# Coseismic Gravity Changes and Crustal Deformation Induced by the 2018 Fiji Deep-Focus Earthquake Observed by GRACE and GRACE-FO Satellites

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{20}and C

_{30}coefficients were replaced with those obtained by the Satellite Laser Ranging (SLR) technique, as these long-wavelength components are measured more accurately by high-altitude SLR satellites than by low-altitude satellites, such as GRACE. The SLR data were downloaded from the ICGEM website. The radius of the filter was set according to the parameters in Tanaka et al. [6] to reduce short-wavelength noise. The principal spatial wavelength of the coseismic gravity change of a deep-focus earthquake is sufficiently long and is not removed by the filter.

_{i}(i = 1–7) are constants estimated by the least squares, the first term is the overall bias, the second term is the secular trend, the third–sixth terms represent annual and semi-annual variations, t

_{0}is the time (in years) at the occurrence of the 2018 Fiji largest earthquake, and H(t − t

_{0}) denotes the Heaviside step function, which provides 0 when t − t

_{0}< 0, otherwise it provides 1. In this equation, the estimated a

_{7}values indicate coseismic gravity jumps at given locations; thus, the spatial distribution of the coseismic gravity change is shown by mapping these values. The standard deviation (1 sigma) was estimated at the same time. Here, I used only one Heaviside step function because it was impossible to separate the two earthquakes based on the time series with only a one-month temporal resolution. In addition, post-seismic components were considered to be zero because post-seismic gravity changes are probably negligible for the first several years after deep-focus earthquakes [9].

## 3. Results

^{2}because there is a tradeoff between the lengths, widths, and amounts of the slips (Section S2 in Supplementary Materials). A square of 100 km on a side is a simplified shape with reference to the USGS infinite fault model. Based on these assumptions, the grid search method was used to estimate the longitude, latitude, rake/strike/dip angles, and amount of slip of the fault to coincide with the observation results.

## 4. Discussion

## Supplementary Materials

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fan, W.; Wei, S.S.; Tian, D.; McGuire, J.J.; Wiens, D.A. Complex and diverse rupture processes of the 2018 Mw 8.2 and Mw 7.9 Tonga-Fiji Deep Earthquakes. Geophys. Res. Lett.
**2019**, 46, 2434–2448. [Google Scholar] [CrossRef][Green Version] - Jia, Z.; Shen, Z.; Zhan, Z.; Li, C.; Peng, Z.; Gurnis, M. The 2018 Fiji M 8.2 and 7.9 deep earthquakes: One doublet in two slabs. Earth Planet. Sci. Lett.
**2020**, 531, 115997. [Google Scholar] [CrossRef] - Kiyani, A.; Shah, M.; Ahmed, A.; Shah, H.H.; Hameed, S.; Adil, M.A.; Naqvi, N.A. Seismo ionospheric anomalies possibly associated with the 2018 M 8.2 Fiji earthquake detected with GNSS TEC. J. Geodyn.
**2020**, 140, 101782. [Google Scholar] [CrossRef] - Mitsui, Y.; Muramatsu, H.; Tanaka, Y. Slow deformation event between large intraslab earthquakes at the Tonga Trench. Sci. Rep.
**2021**, 11, 257. [Google Scholar] [CrossRef] [PubMed] - Shestakov, N.V.; Ohzono, M.; Takahashi, H.; Gerasimenko, M.D.; Bykov, V.G.; Gordeev, E.I.; Chebrov, V.N.; Titkov, N.N.; Serovetnikov, S.S.; Vasilenko, N.F.; et al. Modeling of coseismic crustal movements initiated by the May 24, 2013, M w = 8.3 Okhotsk deep focus earthquake. Dokl. Earth Sci.
**2014**, 457, 976–981. [Google Scholar] [CrossRef] - Tanaka, Y.; Heki, K.; Matsuo, K.; Shestakov, N.V. Crustal subsidence observed by GRACE after the 2013 Okhotsk deep-focus earthquake. Geophys. Res. Lett.
**2015**, 42, 3204–3209. [Google Scholar] [CrossRef][Green Version] - Zhang, Z.-Z.; Chao, B.F.; Lu, Y.; Hsu, H.-T. An effective filtering for GRACE time-variable gravity: Fan filter. Geophys. Res. Lett.
**2009**, 36, L17311. [Google Scholar] [CrossRef] - Wahr, J.; Molenaar, M.; Bryan, F. Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. J. Geophys. Res. Solid Earth
**1998**, 103, 30205–30229. [Google Scholar] [CrossRef] - Xu, C.; Su, X.; Liu, T.; Sun, W. Geodetic observations of the co- and post-seismic deformation of the 2013 Okhotsk Sea deep-focus earthquake. Geophys. J. Int.
**2017**, 209, 1924–1933. [Google Scholar] [CrossRef] - Sun, W.; Okubo, S.; Fu, G.; Araya, A. General formulations of global co-seismic deformations caused by an arbitrary dislocation in a spherically symmetric earth model—Applicable to deformed earth surface and space-fixed point. Geophys. J. Int.
**2009**, 177, 817–833. [Google Scholar] [CrossRef] - Zhang, G.; Shen, W.; Xu, C.; Zhu, Y. Coseismic gravity and displacement signatures induced by the 2013 Okhotsk Mw8.3 earthquake. Sensors
**2016**, 16, 1410. [Google Scholar] [CrossRef] [PubMed][Green Version] - NASA Jet Propulsion Laboratory (JPL). GRACE-FO Monthly Geopotential Spherical Harmonics CSR Release 6.0. 2019. Available online: http://icgem.gfz-potsdam.de/series/01_GRACE/CSR/CSR%20Release%2006%20(GFO) (accessed on 15 November 2022).
- University Of Texas Center for Space Research (UTCSR). 2018 GRACE STATIC FIELD GEOPOTENTIAL COEFFICIENTS CSR RELEASE 6.0. 2018. Available online: http://icgem.gfz-potsdam.de/series/01_GRACE/CSR/CSR%20Release%2006 (accessed on 15 November 2022).
- Wessel, P.; Smith, W.H.F.; Scharroo, R.; Luis, J.; Wobbe, F. Generic mapping tools: Improved version released. Eos Trans. Am. Geophys. Union
**2013**, 94, 409–410. [Google Scholar] [CrossRef]

**Figure 1.**Calculation of the coseismic gravity changes caused by the two 2018 Fiji deep-focus earthquakes based on USGS CMT solutions. The trench is shown by using the mark of the cold front. (

**a**) The result of the 19 August 2018, earthquake. (

**b**) The result of the 6 September 2018, earthquake. (

**c**) The sum of (

**a**,

**b**). The contour intervals of (

**a**–

**c**) are 0.1 μGal, 0.01 μGal, and 0.1 μGal, respectively. Stars indicate the locations of the CMT solutions. The color scale is the same as that used in Figure 2 for comparison.

**Figure 2.**The coseismic gravity change of the Fiji deep-focus earthquake. (

**a**) The distribution of coseismic gravity change obtained by time series analysis of GRACE and GFO data. The broken red and blue lines show the latitudes of 16S and 20S, respectively. The contour interval is 0.1 μGal. The star represents the center of the fault as determined by the model calculation. (

**b**) The standard deviation estimated simultaneously to the coseismic gravity change (the contour interval is 0.01 μGal). (

**c**) The result of the model’s calculation. (

**d**) The difference between the observation and calculation results. (

**e**) The cross section along the 16S and 20S latitudes in (

**a**,

**c**). The black dots represent the observation data shown in (

**a**) with error bars of 1 sigma shown in (

**b**). The red and blue solid curves represent the calculation results shown in (

**c**). (

**f**) Time-variable gravity at the location of the cyan point in (

**a**), with red indicating an increase in gravity. The black dots represent GRACE and GFO data with error bars of 1 sigma. The red line is the modeled function. Annual and semi-annual components are removed from the black dots and red lines. (

**g**) Time variable gravity at the location of the yellow point in (

**a**). Blue is used to indicate a decrease in gravity. Gravity data are distributed between −1.8 μGal and 1.8 μGal, whereas the standard deviations are less than 0.4 μGal. This suggests that least squares worked sufficiently. Abbreviations: GFO, gravity recovery and climate experiment-follow on; GRACE, Gravity Recovery And Climate Experiment; TVG, time-variable gravity.

**Figure 3.**Calculated coseismic gravity changes based on fault parameters in Table 1. The red star marks indicates the estimated epicenter shown in Table 1. (

**a**) The original result, to which no filters or corrections were applied. This is equivalent to the gravity change on the Earth without an ocean. (

**b**) No filters are applied to the results, but sea-water movement is corrected. (

**c**) Spatial smoothing (a fan filter) is applied to the original result (

**a**). (

**d**) Spatial smoothing (a fan filter) is applied to (

**b**), generating the final result. The contour intervals are 0.3 μGal in (

**a**,

**b**), and 0.1 μGal in (

**c**,

**d**).

**Figure 4.**Calculation results of the coseismic surface crustal deformation. (

**a**) Horizontal displacements. The length and direction of the arrows represent the displacements, respectively. The arrows are shown only for displacements of 0.3 cm or more for every 5 degrees of longitude and latitude. The colors also indicate the amounts of the displacements (the lengths of the arrows). The contour intervals are 0.3 cm. (

**b**) Vertical displacements. The positive and negative values indicate uplift and subsidence, respectively. The contour intervals are 0.3 cm.

Latitude | Longitude | Slip | Rake | Depth | Strike | Dip | Length | Width |
---|---|---|---|---|---|---|---|---|

18.0S | 177.2W | 3.7 m | 270 | 590 km * | 20 | 90 | 100 km * | 100 km * |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the author. 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tanaka, Y.
Coseismic Gravity Changes and Crustal Deformation Induced by the 2018 Fiji Deep-Focus Earthquake Observed by GRACE and GRACE-FO Satellites. *Remote Sens.* **2023**, *15*, 495.
https://doi.org/10.3390/rs15020495

**AMA Style**

Tanaka Y.
Coseismic Gravity Changes and Crustal Deformation Induced by the 2018 Fiji Deep-Focus Earthquake Observed by GRACE and GRACE-FO Satellites. *Remote Sensing*. 2023; 15(2):495.
https://doi.org/10.3390/rs15020495

**Chicago/Turabian Style**

Tanaka, Yusaku.
2023. "Coseismic Gravity Changes and Crustal Deformation Induced by the 2018 Fiji Deep-Focus Earthquake Observed by GRACE and GRACE-FO Satellites" *Remote Sensing* 15, no. 2: 495.
https://doi.org/10.3390/rs15020495