# Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Earthquake Catalog Compilation and Labeling

#### 2.2. Hypothesis Formulation

#### 2.3. Synthetic Earthquake Catalogs

_{e}from an exponential distribution with the probability density function defined as

_{e}values as floats, the final number of earthquakes per well was achieved by rounding each number to the closest integer.

#### 2.4. Hypothesis Testing

_{i}and B

_{i}correspond to sample vectors and $\overline{A}$ and $\overline{B}$ are mean values of simulated sample vectors. Vectors used in the cross-correlation analysis were generated by unwrapping the N

_{g}× M

_{g}grid dividing the area of interest where N

_{g}and M

_{g}correspond to the number of cells in the vertical and horizontal direction, respectively. Normalization ensures comparable scaling of the correlation coefficients and increases the efficiency of analysis for stochastic models [29].

_{p}is the number of data points. In this study, the likelihood L is expressed by the previously calculated overlapping area between the NCC probability distributions for perturbed and synthetic catalogs. By definition, the best model is indicated by the lowest BIC value.

#### 2.5. Montney Formation Case Study

**Hypothesis H0 (Null hypothesis):**Induced seismicity is randomly associated with HF wells**Hypothesis A:**Above a cutoff level of SAP, induced seismicity scales linearly with SAP**Hypothesis B:**Induced seismicity occurs exclusively within structural corridors**Hypothesis C:**Induced seismicity occurs exclusively within structural corridors, and preferentially in areas of increased SAP (A and B)

## 3. Results

#### Statistical Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BIC | Bayesian Information Criterion |

HF | Hydraulic Fracturing |

JS | Jensen–Shannon |

KL | Kullback–Leibler |

KS | Kolmogorov–Smirnov |

KSMMA | Kiskatinaw Seismic Monitoring and Mitigation Area |

NCC | Normalized Cross Correlation |

NPGMMA | North Peace Ground Motion Monitoring Area |

SAP | Seismogenic Activation Potential |

## Appendix A

#### Appendix A.1

#### Appendix A.1.1. Kullback–Leibler and Jensen–Shannon Divergence Metrics

#### Appendix A.1.2. Two-Sample Kolmogorov–Smirnoff Tests

#### Appendix A.1.3. Statistical Analysis Results

**Table A1.**Values of Kullback–Leibler, Jensen–Shannon divergence and Kolmogorov–Smirnov statistics for the null and alternative hypotheses. Values are based on the distribution of the correlation coefficient between synthetic and perturbed catalogs.

Earthquake Count | Total Seismic Moment Release | |||||
---|---|---|---|---|---|---|

Hypothesis | KLD | JSD | KS | KLD | JSD | KS |

H0 | 0.017 | 0.064 | 1.0 | 0.41 | 0.30 | 1.0 |

A | 0.0048 | 0.035 | 0.98 | 0.0047 | 0.27 | 0.97 |

B | 0.015 | 0.060 | 1.0 | 0.0078 | 0.30 | 1.0 |

C | 0.0042 | 0.032 | 0.96 | 0.0033 | 0.25 | 0.91 |

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**Figure 1.**Flow chart presenting our generalized workflow. The central column shows the primary part of the workflow. The column on the left shows the steps used for catalog preparation, and for generating perturbed seismicity catalogs. The column on the right outlines steps used to generate a synthetic catalog (example for null hypothesis). N

_{R}corresponds to the number of synthetic catalogs generated for each hypothesis.

**Figure 2.**Key aspects of synthetic earthquake catalog generation. (

**a**) Schematic illustration of a set of 16 wells associated with pad drilling, deliberately emphasizing that the wells are horizontal. Wells are randomly selected as potentially seismogenic (red) according to test conditions. To test hypotheses, additional conditions apply to the random selection process, including location within the structural corridors and/or within area of the increased Seismogenic Activation Potential (

**b**) If a well is selected as potentially seismogenic, the number of associated earthquakes (N

_{e}) is determined based on an exponential probability distribution. Due to the exponential nature of the distribution, most of the potentially seismogenic wells are not associated with any induced earthquake. (

**c**) The locations of N

_{e}events linked to a given well are determined using randomly assigned distance and azimuth values and then converted to map (Cartesian) coordinates. The center of the circular region corresponds to the surface location of the wellhead. Magnitudes of events are selected from a power-law distribution for consistency with the Gutenberg–Richter magnitude-frequency distribution with a b-value of 1.5.

**Figure 3.**Observed seismicity in the Montney play. The tan shaded region shows the extent of the Montney play, blue circles show events associated with hydraulic fracturing in the play region, red circles show other earthquakes and the yellow polygons indicate areas that have established seismic monitoring protocols for the Montney play. Original observed seismicity catalog included seismicity (M

_{L}≥ 1.5) for the time period from January 2014 to May 2022, compiled from earthquake catalogs provided by Alberta Energy Regulator, Natural Resources Canada and British Columbia Oil and Gas Commission. Documented clusters of induced seismicity related to industrial activities outside of the Montney (e.g., the Duvernay play in AB, near Fox Creek) and natural seismicity (brown circles) were removed from the analysis.

**Figure 4.**Distribution of Seismogenic Activation Potential (SAP). The structural corridors [17] are also shown. Green circles correspond to Montney HF wells; data provided by geoLOGIC systems Ltd. © 2023.

**Figure 5.**Comparison of observed seismicity with a single realization of simulated seismicity. Observed seismicity is shown in the upper left panel, while null and alternative hypotheses are presented in the remaining panels. Yellow polygons show established areas of induced seismicity monitoring protocols in the Montney play. The red line shows the Cordilleran deformation front.

**Figure 6.**Earthquake count per cell. The panels are arranged similarly to Figure 5. Results are presented for a single realization of synthetic seismicity catalogs, compared with observed and example perturbed catalogs. The orange line in the middle of the map shows the boundary between the provinces of British Columbia and Alberta at 120${}^{\circ}$ W.

**Figure 7.**Seismic moment release per cell. The panels are arranged similarly to Figure 5. Results for a single realization of synthetic seismicity catalogs compared with observed and example perturbed catalog. Seismic moment was calculated using earthquakes above M2 located within a 20 km radius from the center of a grid cell. The orange line in the middle of the map shows the boundary between the provinces of British Columbia and Alberta.

**Figure 8.**Distribution of Normalized Correlation Coefficient (

**upper**panel) for earthquake count and total seismic moment release (

**lower**panel). PCC denotes Pearson correlation coefficient.

**Figure 9.**Comparison of Normalized Correlation Coefficient distribution between perturbed catalogs and synthetic catalogs for tests H0, A, B and C calculated for earthquake count.

**Figure 10.**Comparison of Normalized Correlation Coefficient distribution between perturbed catalogs and synthetic catalogs for tests H0, A, B and C calculated for total seismic moment release.

Variable | Distribution | Parameters |
---|---|---|

Number of earthquakes per well | exponential | $\beta $ = 10.5 |

Distance R from the well | exponential | $\beta $ = 1.0 |

Azimuth | uniform | value range of [0, 360°] |

EQ magnitude error (Perturbed catalogs only) | uniform | value range of [−0.2, 0.2] |

Location error (Perturbed catalogs only) | uniform | value range of [0, 10 km] |

Hypothesis | Description | Seismogenic Wells Conditions | Number of Parameters |
---|---|---|---|

H0 | Induced seismicity occurs randomly throughout the Montney play region | 15% of all wells selected at random | 0 |

A | Induced seismicity occurs in proportion to SAP, above a threshold level of SAP = 0.2 | Likelihood of an HF well being seismogenic scales linearly with SAP, for SAP > 0.2 | 1 |

B | Induced seismicity occurs only within Structural Corridors | Binary mask (true/false) | 1 |

C | Induced seismicity occurs within structural corridors and scales with SAP | A and B | 2 |

**Table 3.**Average values (± standard deviation) of the Normalized Correlation Coefficient for earthquake count and total seismic moment release.

Hypothesis | Earthquake Count | Total Seismic Moment Release |
---|---|---|

H0 | 0.52 ± 0.064 | 0.39 ± 0.051 |

A | 0.74 ± 0.070 | 0.61 ± 0.050 |

B | 0.68 ± 0.11 | 0.51 ± 0.057 |

C | 0.77 ± 0.068 | 0.67 ± 0.042 |

Perturbed Catalog | 0.94 ± 0.0 | 0.81 ± 0.041 |

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**MDPI and ACS Style**

Wozniakowska, P.; Eaton, D.W.
Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada. *Energies* **2023**, *16*, 5322.
https://doi.org/10.3390/en16145322

**AMA Style**

Wozniakowska P, Eaton DW.
Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada. *Energies*. 2023; 16(14):5322.
https://doi.org/10.3390/en16145322

**Chicago/Turabian Style**

Wozniakowska, Paulina, and David W. Eaton.
2023. "Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada" *Energies* 16, no. 14: 5322.
https://doi.org/10.3390/en16145322