e1500195. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Oklahoma Corporation Commission. Earthquake Response Summary. 2017. Available online: http://www.occeweb.com/News/2017/02-24-17EARTHQUAKE%20ACTION%20SUMMARY.pdf (accessed on 15 October 2018).
- Holland, A.A. Earthquakes Triggered by Hydraulic Fracturing in South-Central Oklahoma. Bull. Seismol. Soci. Am.
**2013**, 103, 1784–1792. [Google Scholar] [CrossRef] - Hough, S.E.; Page, M. A Century of Induced Earthquakes in Oklahoma? Bull. Seismol. Soci. Am.
**2015**, 105, 2863–2870. [Google Scholar] [CrossRef] - Chen, X.; Nakata, N.; Pennington, C.; Haffener, J.; Chang, J.C.; He, X.; Zhan, Z.; Ni, S.; Walter, J.I. The Pawnee earthquake as a result of the interplay among injection, faults and foreshocks. Sci. Rep.
**2017**, 7, 4945. [Google Scholar] [CrossRef] [PubMed] - Hinks, T.; Aspinall, W.; Cooke, R.; Gernon, T. Oklahoma’s induced seismicity strongly linked to waste water injection depth. Science
**2018**, 359, 1251–1255. [Google Scholar] [CrossRef] [PubMed] - Norbeck, J.H.; Rubinstein, J.L. Hydromechanical Earthquake Nucleation Model Forecasts Onset, Peak, and Falling Rates of Induced Seismicity in Oklahoma and Kansas. Geophys. Res. Lett.
**2018**, 45, 2963–2975. [Google Scholar] [CrossRef] - Langenbruch, C.; Zoback, M.D. How will induced seismicity in Oklahoma respond to decreased saltwater injection rates? Sci. Adv.
**2016**, 2, e1601542. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Langenbruch, C.; Weingarten, M.; Zoback, M.D. Physics-based forecasting of man-made earthquake hazards in Oklahoma and Kansas. Nat. Commun.
**2018**, 9, 3946. [Google Scholar] [CrossRef] [PubMed] - Pollyea, R.M.; Mohammadi, N.; Taylor, J.E.; Chapman, M.C. Geospatial analysis of Oklahoma (USA) earthquakes (2011–2016): Quantifying the limits of regional-scale earthquake mitigation measures. Geology
**2018**, 46, 215–218. [Google Scholar] [CrossRef] - Oklahoma Corporation Commission. Oil and Gas Data Files. 2018. Available online: http://www.occeweb.com/OG/ogdatafiles2.htm (accessed on 23 September 2018).
- Oklahoma Geological Survey. Earthquake Catalogs. 2018. Available online: http://www.ou.edu/content/ogs/research/earthquakes/catalogs.html (accessed on 23 September 2018).
- Brumbaugh, D.S. A Comparison of Duration Magnitude to Local Magnitude for Seismic Events Recorded in Northern Arizona. J. Ariz.-Nev. Acad. Sci.
**1989**, 23, 29–31. [Google Scholar] - Habermann, R.E. Seismicity rate variations and systematic changes in magnitudes in teleseismic catalogs. Tectonophysics
**1991**, 193, 277–289. [Google Scholar] [CrossRef] - Woessner, J.; Wiemer, S. Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty. Bull. Seismol. Soci. Am.
**2005**, 95, 684–698. [Google Scholar] [CrossRef] [Green Version] - Gutenberg, B.; Richter, C.F. Frequency of earthquakes in California. Bull. Seismol. Soci. Am.
**1944**, 34, 185–188. [Google Scholar] - Wiemer, S.; Wyss, M. Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan. Bull. Seismol. Soci. Am.
**2000**, 90, 859–869. [Google Scholar] [CrossRef] - Cao, A.; Gao, S.S. Temporal variation of seismic b-values beneath northeastern Japan island arc. Geophys. Res. Lett.
**2002**, 29, 48-1–48-3. [Google Scholar] [CrossRef] - Murray, K.E.; Holland, A.A. Inventory of class II underground injection control volumes in the midcontinent. Okla. City Geol. Soc
**2014**, 65, 98–106. [Google Scholar] - Council, N.R. Induced Seismicity Potential in Energy Technologies; National Academies Press: Washington, DC, USA, 2013. [Google Scholar]
- Crain, K.; Chang, J.C.; Walter, J.I. Geophysical anomalies of Osage County and its relationship to Oklahoma seismicity. In AGU Fall Abstracts; American Geophysical Union: Washington, DC, USA, 2017. [Google Scholar]
- Shah, A.K.; Keller, G.R. Geologic influence of induced seismicity: Constraints from potential field data in Oklahoma. Geophys. Res. Lett.
**2017**, 44, 152–161. [Google Scholar] [CrossRef] - Burt, J.E.; Barber, G.M.; Rigby, D.L. Elementary Statistics for Geographers; Guilford Press: New York, NY, USA, 2009. [Google Scholar]
- Scott, L.M.; Janikas, M.V. Spatial Statistics in ArcGIS. In Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications; Fischer, M.M., Getis, A., Eds.; Springer Berlin Heidelberg: Berlin/Heidelberg, Germay, 2010; pp. 27–41. [Google Scholar]
- Zoback, M.D. Managing the seismic risk posed by wastewater disposal. Earth
**2012**, 57, 38. [Google Scholar] - Oklahoma Corporation Commission. Media Advisory—Ongoing OCC Earthquake Response. 2015. Available online: http://www.occeweb.com/News/2015/03-25-15%20Media%20Advisory%20-%20TL%20and%20related%20documents.pdf (accessed on 15 October 2018).

**Figure 1.**Linear regression plots for (

**a**) M

_{L}vs. m

_{b}and (

**b**) M

_{L}vs. M

_{W}for all seismic events occurred in Oklahoma between January 2006 and December 2017. Conversion equations are shown in Table 2.

**Figure 2.**Cumulative and noncumulative frequency-magnitude distributions on logarithmic scale with the black line indicating magnitude of completeness (M

_{C}) for time series during 2006–2017.

**Figure 3.**(

**a**) Time series of total annual number of earthquakes (N(M

_{L})) with M

_{L}≥ M

_{C}(red bars) and oil/gas industry-related injected volumes of wastewater (IW) in million cubic meters (white triangles) in Oklahoma from 2000 to 2017. (

**b**) Time series of total annual number of earthquakes (N(M

_{L})) with M

_{L}≥ M

_{C}per magnitude range between 2000 and 2017 and oil/gas industry-related volumes of wastewater injected (IW) between 2006 and 2017 in Oklahoma. Note the log scale for N(M

_{L}) in (

**b**).

**Figure 4.**(

**a**) Spatial distribution of earthquakes with M

_{L}≥ M

_{C}occurred in Oklahoma from 2006 to 2017; (

**b**) Spatial distribution of wastewater disposal wells with corresponding IW volume (m

^{3}/year) operated in 2014.

**Figure 5.**(

**a**) Earthquake-clustering occurrence by year. Epicenters’ weighted mean centers (triangles) and standard deviation ellipses of all recorded earthquakes occurred in Oklahoma between 2006 and 2017; (

**b**) Wastewater injection volume weighted mean centers (triangles) and standard deviation ellipses in Oklahoma between 2006 and 2017. The colors in both panels match for the same years, except by 2013 whose dashed lines are intended to improve result visualization. Coordinates of mean weighted centers are computed using Equation (1).

**Figure 6.**Yearly migration patterns between earthquakes weighted epicenters and wastewater injection activity in Oklahoma since 2006. Red and blue lines mean the average displacement of mean weighted centers of wastewater injection and earthquakes between consecutive years. The average displacement distance is also indicated within each compass diagram.

**Figure 7.**(

**a**) Cross-correlation diagram between IW

_{t − i}and N

_{t}for different lags of IW (e.g., i = 0, 1, 2, 3…, n months). Negative numbers mean that IW precedes N

_{t}. (

**b**) Contribution (w

_{i}) of each lag i to the prediction of the total of number of earthquakes in a particular month t (N

_{t}), to be applied to the predictors in Equation (2).

**Figure 8.**Regional induced-earthquake count N

_{t}(M

_{L}≥ M

_{C}) and $\widehat{\mathrm{IW}}$ estimator calibrated between years 2006 and 2017 in the state of Oklahoma. The power law explains 77% of the bivariate behavior of monthly injection and earthquakes number. Upper and lower dashed lines representing standard errors of estimates have been added to the mean predicted values.

**Figure 9.**Model intercomparison experiment using the hydromechanical, seismogenic and parsimonious models for retrospective simulations of seismicity in Oklahoma between 2008 and 2018 in light of observed (declustered) seismic events and monthly waste water injection rates.

Magnitude Type | Number of Earthquakes |
---|---|

Duration magnitude (M_{d}) | 1763 |

Body-wave magnitude (m_{b}) | 364 |

Local Magnitude (M_{L}) | 25,956 |

Moment Magnitude (M_{w}) | 438 |

**Table 2.**Mathematical regressions adopted and derived to homogenize M

_{d}, m

_{b}and M

_{w}seismic magnitudes to local (Richter) magnitude, M

_{L}.

Expression | Sample Size | R^{2} | Reference |
---|---|---|---|

${\mathrm{M}}_{\mathrm{L}}=0.936{\mathrm{M}}_{\mathrm{d}}-0.16$ | 17 | 0.95 | Brumbaugh, 1989 [23] |

${\mathrm{M}}_{\mathrm{L}}=0.85{\mathrm{m}}_{\mathrm{b}}+0.52$ | 252 | 0.84 | Hong et al (this paper) |

${\mathrm{M}}_{\mathrm{L}}=0.96{\mathrm{M}}_{\mathrm{W}}+0.35$ | 440 | 0.81 | Hong et al (this paper) |

**Table 3.**Predicting N

_{t}(number of earthquakes/year) in terms of hypothetical scenarios of different weighted average ($\widehat{\mathrm{IW}}$; Equation (2)) or monthly constant IW in light of historical records and benchmark periods. Uncertainty interval estimates have been added to each predicted N

_{t}. Historical benchmark periods have been extracted from section 4 this manuscript for reasons of comparison.

$\widehat{\mathbf{I}\mathbf{W}}$ (×10 ^{6} m^{3}/month) | N_{t} (number/year) | N_{t} Interval [min, max] (number/year) | Historical Benchmark Period | Sustainable Limit? |
---|---|---|---|---|

1 | 3.5 × 10^{−5} | 2.53 × 10^{−5},5.87 × 10 ^{−5} | - | - |

3 | 0.03 | 0.02, 0.05 | - | - |

5 | 0.76 | 0.50, 1.17 | - | - |

5.6 | 1.54 | 1.01, 2.34 | 1884–2002 | Pre- 2002 |

6.8 | 5.07 | 3.32, 7.21 | 2003–2008 | Pre oil and gas boom (2003–2008) |

7 | 6.05 | 3.97, 9.23 | - | - |

9 | 28.4 | 18.6, 43.3 | - | - |

11 | 97.5 | 64.0, 148.6 | - | - |

13 | 272 | 179, 415 | - | - |

15 | 657 | 431, 1001 | - | - |

15.2 | 712 | 467, 1086 | 2009–2017 | Peak period |

15.4 | 788 | 517, 1200 | 2017 | Oil/gas price fall/OCC regulation |

17 | 1417 | 930, 2161 | - | - |

18.7 | 2547 | 1671, 3882 | 2015 | Peak year |

19 | 2809 | 1843, 4281 | - | - |

20 | 3851 | 2527, 5869 | - | - |

21 | 5198 | 3411, 7922 | - | - |

23 | 9095 | 5968, 13861 | - | - |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hong, Z.; Moreno, H.A.; Hong, Y.
Spatiotemporal Assessment of Induced Seismicity in Oklahoma: Foreseeable Fewer Earthquakes for Sustainable Oil and Gas Extraction? *Geosciences* **2018**, *8*, 436.
https://doi.org/10.3390/geosciences8120436

**AMA Style**

Hong Z, Moreno HA, Hong Y.
Spatiotemporal Assessment of Induced Seismicity in Oklahoma: Foreseeable Fewer Earthquakes for Sustainable Oil and Gas Extraction? *Geosciences*. 2018; 8(12):436.
https://doi.org/10.3390/geosciences8120436

**Chicago/Turabian Style**

Hong, Zhen, Hernan A. Moreno, and Yang Hong.
2018. "Spatiotemporal Assessment of Induced Seismicity in Oklahoma: Foreseeable Fewer Earthquakes for Sustainable Oil and Gas Extraction?" *Geosciences* 8, no. 12: 436.
https://doi.org/10.3390/geosciences8120436