Tsunami Waveform Inversion Research Articles

Tsunami waveform inversion using Green’s functions with advection effects: application to the 2003 Tokachi–Oki earthquake

We explored nonlinear effects within the context of tsunami waveform inversion, wherein Green's functions were linearly superimposed to estimate earthquake slips. We focused on these effects while developing a source model for the 2003 Tokachi–Oki earthquake off Hokkaido, Japan. A source model for this earthquake was developed based on linear tsunami waveform inversion using Green’s functions and tsunami waveforms observed at tide gauge stations. Subsequently, tsunami waveforms from the source were simulated at the stations using nonlinear long-wave theory and compared with those estimated by inversion. The comparisons demonstrated that the waveforms had a non-negligible discrepancy that was attributed to advection effects, even for the primary wave used in the inversion at the two stations. This result strongly suggests that advection effects should be considered in the source modeling of the 2003 earthquake based on tsunami waveforms observed by tide gauges. Based on these results, a new tsunami waveform inversion technique that incorporates linearly approximated advection effects and maintain the framework of linear tsunami waveform inversion using Green’s functions is proposed and applied. The proposed method successfully mimicked the advection effects during the 2003 tsunami, reproduced better tsunami waveforms, and developed a source model for the 2003 earthquake using these effects. The peak slip amount and seismic moment were greater in the source model with advection effects than those without the effects. This finding suggests that the values in the source models developed for other earthquake events without considering these effects may have been underestimated.Graphical abstract

Estimation of the Seismic Source of the 1974 Lima Peru Earthquake and Tsunami (Mw 8.1)

In this investigation, we have conducted a long period teleseismic and tsunami waveform inversion to obtain the slip distribution of the 1974 Lima-Perú earthquake occurred in the central region of Peru. According to teleseismic inversion, the rupture process was complex with a duration of 90 s approximately and the main asperity was located in the northern side of the rupture geometry, offshore Lima and Callao. According to tsunami waveform inversion the main asperity was located in the southern side of the fault plane, offshore Cañete. However, a joint inversion of teleseismic and tsunami waveforms averaged the contribution of the two datasets and could give a better result. The maximum slip from the joint inversion was 7.25 m, and the moment magnitude was Mw 8.1. Despite the occurrence of this earthquake (almost 50 years ago), there is a high seismic potential to trigger a tsunamigenic earthquake in the central region of Peru. According to the interseismic coupling the next earthquake in the central region of Peru is ready to occur and it would be of 8.5–8.8 Mw.

Sensitivity of slip distribution on tsunami trace heights and geological evidences: a case study of the 2011 Tohoku-Oki earthquake

We examined whether it is possible to estimate the tsunami source model of the 2011 Tohoku-Oki earthquake from a comparison of numerical simulations of tsunami propagation and sediment transport, the measured trace heights, and the sediment thickness of tsunami deposits. Twelve models with different subfault numbers were prepared based on a reference model inferred from tsunami waveform inversion. The reference model with 55 subfaults considering rupture propagation and the model with instantaneous slip successfully reproduced both the tsunami trace heights and sediment thickness distribution of tsunami deposits in the Idagawa Lowland and Sendai Plain. Other models with the same moment magnitude but fewer subfaults could not reproduce the observed trace heights, and the reproducibility of sediment thickness distribution strongly depended on the slip distribution. Models with increased slip amounts and moment magnitude could reproduce the trace heights; however, the simulated sediment thickness was underestimated for the Idagawa Lowland while overestimated for the Sendai Plain. Our results indicate that the combination of trace heights, sediment thickness of tsunami deposits, and numerical simulations of tsunami propagation and sediment transport can be used to estimate historical earthquakes and tsunamis. Efforts should be made to increase the number of subfaults for the study of historical events, although the obtained solutions may not be unique because of fewer trace heights or tsunami deposit data.

Re-Estimating a Source Model for the 1923 Kanto Earthquake by Joint Inversion of Tsunami Waveforms and Coseismic Deformation Data

ABSTRACT The 1923 Kanto earthquake generated not only strong motions that caused a devastating disaster around the metropolitan Tokyo area but also a large tsunami. Although the slip distribution of the 1923 Kanto earthquake has been estimated by several researchers, tsunami waveforms observed at tide gauges near the source have never been used. In this study, the slip distribution of the 1923 Kanto earthquake was estimated using joint inversion of tsunami waveforms and vertical crustal deformations reported in historical documents. The estimated slip distribution was generally consistent with those estimated in the previous studies except for a large slip of 9 m along the western portion of the plate interface, up-dip near the Sagami trough. The east coast of the Izu Peninsula was inundated by the tsunami and surveyed after the tsunami to determine tsunami heights in the inundation areas. The tsunami inundation computed from the estimated slip distribution explained the tsunami heights, and the large slip played an important role in large inundation. These results indicate that the large slip west of the Sagami trough is essential for explaining the observed tsunami caused by the 1923 Kanto earthquake.

The 2021 Loyalty Islands Earthquake (Mw 7.7): Tsunami Waveform Inversion and Implications for Tsunami Forecasting for New Zealand

AbstractA tsunamigenic earthquake with thrust faulting mechanism occurred southeast of the Loyalty Islands, New Caledonia, in the Southern Vanuatu subduction zone on the 10th of February 2021. The tsunami was observed at coastal gauges in the surrounding islands and in New Zealand. The tsunami was also recorded at a new DART network designed to enhance the tsunami forecasting capability of the Southwestern Pacific. We used the tsunami waveforms in an inversion to estimate the fault slip distribution. The estimated major slip region is located near the trench with maximum slip of 4 m. This source model with an assumed rupture velocity of 1.0 km/s can reproduce the observed seismic waves. We evaluated two tsunami forecasting approaches for coastal regions in New Zealand: selecting a pre‐computed scenario, and interpolating between two pre‐computed scenarios. For the evaluation, we made a reference map of tsunami threat levels in New Zealand using the estimated source model. The results show that the threat level maps from the pre‐computed Mw 7.7 scenario located closest to the epicenter, and from an interpolation of two scenarios, match the reference threat levels in most coastal regions. Further improvements to enhance the system toward more robust warnings include expansion of scenario database and incorporation of tsunami observation around tsunami source regions. We also report on utilization of the coastal gauge and DART station data for updating forecasts in real‐time during the event and discuss the differences between the rapid‐response forecast and post‐event retrospective forecasts.

Seismic Source of 1966 Huacho Peru Earthquake (Mw 8.1) from Tsunami Waveform Inversion

Seismic Source of 1966 Huacho Peru Earthquake (Mw 8.1) from Tsunami Waveform Inversion

Slip distribution of the 2005 Nias earthquake (Mw 8.6) inferred from geodetic and far-field tsunami data

SUMMARYWe estimated the slip distribution on the fault of the 2005 Nias earthquake (Mw 8.6) by inversions of local GPS and coastal uplift/subsidence data and tsunami waveform data. The 2005 Nias earthquake occurred approximately three months after the 2004 Sumatra–Andaman earthquake (Mw 9.1) at the southern extension off Sumatra Island, Indonesia. The tsunami from the 2005 earthquake caused significantly less damage than the 2004 tsunami, yet was recorded at tide gauges and ocean bottom pressure gauges around the Indian Ocean, including the coasts of Africa and Antarctica. The elastic and gravitational coupling between the solid earth and the ocean causes not only a traveltime delay but also the change of waveforms of far-field tsunamis relative to the prediction based on the long-wave theory. We corrected the computed tsunami Green's functions for the elastic and gravitational coupling effect in the tsunami waveform inversion. We found a diffused slip (∼2 m over an area of 400 km × 100 km) at deeper parts (20–54 km) of the fault with a large localized slip (7 m over 100 km × 100 km) slightly south of the epicentre. The large slips at deeper parts of the fault were responsible for the small tsunami generation. Inversion using far-field tsunami data yielded a slip distribution similar to that obtained using local geodetic data alone and that from the joint inversion of local geodetic and far-field tsunami data, which is also similar to slip distributions from previous studies based on local geodetic data. This demonstrates that far-field tsunami waveforms, once corrected for propagation effects, can be used to estimate the slip distribution of large submarine earthquakes leading to results that are similar to those obtained using sparse local geodetic data.

An Optimized Array Configuration of Tsunami Observation Network Off Southern Java, Indonesia

AbstractHistorical records have proven that the southern coasts of Java, Indonesia, are prone to tsunamis. The existing tsunami observing system using bottom pressure gauges, also known as tsunameters, composes a global network but is too sparse for regional tsunami forecasts. The nearest tsunameter to Indonesia is located approximately 500‐km offshore, which is not very useful for the area, particularly for a tsunami source in eastern part of the Sunda megathrust. Here we propose a methodology to optimally place offshore tsunameters with the main consideration of operational costs, which is proportional to the number of observation points. We use a stochastic slip model of earthquakes with Mw 8.8–9.2 to generate multiple tsunami source realizations representing possible future events in the region. Based on the sources, we then identify a potential zone where an early tsunami detection is feasible. Furthermore, empirical orthogonal functions derived from tsunami simulations are used to determine the initial locations for tsunameter placement inside the specified zone. Finally, we apply an optimization scheme to improve the initial locations that facilitates both tsunami forecasts and source characterizations through a tsunami waveform inversion analysis. Our result indicates that six tsunameters are sufficient to efficiently cover the major seismogenic region in the study area.

Numerical modeling of the 2015 Illapel Tsunami source by the inversion of DART buoys data

The problem of the tsunami source reconstruction from the remote measurements of an arriving waves in the deep-water tsunamimeters is considered as an inverse problem of mathematical physics in the class of the ill-posed problems. The latter determines the inevitable instability of the numerical solution. We propose a method providing more control on the numerical instability of the solution. The DART buoys data allows one to apply the linear shallow-water theory for the wave propagation and the r-solution method for the tsunami waveform inversion. The applied approach is independent from the earthquake source characteristics, because the only observed tsunami waveforms and a roughly estimated tsunami source area are used. A good coincidence of observed and computed tsunami waveforms was a criterion of the quality of the inversion. In this paper we study the 16 September 2015 Illapel (Chile) event and conduct a reconstruction of a tsunami source.

Performance of uniform and heterogeneous slip distributions for the modeling of the November 2016 off Fukushima earthquake and tsunami, Japan

The Mw 6.9 earthquake off Fukushima Prefecture, Japan, of 22 November 2016 was followed by a tsunami that struck the Japanese coast from Hokkaido in northern Japan to Wakayama Prefecture in western Japan. We compared the performance of a seismologically deduced single-fault model, a seismologically deduced finite fault slip model (FFM), an optimized single-fault model based on tsunami data, the FFM with horizontal shift, and the tsunami waveform inversion models of the previous studies considered for this earthquake regarding reproduction of tsunami waves by tsunami computations. It is important to discuss how these models work well because it is sometimes desirable to obtain an earthquake source model to estimate tsunami waves with a simple process obtained with limited data from the viewpoint of tsunami prediction. The seismologically deduced FFM has an advantage in terms of the information of slip regions of fault plane and was superior to the seismologically deduced single-fault model, especially in predicting amplitudes of tsunami waves. This means that when only with seismic data, the FFM could narrow the range of forecast of tsunami amplitude. In the comparison of models optimized with tsunami data, the single-fault model showed the almost equivalent performance of the tsunami waveform inversion models of previous studies regarding the waveform coincidence with observations and the horizontal location at the negative peak of the initial sea surface displacement. In case the main generation region of the tsunami is concentrated in one place, the tsunamis can be expressed by a single-fault model by conducting the detailed grid search. We also confirmed that the centroid location of centroid moment tensor (CMT) solution and the absolute location of the FFM were not necessarily suitable to express tsunamis, while the moment magnitude, the focal mechanism, the centroid depth of CMT solution, and the relative slip distribution of the FFM were effective to represent tsunamis. Since this event occurred at the shallow depth, the speed of tsunami wave is particularly slow. Therefore, it would be advisable to pay attention to the horizontal uncertainty to apply seismologically obtained solution to tsunami forecast, especially when a tsunami occurs in shallow water.

Improving Forecast Accuracy With Tsunami Data Assimilation: The 2009 Dusky Sound, New Zealand, Tsunami

AbstractWe use tsunami waveforms recorded on deep water absolute pressure gauges (Deep‐ocean Assessment and Reporting of Tsunamis), coastal tide gauges, and a temporary array of seafloor differential pressure gauges (DPG) to study the tsunami generated by the 15 July 2009 magnitude 7.8 Dusky Sound, New Zealand, earthquake. We first use tsunami waveform inversion applied to Deep‐ocean Assessment and Reporting of Tsunamis seafloor pressure gauge and coastal tide gauge data to estimate the fault slip distribution of the Dusky Sound earthquake. This fault slip estimate is then used to generate synthetic tsunami waveforms at each of the DPG sites. DPG instruments are unfortunately not well calibrated, but comparison of the synthetic tsunami waveforms to those observed at each DPG site allows us to determine an appropriate amplitude scaling to apply. We next use progressive data assimilation of the amplitude‐scaled DPG observations to retrospectively forecast the Dusky Sound tsunami wavefields and find a good match between forecast and observed tsunami wavefields at the Charleston tide gauge station on the west coast of New Zealand's South Island. While an advantage of the data assimilation method is that no initial condition is needed, we find that our forecast is improved by merging tsunami forward modeling from a rapid W‐phase earthquake source solution with the data assimilation method.

Contribution from Multiple Fault Ruptures to Tsunami Generation During the 2016 Kaikoura Earthquake

The 2016 Kaikoura, New Zealand, earthquake was one of the most complex ruptures ever recorded. The epicentre was located well inland, but the rupture area extended offshore and generated a modest tsunami which was recorded by tide gauges. Here, we present a detailed estimate of seafloor vertical displacement during the earthquake sequence by a joint inversion of tsunami waveforms and vertical displacement data observed at GPS stations and obtained by field surveys. The combined dataset provides a solution with good resolution, capable of resolving test sources of 20 km of characteristic diameter throughout the study area. We found two seafloor uplift regions which are located very close to the coast, one is located offshore of the Kaikoura peninsula and the other larger uplift region is located near the Kekerengu and Needles faults. To estimate crustal deformation with a complete spatial coverage of the event, the estimated seafloor vertical displacement was combined with the inland vertical displacement from InSAR and GPS datasets. This vertical displacement is then inverted for the fault slip distributions of the Needles, Jordan–Kekerengu, Papatea, Hundalee, Hump faults, and a newly identified fault beneath Kaikoura. We also found that the Needles fault is probably an offshore extension of the Kekerengu fault. The seismic moment calculated from the fault slip distributions by assuming a rigidity of 2.7 × 1010 N/m2, is 5.19 × 1020 Nm or equivalent to Mw 7.8. This total seismic moment estimate is consistent with that of the Global Centroid Moment Tensor solution. The tsunami potential energy calculated from the seafloor vertical displacement is 9.40 × 1012 J, of which about 70% is attributed to movement on the faults known to have ruptured, suggesting a secondary source for tsunami generation.

Tsunami Source Inversion Using Tide Gauge and DART Tsunami Waveforms of the 2017 Mw8.2 Mexico Earthquake

On September 8, 2017 (UTC), a normal-fault earthquake occurred 87 km off the southeast coast of Mexico. This earthquake generated a tsunami that was recorded at coastal tide gauge and offshore buoy stations. First, we conducted a numerical tsunami simulation using a single-fault model to understand the tsunami characteristics near the rupture area, focusing on the nearby tide gauge stations. Second, the tsunami source of this event was estimated from inversion of tsunami waveforms recorded at six coastal stations and three buoys located in the deep ocean. Using the aftershock distribution within 1 day following the main shock, the fault plane orientation had a northeast dip direction (strike = 320^{circ }, dip = 77^{circ }, and rake =-92^{circ }). The results of the tsunami waveform inversion revealed that the fault area was 240 km × 90 km in size with most of the largest slip occurring on the middle and deepest segments of the fault. The maximum slip was 6.03 m from a 30 × 30 km2 segment that was 64.82 km deep at the center of the fault area. The estimated slip distribution showed that the main asperity was at the center of the fault area. The second asperity with an average slip of 5.5 m was found on the northwest-most segments. The estimated slip distribution yielded a seismic moment of 2.9 times 10^{21} Nm (Mw = 8.24), which was calculated assuming an average rigidity of 7times 10^{10} N/m2.

Fault Slip Distribution of the 2016 Fukushima Earthquake Estimated from Tsunami Waveforms

The 2016 Fukushima normal-faulting earthquake (Mjma 7.4) occurred 40 km off the coast of Fukushima within the upper crust. The earthquake generated a moderate tsunami which was recorded by coastal tide gauges and offshore pressure gauges. First, the sensitivity of tsunami waveforms to fault dimensions and depths was examined and the best size and depth were determined. Tsunami waveforms computed based on four available focal mechanisms showed that a simple fault striking northeast-southwest and dipping southeast (strike = 45°, dip = 41°, rake = −95°) yielded the best fit to the observed waveforms. This fault geometry was then used in a tsunami waveform inversion to estimate the fault slip distribution. A large slip of 3.5 m was located near the surface and the major slip region covered an area of 20 km × 20 km. The seismic moment, calculated assuming a rigidity of 2.7 × 1010 N/m2 was 3.70 × 1019 Nm, equivalent to Mw = 7.0. This is slightly larger than the moments from the moment tensor solutions (Mw 6.9). Large secondary tsunami peaks arrived approximately an hour after clear initial peaks were recorded by the offshore pressure gauges and the Sendai and Ofunato tide gauges. Our tsunami propagation model suggests that the large secondary tsunami signals were from tsunami waves reflected off the Fukushima coast. A rather large tsunami amplitude of ~75 cm at Kuji, about 300 km north of the source, was comparable to those recorded at stations located much closer to the epicenter, such as Soma and Onahama. Tsunami simulations and ray tracing for both real and artificial bathymetry indicate that a significant portion of the tsunami wave was refracted to the coast located around Kuji and Miyako due to bathymetry effects.

Rupture process of the 2016 Wharton Basin strike‐slip faulting earthquake estimated from joint inversion of teleseismic and tsunami waveforms

AbstractThe 2016 Wharton Basin strike‐slip faulting earthquake generated a small tsunami that was clearly recorded at deep ocean stations. Teleseismic inversions were made on four different nodal planes suggested by Global Centroid Moment Tensor and W‐phase solutions. Tsunami waveforms computed for the north‐south striking westward dipping plane were most similar to the observations. With this fault plane, joint inversions of teleseismic and tsunami waveforms were used to estimate the kinematic rupture process. The weights of teleseismic and tsunami waveforms were found to make both data sets equally contribute to the solution. Misfit analysis of both data sets favored a rupture model with rupture front speed of 2.0 km/s. The seismic moment was estimated to be 7.69 × 1020 Nm (Mw 7.9), most of it was released within 30 s and it peaked at 15 s. Subfaults with slip larger than 5 m were located from near surface to 30 km depth.

Rupture Process of the 1969 and 1975 Kurile Earthquakes Estimated from Tsunami Waveform Analyses

The 1969 and 1975 great Kurile earthquakes occurred along the Kurile trench. Tsunamis generated by these earthquakes were observed at tide gauge stations around the coasts of the Okhotsk Sea and Pacific Ocean. To understand rupture process of the 1969 and 1975 earthquakes, slip distributions of the 1969 and 1975 events were estimated using tsunami waveform inversion technique. Seismic moments estimated from slip distributions of the 1969 and 1975 earthquakes were 1.1 × 1021 Nm (Mw 8.0) and 0.6 × 1021 Nm (Mw 7.8), respectively. The 1973 Nemuro-Oki earthquake occurred at the plate interface adjacent to that ruptured by the 1969 Kurile earthquake. The 1975 Shikotan earthquake occurred in a shallow region of the plate interface where was not ruptured by the 1969 Kurile earthquake. Further, like a sequence of the 1969 and 1975 earthquakes, it is possible that a great earthquake may occur in a shallow part of the plate interface a few years after a great earthquake that occurs in a deeper part of the same region along the trench.

Tsunami waveform inversion for sea surface displacement following the 2011 Tohoku earthquake: Importance of dispersion and source kinematics

AbstractThis paper considers the importance of model parameterization, including dispersion, source kinematics, and source discretization, in tsunami source inversion. We implement single and multiple time window methods for dispersive and nondispersive wave propagation to estimate source models for the tsunami generated by the 2011 Tohoku‐Oki earthquake. Our source model is described by sea surface displacement instead of fault slip, since sea surface displacement accounts for various tsunami generation mechanisms in addition to fault slip. The results show that tsunami source models can strongly depend on such model choices, particularly when high‐quality, open‐ocean tsunami waveform data are available. We carry out several synthetic inversion tests to validate the method and assess the impact of parameterization including dispersion and variable rupture velocity in data predictions on the inversion results. Although each of these effects has been considered separately in previous studies, we show that it is important to consider them together in order to obtain more meaningful inversion results. Our results suggest that the discretization of the source, the use of dispersive waves, and accounting for source kinematics are all important factors in tsunami source inversion of large events such as the Tohoku‐Oki earthquake, particularly when an extensive set of high‐quality tsunami waveform recordings are available. For the Tohoku event, a dispersive model with variable rupture velocity results in a profound improvement in waveform fits that justify the higher source complexity and provide a more realistic source model.

Fault slip distribution of the 2014 Iquique, Chile, earthquake estimated from ocean‐wide tsunami waveforms and GPS data

AbstractWe applied a new method to compute tsunami Green's functions for slip inversion of the 1 April 2014 Iquique earthquake using both near‐field and far‐field tsunami waveforms. Inclusion of the effects of the elastic loading of seafloor, compressibility of seawater, and the geopotential variation in the computed Green's functions reproduced the tsunami traveltime delay relative to long‐wave simulation and allowed us to use far‐field records in tsunami waveform inversion. Multiple time window inversion was applied to tsunami waveforms iteratively until the result resembles the stable moment rate function from teleseismic inversion. We also used GPS data for a joint inversion of tsunami waveforms and coseismic crustal deformation. The major slip region with a size of 100 km × 40 km is located downdip the epicenter at depth ~28 km, regardless of assumed rupture velocities. The total seismic moment estimated from the slip distribution is 1.24 × 1021 N m (Mw 8.0).

Randomly distributed unit sources to enhance optimization in tsunami waveform inversion

Abstract. In tsunami waveform inversion using the conventional Green's function technique, an optimal solution is sometimes difficult to obtain because of various factors. This study proposes a new method to both optimize the determination of the unknown parameters and introduce a global optimization method for tsunami waveform inversion. We utilize a genetic algorithm that further enhanced by a pattern search method to find an optimal distribution of unit source locations prior to the inversion. Unlike the conventional method that characterized by equidistant unit sources, our method generates a random spatial distribution of unit sources inside the inverse region. This leads to a better approximation of the initial profile of a tsunami. The method has been tested using an artificial tsunami source with real bathymetry data. Comparison results demonstrate that the proposed method has considerably outperformed the conventional one in terms of model accuracy.

DETERMINATION OF THE INITIAL SEA SURFACE DEFORMATION CAUSED BY A TSUNAMI USING GENETIC ALGORITHM

The characteristics of a tsunami is largely determined by its initial source, which can be defined as a perturbation to the equilibrium state of the ocean hydrodynamic. For tsunamis generated by earthquakes, the initial source (as a form of sea surface deformation) is driven by a coseismic vertical displacement of the seabed. Assuming that the rupture process occurs instantaneously, the sea surface deformation can be inferred from recorded tsunami waveforms. Tsunami waveform inversion using the Green’s function technique with least squares optimization is the most widely used method. However, this method can sometimes suffer from ill-posed problems, because of the non-uniqueness of the inversion results. This study proposes a genetic algorithm that helps the traditional least squares method find an optimum solution. We applied the method to an artificial tsunami source with a complex profile. We achieved significant improvements by determining the optimum spatial distribution of the unit sources (the Green’s function) prior to the inversion. In contrast with the regular Green’s function that has equidistant unit sources, our method generates a random spatial distribution. This random characteristic leads to a better approximation of the initial sea surface deformation.