# Seismic Impact of Large Earthquakes on Estimating Global Mean Ocean Mass Change from GRACE

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## Abstract

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## 1. Introduction

## 2. Data and Method

_{20}terms with the Satellite Laser Ranging (SLR) observations [32]. Since the degree-1 terms, representing the geocenter motion were absent in the GRACE monthly solutions, we used the degree-1 coefficients provided by the GRACE project (GRACE Technical Note 13) [33] to include the geocenter motion effect, which are derived from GRACE observations using an improved method [12,34]. Then we calculated the global gridded (1° × 1°) surface mass change fields (with respect to the mean field 2003.01–2015.12) from the 142 monthly solutions. By least squares fitting of the time series at each grid point of these monthly solutions, we obtained the global mass change rate distribution.

_{1}and C

_{2}are the constant terms before and after the earthquake. p is the total post-seismic gravity change reached at the end of relaxation. τ is the e-folding relaxation time of the post-seismic changes. Here we chose τ = 7 months in the Sumatra and Chile earthquake regions fitting. We also chose τ = 4 months in the Tohoku-Oki earthquake region fitting (the selection of the parameter τ on the time series fitting will be discussed later in Section 4). t

_{eq}is the earthquake occurrence time. Figure 2a shows an example of the time series fitting at a selected point B (36.5°N, 145.5°E) in the Tohoku-Oki earthquake region. When the time series at the point includes the seismic effects of two earthquakes, the fitting equation can be expressed as:

_{1}is the pre-seismic constant of the first earthquake, C′

_{2}is the post-seismic constant of the first earthquake, and C′

_{3}is the post-seismic constant of the second earthquake. t

_{eq}

_{1}and t

_{eq}

_{2}represent the occurrence times of the first and second earthquakes, respectively. τ

_{1}and τ

_{2}are the e-folding relaxation time parameters of the post-seismic change corresponding to the first and second earthquakes, respectively. Note here it is implicitly assumed that the post-seismic deformation of the first event is fully relaxed before the second event occurs. This assumption should make sense for the case of Sumatra earthquake region because the interval between the two events is more than 7 years, during which most post-seismic deformation of the 2004 Sumatra earthquake has been relaxed. Figure 2b shows an example of the time series fitting at a selected point A (2.5°N, 93.5°E) in the Sumatra earthquake region.

## 3. Results

#### 3.1. Seismic Effect Correction

#### 3.2. Impact of Seismic Effect on the GMOM Change Rate

## 4. Discussion

#### 4.1. Uncertainty Estimate of GMOM Change Rate

_{20}terms) might also have notable contribution to the GMOM rate uncertainty. Therefore, the true uncertainty level could be even larger.

#### 4.2. Uncertainty Estimate of Seismic Impact on the GMOM Change Rate

#### 4.3. Comparison with Estimates from Altimery and Argo

#### 4.4. Seismic Impact for Shorter Time Spans and Regional Scales

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The spatial distribution of equivalent water height (EWH) trend rates 2003–2015 from the Gravity Recovery and Climate Experiment (GRACE) Release-06 (RL06) solutions, with the glacial isostatic adjustment (GIA) effect removed and (

**b**) the time series at point A (2.5°N, 93.5°E) from GRACE, and the linear trend fitted by least squares fitting.

**Figure 2.**The time series fitting examples at two selected points, with the co- and post-seismic terms taken into account. (

**a**) The time series fitting includes the effect of only one earthquake (i.e., the March 2011 Tohoku-Oki earthquake) and (

**b**) the fitting includes the effect of two earthquakes (i.e., the December 2004 and April 2012 Sumatra earthquakes). The red curve represents the original time series observed by GRACE. The blue curves represent the fitted co- and post-seismic terms. The vertical dashed lines denote the occurrence months of the earthquakes.

**Figure 3.**(

**a**) The EWH rate distribution in the Sumatra earthquake region, (

**b**) the rate distribution after the seismic effect correction, (

**c**) the time series at the point D (3.5°N, 94.5°E), and (

**d**) the time series at the point E (10.5°N, 98.5°E).

**Figure 4.**(

**a**) The EWH rate distribution in the Tohoku-Oki earthquake region, (

**b**) the rate distribution after the seismic effect correction, (

**c**) the time series at the point F (36.5°N, 144.5°E), and (

**d**) the time series at the point G (39.5°N, 138.5°E).

**Figure 5.**(

**a**) The equivalent water height rate distribution in the Chile earthquake region, (

**b**) the rate distribution after the seismic effect correction; (

**c**) the time series at the point H (−37.5°N, 283.5°E); and (

**d**) the time series at the point I (−35.5°N, 291.5°E).

**Figure 6.**The global mean ocean mass (GMOM) change rates using forward modeling recovery after 100 iterations. The red curve represents the GMOM change rate without seismic correction. The blue curve denotes the GMOM change rate with correction for the Sumatra earthquake region. The magenta curve represents the GMOM change rate with the corrections for the Sumatra and Tohoku-Oki earthquake regions. The black curve denotes the GMOM change rate with the corrections for the three regions.

**Figure 7.**(

**a**) The global EWH change rate distribution corrected only for the Sumatra earthquake region; (

**b**) the global rate distribution corrected for the Sumatra and Tohoku-Oki earthquake regions; and (

**c**) the global rate distribution corrected for the Sumatra, Tohoku-Oki, and Chile earthquake regions.

**Table 1.**Gravity Recovery and Climate Experiment (GRACE) global mean ocean mass (GMOM) change rates from forward modeling (FM) recovery for the period 2003–2015 without and with the seismic corrections.

Without Correction | With Correction for Sumatra Region | With Correction for Sumatra + Tohoku-Oki Regions | With Correction for the Three Regions | |
---|---|---|---|---|

GMOM rate (mm/yr) | 2.12 ± 0.11 * | 2.08 ± 0.12 * | 2.07 ± 0.12 * | 2.05 ± 0.12 * |

**Table 2.**The GMOM rates from Center for Space Research (CSR), Geoforschungszentrum (GFZ), and Jet Propulsion Laboratory (JPL) RL06 solutions for the period January 2003 to December 2015. The uncertainties are from 2 sigma of the least-squares fitting.

Without Correction (mm/year) | With Correction (mm/year) | |
---|---|---|

CSR RL06 | 2.12 ± 0.11 | 2.05 ± 0.12 |

GFZ RL06 | 2.05 ± 0.11 | 1.97 ± 0.11 |

JPL RL06 | 2.16 ± 0.11 | 2.07 ± 0.11 |

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**MDPI and ACS Style**

Tang, L.; Li, J.; Chen, J.; Wang, S.-Y.; Wang, R.; Hu, X. Seismic Impact of Large Earthquakes on Estimating Global Mean Ocean Mass Change from GRACE. *Remote Sens.* **2020**, *12*, 935.
https://doi.org/10.3390/rs12060935

**AMA Style**

Tang L, Li J, Chen J, Wang S-Y, Wang R, Hu X. Seismic Impact of Large Earthquakes on Estimating Global Mean Ocean Mass Change from GRACE. *Remote Sensing*. 2020; 12(6):935.
https://doi.org/10.3390/rs12060935

**Chicago/Turabian Style**

Tang, Lu, Jin Li, Jianli Chen, Song-Yun Wang, Rui Wang, and Xiaogong Hu. 2020. "Seismic Impact of Large Earthquakes on Estimating Global Mean Ocean Mass Change from GRACE" *Remote Sensing* 12, no. 6: 935.
https://doi.org/10.3390/rs12060935