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# Possible correlation between annual gravity change and shallow background seismicity rate at subduction zone by surface load

- Yuta Mitsui
^{1}Email authorView ORCID ID profile and - Kyohei Yamada
^{1}

**Received:**16 August 2017**Accepted:**30 November 2017**Published:**11 December 2017

## Abstract

## Keywords

- GRACE
- Gravity change
- ETAS model
- Background seismicity rate
- Surface load
- Pore pressure

## Introduction

Fault slips of earthquakes can perturb the Earth’s gravity field (Imanishi et al. 2004; Han et al. 2006), as formulated in elastomechanics (Okubo 1991; Sun and Okubo 1998). Larger earthquakes cause greater perturbation of gravity. Only large earthquakes remain the gravity signals, because of limitation in accuracy of gravity measurement.

By contrast, since gravity changes mainly reflect annually varying shallow water storage as discussed in Hydrology (e.g., Wahr et al. 2004), we expect another relation between earthquakes and gravity changes: some shallow earthquakes may be triggered by water movement around the surface (e.g., Bettinelli et al. 2008; Johnson et al. 2017). In this relation, not only large earthquakes but also small earthquakes should be involved. The physical origins of the earthquake triggering due to water movement around the surface are effects of pore-fluid pressure increase (e.g., Talwani et al. 2007) or elastic surface load (e.g., Heki 2003) on faults.

Nowadays, the Gravity Recovery and Climate Experiment (GRACE) satellites have allowed us to monitor large-scale mass movements. The GRACE satellites investigate 100- to 1000-km-scale gravity changes with an interval of approximately 1 month and can detect great perturbations of gravity due to large (> Mw 8.2) earthquakes (Han et al. 2006; Heki and Matsuo 2010; Han et al. 2013; Tanaka et al. 2015b). However, the relation between gravity changes and small earthquakes that may represent the earthquake triggering mechanisms is not well investigated.

Thus, we examine whether the GRACE gravity changes correlate with occurrences of (small) earthquakes on a global scale. We especially focus on plate subduction zones where earthquakes concentrate.

## Materials and methods

### Gravity data

We use GRACE level-3 gravity data for land, represented by equivalent water thickness (units: cm), from April 2002 to July 2016, provided by the Physical Oceanography, Distributed Active Archive Center at JPL (Swenson and Wahr 2006; Landerer and Swenson 2012; Swenson 2012). These data were scaled with a worldwide hydrology model in the Global Land Data Assimilation System (Rodell et al. 2004). In particular, we use the GRACE gravity data (analyzed by UTCSR) multiplied by a scaling factor at each spatial grid. Originally, the spatial grid is 1 degree square in latitude and longitude, and a 300-km-wide Gaussian filter to reduce spatial noise is applied. Hence, we spatially average the data every 10 degrees of latitude/longitude only for the grids with finite values (and excluding cases of very few grids), although an actual scale of surface water load may be smaller especially in islands area. The time-series data represent anomalies relative to the 2004.0–2009.999 time–mean baseline. The sampling interval is approximately 1 month. For deficient time-series data, we linearly interpolate the data from the last and the next data. About 10% of the time-series data (18/172) are interpolated.

*∆g*) with time

*t*(month) at each spatial grid is modeled as

*A*) represents an offset, the second term (

*Bt*) represents a linear trend, and the residual terms represent annual change. Using observation Eq. (1) for the gravity change, we estimate coefficients

*A*,

*B*,

*C*, and

*D*by linear regression using QR decomposition. In the following section, we use the amplitude of the annual gravity change \(\sqrt {C^{2} + D^{2} }\). Further, we tried adding terms of semi-annual change to Eq. (1), but the amplitude of the annual change did not almost change.

### Earthquake data

In order to evaluate the occurrence of earthquake, we use the ANSS Comprehensive Earthquake Catalogue data from the United States Geological Survey (USGS). We consider only shallow earthquakes at subduction zones, the focal depths of which are shallower than 30 km. Since earthquake occurrences consist of aftershocks (Omori 1894) and other types of background seismicity, we extract the background seismicity rate, *μ*, using the epidemic-type aftershock sequence (ETAS) model (Ogata 1988).

*λ*(

*t*) at time

*t*is the sum of the background seismicity rate

*μ*and the prior aftershock sequences and is given by

*M*

_{ i }is the magnitude of the

*i*th earthquake during the observation period,

*M*

_{ c }is the minimum earthquake magnitude, and the other parameters (

*K*,

*c*,

*α*, and

*p*) are constants.

In order to estimate the five ETAS parameters in logarithmic form (log *μ*, log *K*, log *c*, log *α*, and log *p*), we adopt two optimization methods for comparison: a limited-memory modification of the quasi-Newton method with box constraints (Byrd et al. 1995) and the differential evolution method (Storn and Price 1997) that is a kind of evolutionary computation to search large spaces of candidate solutions. We assume the initial parameter values (*μ*, *K*, *c*, *α*, *p*) = (1, 1, 1, 1, 1) and estimate their optimal values in the ranges of 0.0001–1, 0.1–100, 0.01–10, 0.01–10, and 0.01–10, respectively.

*M*

_{ c }= 4.5 in order to remove the seismicity of small earthquakes from the Gutenberg–Richter law (Gutenberg and Richter 1944). As a basis for the

*M*

_{ c }value, Fig. 1 illustrates the relationship between the number of earthquakes and earthquake magnitudes for the world in the ANSS comprehensive catalogue. The value of

*M*

_{ c }= 4.5 is the same as that in a previous study estimating the ETAS parameters from the ANSS catalogue (Ide 2013).

The study period to estimate the ETAS parameters is from April 2002 to July 2016, and the spatial range is 10 degrees of latitude/longitude, which is the same as the GRACE data.

We perform correlation analysis for the amplitudes of the annual gravity changes \(\sqrt {C^{2} + D^{2} }\) and the background seismicity rate *μ*. As described in the introduction section, our aim is to clarify the relation between gravity change and occurrence of small earthquakes. Thus, we exclude the areas experienced large earthquakes of magnitude greater than 7.5 in the study period. This deselection is also useful to avoid (aseismic) stressing effects of postseismic deformation within the areas, probably increasing the background seismicity rate *μ* (Llenos et al. 2009).

## Results

Estimated amplitude of the annual gravity change and their 95% confidence intervals, as equivalent water thickness (units: cm), within each spatial area

Long. (°) | Lati. (°) | Annu. grav. (cm) | 95% (low) (cm) | 95% (up) (cm) |
---|---|---|---|---|

5 | 35 | 1.25 | 0.94 | 1.57 |

15 | 35 | 0.98 | 0.62 | 1.33 |

25 | 35 | 3.12 | 2.72 | 3.53 |

35 | 35 | 4.33 | 3.88 | 4.78 |

115 | − 5 | 3.18 | 2.50 | 3.86 |

135 | 35 | 2.50 | 1.84 | 3.15 |

165 | 55 | 8.71 | 7.84 | 9.59 |

175 | − 45 | 1.81 | 1.52 | 2.10 |

175 | − 35 | 2.45 | 2.08 | 2.83 |

195 (− 165) | 55 | 0.72 | 0.63 | 0.81 |

205 (− 155) | 55 | 5.57 | 4.96 | 6.18 |

215 (− 145) | 55 | 0.55 | 0.49 | 0.60 |

235 (− 125) | 45 | 12.85 | 11.91 | 13.79 |

255 (− 105) | 25 | 3.09 | 2.67 | 3.51 |

265 (− 95) | 15 | 9.84 | 8.92 | 10.77 |

275 (− 85) | − 5 | 0.45 | 0.32 | 0.58 |

275 (− 85) | 5 | 8.23 | 7.45 | 9.00 |

285 (− 75) | − 55 | 3.48 | 2.69 | 4.28 |

285 (− 75) | − 45 | 5.74 | 5.05 | 6.43 |

285 (− 75) | 15 | 3.31 | 2.97 | 3.66 |

295 (− 65) | − 55 | 1.59 | 1.18 | 2.00 |

*μ*. We confirm that the results of QN method and DE method are almost the same; therefore, we rely on the estimated values.

Estimated background seismicity rate *μ* by QN method (with 95% confidence intervals) and by DE method

Long. (°) | Lati. (°) |
| 95% (low) (day | 95% (up) (day |
| EQ. number | Conv. rate (cm/year) |
---|---|---|---|---|---|---|---|

5 | 35 | 0.0095 | 0.0068 | 0.0133 | 0.0095 | 80 | 1 |

15 | 35 | 0.0029 | 0.0015 | 0.0054 | 0.0029 | 22 | 1 |

25 | 35 | 0.0282 | 0.0175 | 0.0455 | 0.0288 | 497 | 4 |

35 | 35 | 0.0166 | 0.0133 | 0.0208 | 0.0118 | 84 | 1 |

115 | − 5 | 0.0114 | 0.0058 | 0.0224 | 0.0114 | 111 | 6 |

135 | 35 | 0.0132 | 0.0092 | 0.0189 | 0.0133 | 278 | 5 |

165 | 55 | 0.0121 | 0.0088 | 0.0167 | 0.0122 | 87 | 7 |

175 | − 45 | 0.0126 | 0.0090 | 0.0176 | 0.0127 | 237 | 3 |

175 | − 35 | 0.0072 | 0.0050 | 0.0103 | 0.0072 | 45 | 5 |

195 (− 165) | 55 | 0.0030 | 0.0018 | 0.0050 | 0.0030 | 16 | 6 |

205 (− 155) | 55 | 0.0070 | 0.0050 | 0.0099 | 0.0065 | 37 | 6 |

215 (− 145) | 55 | 0.0004 | 0.0001 | 0.0017 | 0.0004 | 3 | 5 |

235 (− 125) | 45 | 0.0114 | 0.0082 | 0.0157 | 0.0114 | 83 | 4 |

255 (− 105) | 25 | 0.0098 | 0.0067 | 0.0143 | 0.0098 | 108 | 2 |

265 (− 95) | 15 | 0.0337 | 0.0237 | 0.0479 | 0.0337 | 384 | 6 |

275 (− 85) | − 5 | 0.0049 | 0.0030 | 0.0079 | 0.0049 | 74 | 6 |

275 (− 85) | 5 | 0.0212 | 0.0165 | 0.0271 | 0.0212 | 180 | 5 |

285 (− 75) | − 55 | 0.0019 | 0.0010 | 0.0037 | 0.0007 | 11 | 1 |

285 (− 75) | − 45 | 0.0056 | 0.0028 | 0.0108 | 0.0056 | 65 | 7 |

285 (− 75) | 15 | 0.0076 | 0.0050 | 0.0116 | 0.0075 | 133 | 1 |

295 (− 65) | − 55 | 0.0004 | 0.0001 | 0.0017 | 0.0004 | 2 | 1 |

*p*value of 1.7%. Thus, there is moderate positive correlation between the annual gravity amplitudes and the background seismicity rates. Additionally, we examine correlation between the amplitudes of the annual gravity changes and earthquake numbers (including aftershock effects) in Table 2. In this case, the correlation coefficient is 0.23 with a

*p*value of 31%, which is not a reliable correlation. It is necessary to estimate the background seismicity rate for extracting features of earthquake occurrence without aftershock effects.

## Discussion

### Examination of effects of pore pressure and surface load

What causes the positive correlation between the annual gravity amplitudes and the background seismicity rates? As described in the introduction section, the relation between gravity change and occurrence of small earthquakes may reflect the earthquake triggering due to water movement around the surface. The possible two mechanisms are friction reduction by pore-fluid pressure increase and elastic stress change due to surface load on faults.

Next, we examine the latter effect of elastic surface load. As equivalent water thickness, the mass estimated from the GRACE data was on the order of 1–10 cm (Table 1). If we assume that the mass concentrates on the surface for simplicity, we can evaluate hydrostatic pressure of the mass as source of surface load. From the following parameters: 1000 kg/m^{3} for water density, 9.8 m/s^{2} for gravitational acceleration, and 0.1 m for water thickness, we obtain the hydrostatic pressure about 1 kPa on the surface.

However, not only our study but also a recent study about regional seismicity in California (Johnson et al. 2017) revealed that seasonal water storage, causing stress change on faults as small as 1 kPa, modulated seismicity rates. Recently, on the basis of seismicity analysis (of tremors) about tidal responses, Ide and Tanaka (2014) and Tanaka et al. (2015a) suggested exponential dependence of stress changes on fault slip rates. This corresponds to the rate and state friction framework (Dieterich 1994) based on laboratory rock experiment. Using the rate and state framework, Beeler and Lockner (2003) predicted correlation between earthquake occurrence and periodic stress only in cases of longer periods than earthquake nucleation time. Our result may correspond to their prediction, since the period of the stress changes in our study is annual. Moreover, Tanaka (2014) implied a resonance effect of periodic force on seismicity.

### Not clear relation between annual gravity phase and seismicity

### Other possible mechanisms behind the correlation

Our analyses in this study targeted at subduction zones. We have two problems. First, other tectonic factors, possibly contributing the background seismicity rates (e.g., Nishikawa and Ide 2015), might contaminate the effects of periodic stress perturbation. Thus, inland areas may be more suitable for analyzing the effects of the periodic water mass movements. Since the global seismicity catalogue does not contain sufficient numbers of small (but over *M* 4.5) inland earthquakes, we did not analyze the inland areas in this study. Second, we did not consider atmospheric and oceanic load effects. Annual changes of atmospheric pressure can be on the order of 1 kPa (Ohtake and Nakahara 1999), comparable to that by the water mass movements in this study. Annual changes of ocean bottom pressure can be also as large as 1 kPa (Tanaka et al. 2015a). These load effects may also modulate seismicities. The above problems would be the focus of our future work.

## Conclusions

Through correlation analysis, we find a moderate positive correlation between the amplitudes of the annual gravity changes and the shallow background seismicity rates at the worldwide subduction zones excluding the source areas of large earthquakes. This implies that annual water cycle can activate shallow earthquakes, although the surface load elastostatic stress changes are on the order of or below 1 kPa, as small as the regional case in the previous study.

## Declarations

### Authors’ contributions

YM performed the data analyses and wrote the paper. KY helped the analyses and discussed the results. Both authors read and approved the final manuscript.

### Acknowledgements

We used generic mapping tools (Wessel et al. 2013) to draw maps. The time-variable gravity and seismicity data were provided by JPL and USGS. We acknowledge support from the Japan Society for the Promotion of Science (JSPS) KAKENHI, Grant Numbers JP16K17791 and JP16H06477. Kyohei Yamada was formerly at Department of Geosciences, Shizuoka University, 836, Ohya, Surugaku, Shizuoka 422–8529, Japan.

### Competing interests

The authors declare that they have no competing interests.

### Consent for publication

Not applicable.

### Ethics approval and consent to participate

Not applicable.

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## Authors’ Affiliations

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