Tsunami Waveforms Research Articles

Adaptive Tsunami Source Inversion Using Optimizations and the Reciprocity Principle

AbstractWe propose an advanced two‐step tsunami source inversion method with adaptive Green's functions by applying an optimization and a reciprocity principle. The method first reconstructs the sea surface displacement from observed tsunami waveforms based on a superposition of Gaussian‐shaped unit sources. In the first step, we optimize the unit source locations that give the best fit of waveforms to observations. This leads to nonequidistantly distributed unit sources, in which the synthetic waveforms from such sources to the observation points are generated using the reciprocity principle to save computational efforts of Green's functions. In the second step, the reconstructed sea surface displacement is used to estimate the slip on a finite fault plane. We also optimize the fault parameters that produce the closest displacement pattern to the first step result. Therefore, our method provides best fitting of waveforms and optimum fault parameters with automation for the process. The current method improves our previous studies, in terms of the construction of tsunami Green's functions using the reciprocity principle and determination of fault parameters through the optimization. We test the proposed method using tsunami data of the 2004 Kii Peninsula, Japan event generated by an Mw 7.4 intraplate earthquake. The overall waveform fit that resulted from our method shows much better agreement with the observations compared to that of the conventional approach, and the estimated fault depth is more consistent with the relocated aftershock distribution.

Solving the Puzzle of the September 2018 Palu, Indonesia, Tsunami Mystery: Clues from the Tsunami Waveform and the Initial Field Survey Data

On September 28, 2018, following a magnitude 7.5 strike-slip fault earthquake, an unexpected tsunami inundated the coast of Palu bay, Sulawesi, Indonesia, causing many casualties and extensive property damage. However, the earthquake’s mechanism rarely generates a destructive tsunami. The tidal record at Pantoloan, located along the coast of Palu bay, indicates that the tsunami arrived 6 min after the earthquake and generated 2 m of receding water. It had a maximum wave height of 2 m and arrived approximately 2 min later. The tsunami had a relatively short period and caused devastation as far inland as 300 m. Additionally, 8 m high watermarks were observed near the coast; the flow depth decreased to 3.5 m inland (Fig. 1). Amateur videos and eyewitness accounts indicate that the tsunami did not enter the bay through its mouth but obliquely from an area inside the bay. Our hypothesis, therefore, is that the killer tsunami was most likely generated by an underwater landslide occurring inside Palu bay. While detailed bathymetric data are still needed to confirm this hypothesis, in this article we provide a preliminary analysis of the available data, supported by the results of a field survey, to strengthen this hypothesis and provide direction for further post-tsunami surveys and analysis.

Prediction of Tsunami Waves by Uniform Slip Models

AbstractConventional tsunami warning systems for local and far‐field areas utilize uniform slip models to predict tsunami waves. The reasons are twofold. First, it is challenging to develop accurate finite‐fault slip models in a short time after an earthquake. Second, tsunami waves are long waves, and hence, the main feature may be predicted without knowing earthquake rupture details. Still, there have been few studies that quantitatively analyze the errors caused by uniform slip models. In this paper, we evaluate if and how such models may be applied for tsunami warnings. For the 2011 Tohoku, 2014 Iquique, and 2015 Illapel tsunamis, we first construct optimum uniform slip models with minimum tsunami waveform misfit and then compare the synthetic tsunami waves with finite‐fault model predictions. Predictions from both type of models match the tsunami data very well, indicating that the prediction errors caused by neglecting slip heterogeneity are insignificant. Further, we derive a common relation between the rupture area and earthquake magnitude. Additionally, the optimum rupture length and width ratio in terms of predicting tsunami waves is determined to be 1 for the three earthquakes. Lastly, we find that moving the uniform slip model to the center of global Centroid Moment Tensor solution produces reasonably small errors in the predicted waveforms. Applying the methodology to three more historic tsunamis shows that uniform slip models can well recover the Deep‐ocean Assessment and Reporting of Tsunamis system recordings, but the rupture center can differ from the global Centroid Moment Tensor solution. Our findings can potentially prompt more reliable tsunami warning strategies for future events.

Limitations of the Resolvability of Finite‐Fault Models Using Static Land‐Based Geodesy and Open‐Ocean Tsunami Waveforms

AbstractFinite‐fault inversions are a common technique, employed following large earthquakes, used to understand the nature of slip along a fault. Using multiple data sets, including static offsets from geodetic instruments and tsunami wave heights from open‐ocean gauges, a richer perspective on the expected slip distribution than using a singular tool is created. However, the model resolution obtained from open‐ocean tsunami data and techniques used to subsample that data have not been widely evaluated. Static geodetic data can provide near‐complete model resolution of the subduction megathrust near the trench, if data are local. However, model resolution falls off precipitously as distance between instrument and fault increases when geodetic data are limited to more distal on‐land sites. Tsunami data derived from open‐ocean waveforms are less dependent on station to fault distance, but offshore model resolution is lost due to necessary data processing, such as windowing, often necessary to avoid coastal reflections. This primarily affects the resolution in the downdip direction, which often arrives at open‐ocean stations later in the waveform. Spatial detail is also limited by the minimum subfault size that will satisfy the longwave approximation, which is dependent on the water depth. For most cases, this subfault limit is approximately 20 by 20 km. In many environments, the sparsity of offshore geodetic instruments, and the large distances between estimated slip and coastal geodetic gauges, makes the inclusion of open‐ocean data, if available, highly advantageous. Still it is possible even with the pairing of on‐land and offshore data sets for poorly resolved zones to exist. In these cases further resolution can be recovered through the incorporation of additional data sets such as strong‐motion data and seismic waveforms through a seismic‐geodetic inversion.

Using Tsunami Waves Reflected at the Coast to Improve Offshore Earthquake Source Parameters: Application to the 2016 Mw 7.1 Te Araroa Earthquake, New Zealand

AbstractThe Te Araroa earthquake occurred on 2 September 2016 (local time) offshore of the northeastern coast of New Zealand's North Island (Mw 7.1). When this event occurred, ocean bottom pressure gauges (OBPs), installed ~170 km south of the source area, clearly recorded direct tsunami from the source to OBPs (~ −1.5 cm), and tsunami from coastal reflections (~2 cm). We estimate the centroid location that best reproduces the OBP waveforms. When using the direct wave alone, the centroid location is poorly constrained, with a horizontal uncertainty of ~100 km. By combining both direct and reflected tsunami waveforms, we obtain a centroid location near the Global Centroid Moment Tensor centroid (~80 km northeast from the coast) with smaller uncertainty (~40 km). We also estimate the earthquake source dimension (length and width) and found that the models using coastal reflections require a source dimension larger than ~30 km long. Based on the slip distribution obtained by the finite fault inversion, we obtain an energy‐based stress drop ΔσE of 1.0 MPa, consistent with typical earthquake stress drop values. This study shows that the information added by coastal reflected tsunami provides much tighter constraints on the centroid location, source dimension, and stress drop of offshore earthquakes, which is difficult to obtain from the onshore seismic data alone. Future studies should utilize the information provided by coastal reflected waves to improve earthquake source modeling using ocean bottom pressure data.

Source Models of the 2012 Haida Gwaii (Canada) and 2015 Illapel (Chile) Earthquakes and Numerical Simulations of Related Tsunamis

Seismological observations provide essential input parameters for numerical tsunami simulations. Here, we present source mechanism parameters, finite-fault source rupture models and numerical tsunami simulation results for the destructive October 28, 2012 Haida Gwaii-Canada (Mw 7.7) and September 16, 2015 Illapel-Chile (Mw 8.3) earthquakes and resulting tsunamis. These two earthquakes were controlled by active tectonic features along the subduction zones that had developed in response to the convergent movements of lithospheric plates. The faulting geometry (strike, dip, and rake angles), focal depth, fault dimensions, average and maximum slip values on the fault planes and seismic moments of the earthquakes are estimated by analyzing teleseismic long-period P- and SH-waves and broadband P-waveforms and using waveform inversion and hybrid back-projection methods. The obtained slip models of the earthquakes reveal heterogeneous slip distributions on fault planes with long source durations (~ 80 s and 150 s) and low stress drop values (10–15 bars). Numerical simulations of tsunami wave propagation are further performed using the uniform and non-uniform slip models and nonlinear long-wave equations in spherical coordinates. The shape and arrival times of leading tsunami waves are adequately constrained particularly with the heterogeneous slip distribution models. The general characteristics of synthetic tsunami waveforms (e.g., amplitude, shape, arrival time) calculated using the non-uniform slip model, are more consistent with the observed tsunami records than those of a uniform slip model. It is further seen that simulation results using preliminary and fast slip models for both earthquakes give only approximate early tsunami estimates; tsunami wave heights and arrival times to the coasts are mostly not well simulated. The results indicate that tsunami simulations based on finite-fault source slip models likely contribute to the determination of tsunamigenic coastal regions by revealing locations, arrival times, amplitudes, and directions of tsunami waves within a close approximation to observed records off-shore and far from the source region. They provide sufficient information to facilitate tsunami warning and mitigation challenges after the destructive earthquakes. We further suggest that joint inversions of GPS, tsunami, teleseismic and strong ground motion records and higher resolution bathymetry data are needed in order to obtain better correlations between observed and synthetic tsunami data, especially for the later arriving waves.

Effects of tsunami waveform on overtopping and inundation on a vertical seawall

Effects of tsunami waveform on overtopping and inundation on a vertical seawall

Strain budget of the Ecuador–Colombia subduction zone: A stochastic view

The 2016 Pedernales earthquake (MW=7.8) ruptured a portion of the Colombia–Ecuador subduction interface where several large historical earthquakes have been documented since the great 1906 earthquake (M=8.6). Considering all significant ruptures that occurred in the region, it has been suggested that the cumulative moment generated co-seismically along this part of the subduction over the last century exceeds the moment deficit accumulated inter-seismically since 1906. Such an excess challenges simple models with earthquakes resetting the elastic strain accumulated inter-seismically in locked asperities. These inferences are however associated with large uncertainties that are generally unknown. The impact of spatial smoothing constraints on co-seismic and inter-seismic models also prevents any robust assessment of the strain budget. We propose a Bayesian kinematic slip model of the 2016 Pedernales earthquake using the most comprehensive dataset to date including InSAR and GPS offsets, tsunami waveforms, and kinematic records from high-rate GPS and strong-motions. In addition, we use inter-seismic geodetic velocities to produce a probabilistic inter-seismic coupling model of the subduction interface. Our stochastic co-seismic and inter-seismic solutions include the ensemble of all plausible models consistent with our prior information and that fit the observations within uncertainties. The analysis of these model ensembles indicates that an excess of co-seismic moment during the 1906–2016 period is likely in Central Ecuador only if we assume that 1942 and 2016 earthquakes are colocated. If this assumption is relaxed, we show that this conclusion no longer holds given uncertainties in co- and inter-seismic processes. The comparison of 1942 and 2016 teleseismic records reveals large uncertainties in the location of the 1942 event, hampering our ability to draw strong conclusions on the unbalanced moment budget in the region. Our results also show a heterogeneous coupling of the subduction interface that coincides with two slip asperities in our co-seismic model for the 2016 Pedernales earthquake and with the location of historical ruptures in 1958, 1979 and 1998. The spatial variability in coupling and complexity in earthquake history suggest strong heterogeneities in frictional properties of the subduction megathrust.

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.

Synthesis and Source Characteristics of Tsunamis in the Sea of Japan Based on Normal‐Mode Method

AbstractThe normal‐mode method, which is widely used in seismology, was applied to characterize the free oscillation and tsunami sources in the Sea of Japan. Improvements in matrix storage, and incorporation of a modern sparse eigensolver, enabled us to calculate 6,000 high‐resolution normal‐mode solutions for the Sea of Japan, down to a period of 8 min. We used kurtosis to group these modes into three types: 622 basin‐wide modes, 4,953 regional modes, and 425 local modes. By the superposition of these modes, tsunami waveforms were synthetized for the 1983 Sea of Japan earthquake (Mw 7.7). Comparisons of synthesized waveforms with those computed by the finite difference method as well as observations showed good agreement at periods longer than 8 min. The excitation weights for 60 fault models along the eastern margin of the Sea of Japan were computed, and they showed that the average excitation was larger for the sources located at shallower water depth or with larger magnitude. Among the three types of modes, the regional modes played the most important role and affected a wide coastal area.

Pneumatic long-wave generation of tsunami-length waveforms and their runup

An experimental study is conducted using a pneumatic long-wave generator (also known as a Tsunami Generator). Scaled tsunami waveforms are produced with periods in the range of 5–230 s and wave amplitudes between 0.03 and 0.14 m in water depths of 0.7–1.0 m. Using Froude similitude in scaling, at scale 1:50, these laboratory waves are theoretically dynamically equivalent to prototype tsunami waveforms with periods between 1 and 27 min and positive wave amplitude between 1.5 and 7.0 m in water depths of 50 m. The purpose of these tests is to demonstrate that the pneumatic method can generate long waves in relatively short flumes and to investigate their runup. Standard wave parameters, (free-surface, wave celerity and velocity profiles) are used to characterise the waveforms. It is shown that for the purpose of runup and onshore ingression, minimal interference from the re-reflected waves is observed.By generating tsunami waveforms with periods greater than ≈ 80 s (≈9.5 mins prototype scale) the available experimental data set is expanded and used to develop a new runup equation. Contrary to the shorter waves, shoaling of these longer waves is insignificant. For waveforms with periods greater ≈ 100 s the runup is best described by wave steepness not potential energy. When tested against available runup equations the results are mixed; most perform poorly for scaled tsunami length periods. A segmented regression analysis is performed on the data set and an empirical runup relationship is provided based on a new parameter termed the ‘Relative Slope Length’.The tests show the definition of offshore wave amplitude is non-trivial and may greatly affect the predicted relative runup of a given wave. It is noted that this appears to be a general issue for all types of tsunami simulation in the laboratory. Together these observations and proposed runup model provide a framework for future numerical studies of the topic.

Effectiveness of N-waves for predicting morphological changes due to tsunamis

The research on morphological changes caused by tsunamis has increased considerably in the last few years, yet the processes behind this phenomenon are still not fully understood. This paper analyzes and compares numerical simulations of morphological changes caused by the leading elevation and leading depression N-waves and tsunami waves propagating over a channel with a simple bed slope. The simulations were carried out by means of a coupled flow, sediment transport and morphodynamic two-dimensional-vertical numerical model. The modeled channel bed was composed of cohesionless sediments, and range of values for the bed slope and the wave height were employed. Four tsunami waveforms were studied to test the appropriateness of N-waves in modeling the morphological changes caused by tsunamis. On the modeling performed here, runup values were quite well represented by N-waves. N-waves also represented qualitatively well the morphological changes caused by tsunamis. Yet, values of flow velocities and suspended sediment concentration showed more severe deviations from the modeled results corresponding with tsunami waves, very likely due to differences on the steepness of the waves. Therefore, even when N-waves can and have been used to represent tsunami runup and inundation distance, our results suggest that they should be considered with caution when intended to predict magnitudes of tsunami flow velocities and consequently morphological changes. The use of N-waves to simulate morphological changes caused by tsunamis is not yet converging and must be further investigated.

Simulation of a Dispersive Tsunami due to the 2016 El Salvador\u2013Nicaragua Outer-Rise Earthquake (Mw 6.9)

The 2016 El Salvador–Nicaragua outer-rise earthquake (Mw 6.9) generated a small tsunami observed at the ocean bottom pressure sensor, DART 32411, in the Pacific Ocean off Central America. The dispersive observed tsunami is well simulated using the linear Boussinesq equations. From the dispersive character of tsunami waveform, the fault length and width of the outer-rise event is estimated to be 30 and 15 km, respectively. The estimated seismic moment of 3.16 × 1019 Nm is the same as the estimation in the Global CMT catalog. The dispersive character of the tsunami in the deep ocean caused by the 2016 outer-rise El Salvador–Nicaragua earthquake could constrain the fault size and the slip amount or the seismic moment of the event.

Analysis of Spatio-Temporal Tsunami Source Models for Reproducing Tsunami Inundation Features

A powerful tsunami triggered by the Mw 9.0 Tohoku earthquake struck the northern Pacific coast of Japan in 2011, destroying several coastal communities in Iwate Prefecture, Miyagi Prefecture, and Fukushima Prefecture. Here, we investigate a new spatio-temporal slip model (model B) developed by the Cabinet Office of the Government of Japan. This slip model was compared against the non-uniform slip model estimated using tsunami waveform data (model A). We focused our analysis on two areas that were destroyed by the tsunami. The town of Onagawa and the coastal Sendai Plain area were selected because they were located in front of the epicentre, where the most significant slips were registered. Our simulation results revealed that the spatio-temporal slip distribution better replicated the observed data. Regarding the tsunami waveforms from the coastal tide gauge station and offshore stations, the Cabinet Office’s slip model showed an approximately 30% better accuracy relative to the non-uniform slip model. Furthermore, by comparing the local inundation features at two locations with unique topographic and coastal morphological characteristics, we also found that model B better replicated the measured inundation depths. Finally, considering that tsunami-induced damage is a direct function of various inundation features such as the flow depth and flow velocity, this new slip model can generate more realistic damage scenarios for future tsunami assessments.

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.

Ray Tracing for Dispersive Tsunamis and Source Amplitude Estimation Based on Green’s Law: Application to the 2015 Volcanic Tsunami Earthquake Near Torishima, South of Japan

Ray tracing, which has been widely used for seismic waves, was also applied to tsunamis to examine the bathymetry effects during propagation, but it was limited to linear shallow-water waves. Green’s law, which is based on the conservation of energy flux, has been used to estimate tsunami amplitude on ray paths. In this study, we first propose a new ray tracing method extended to dispersive tsunamis. By using an iterative algorithm to map two-dimensional tsunami velocity fields at different frequencies, ray paths at each frequency can be traced. We then show that Green’s law is valid only outside the source region and that extension of Green’s law is needed for source amplitude estimation. As an application example, we analyzed tsunami waves generated by an earthquake that occurred at a submarine volcano, Smith Caldera, near Torishima, Japan, in 2015. The ray-tracing results reveal that the ray paths are very dependent on its frequency, particularly at deep oceans. The validity of our frequency-dependent ray tracing is confirmed by the comparison of arrival angles and travel times with those of observed tsunami waveforms at an array of ocean bottom pressure gauges. The tsunami amplitude at the source is nearly twice or more of that just outside the source estimated from the array tsunami data by Green’s law.

Tsunami Analysis Method with High-Fidelity Crustal Structure and Geometry Model

Higher fidelity seafloor topography and crustal structure models have become available with accumulation of observation data. Previous studies have shown that the consideration of such high-fidelity models produces significant effects, in some cases, on crustal deformation results that are used as inputs for tsunami analysis. However, it is difficult to apply high-fidelity model of crustal deformation computations to tsunami computations because of large computational costs. In this paper, we propose a new crustal deformation computation method for estimating inputs for tsunami computations, which is based on a finite element analysis method with remarkable reduction of computation costs by efficient use of the arithmetic space and the solution space. This finite element analysis method enables us to conduct [Formula: see text]-times crustal deformation computations using high-fidelity models with a degree of freedom on the order of [Formula: see text] for the 2011 Tohoku earthquake example. Tsunami computations with typical settings are conducted as an application example to present the advantages and characteristics of the proposed method. Comparisons between results of the proposed and the conventional method reveal that large shallow fault slip around the trench axis may lead to significant differences in tsunami waveforms and inundation height distributions in some cases.

The 2016 Kaikōura earthquake: Simultaneous rupture of the subduction interface and overlying faults

The distribution of slip during an earthquake and how it propagates among faults in the subduction system play a major role in seismic and tsunami hazards, yet they are poorly understood because offshore observations are often lacking. Here we derive the slip distribution and rupture evolution during the 2016 Mw 7.9 Kaikōura (New Zealand) earthquake that reconcile the surface rupture, space geodetic measurements, seismological and tsunami waveform records. We use twelve fault segments, with eleven in the crust and one on the megathrust interface, to model the geodetic data and match the major features of the complex surface ruptures. Our modeling result indicates that a large portion of the moment is distributed on the subduction interface, making a significant contribution to the far field surface deformation and teleseismic body waves. The inclusion of local strong motion and teleseismic waveform data in the joint inversion reveals a unilateral rupture towards northeast with a relatively low averaged rupture speed of ∼1.5 km/s. The first 30 s of the rupture took place on the crustal faults with oblique slip motion and jumped between fault segments that have large differences in strike and dip. The peak moment release occurred at ∼65 s, corresponding to simultaneous rupture of both plate interface and the overlying splay faults with rake angle changes progressively from thrust to strike-slip. The slip on the Papatea fault produced more than 2 m of offshore uplift, making a major contribution to the tsunami at the Kaikōura station, while the northeastern end of the rupture can explain the main features at the Wellington station. Our inversions and simulations illuminate complex up-dip rupture behavior that should be taken into consideration in both seismic and tsunami hazard assessment. The extreme complex rupture behavior also brings new challenges to the earthquake dynamic simulations and understanding the physics of earthquakes.

Numerical Procedure to Forecast the Tsunami Parameters from a Database of Pre-Simulated Seismic Unit Sources

We have implemented a numerical procedure to forecast the parameters of a tsunami, such as the arrival time of the front of the first wave and the maximum wave height in real and virtual tidal stations along the Peruvian coast, with this purpose a database of pre-computed synthetic tsunami waveforms (or Green functions) was obtained from numerical simulation of seismic unit sources (dimension: 50 × 50 km2) for subduction zones from southern Chile to northern Mexico. A bathymetry resolution of 30 arc-sec (approximately 927 m) was used. The resulting tsunami waveform is obtained from the superposition of synthetic waveforms corresponding to several seismic unit sources contained within the tsunami source geometry. The numerical procedure was applied to the Chilean tsunami of April 1, 2014. The results show a very good correlation for stations with wave amplitude greater than 1 m, in the case of the Arica tide station an error (from the maximum height of the observed and simulated waveform) of 3.5% was obtained, for Callao station the error was 12% and the largest error was in Chimbote with 53.5%, however, due to the low amplitude of the Chimbote wave (<1 m), the overestimated error, in this case, is not important for evacuation purposes. The aim of the present research is tsunami early warning, where speed is required rather than accuracy, so the results should be taken as preliminary.

Tsunami Generation and Propagation by a Curvilinear Stochastic Spreading Seismic Faulting in Linearized Water Wave Theory

The generation and propagation of tsunami caused by a curvilinear stochastic seismic faulting driven by two Gaussian white noise processes in the [Formula: see text]- and [Formula: see text]-directions are investigated. This model is used to study the tsunami build up and propagation during and after a realistic curvilinear source model represented by a random spreading slip-fault model. The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to geometric spreading and dispersion. The increase of the normalized noise intensities on the random bottom leads to an increase in oscillations and amplitude of the free surface elevation. Tsunami waveforms using linearized shallow water theory for constant water depth are analyzed analytically by transform methods. The mean and variance of the random tsunami waves are derived and analyzed as a function of the noise intensities, propagated uplift length and the average depth of the ocean along the generation and propagation path.