Probabilistic near-field tsunami source and tsunami run-up distribution inferred from tsunami run-up records in northern Chile

Understanding a tsunami source and its impact is vital to assess a tsunami hazard. Thanks to the efforts of the tsunami survey teams, high-quality tsunami run-up data exists for contemporary events. Still, it has not been widely used to infer a tsunami source and its impact mainly due to the computational burden of the tsunami forward model. In this study, we propose a TRRF-INV (Tsunami Run-up Response Function-based INVersion) model that can provide probabilistic estimates of a near-field tsunami source and tsunami run-up distribution from a small number of run-up records. We tested the TRRF-INV model with synthetic tsunami scenarios in northern Chile and applied it to the 2014 Iquique, Chile, tsunami event as a case study. The results demonstrated that the TRRF-INV model can provide a reasonable tsunami source estimate to first order and estimate tsunami run-up distribution well. Moreover, the case study results agree well with the United States Geological Survey report and the global Centroid Moment Tensor solution. We also analyzed the performance of the TRRF-INV model depending on the number and the uncertainty of run-up records. We believe that the TRRF-INV model has the potential for supporting accurate hazard assessment by (1) providing new insights from tsunami run-up records into the tsunami source and its impact, (2) using the TRRF-INV model as a tool to support existing tsunami inversion models, and (3) estimating a tsunami source and its impact for ancient events where no data other than estimated run-up from sediment deposit data exists.

new computer model is tested for thousands of artificial earthquake scenarios and a his-mating the earthquake's magnitude and resulting tsunami run-up by relying on the early arrival of seismic waveform data alone (Hoshiba & Ozaki, 2014). The third type is a tsunami 66 inversion model that uses tsunami sediment deposit data to infer the historical tsunami 67 source, especially for the paleotsunami events (e.g. Ioki Nanayama et al., 2003). Once a tsunami source is estimated, 69 a tsunami forward model -usually a high-fidelity physics-based numerical model that 70 can simulate tsunami propagation and inundation processes from a given tsunami source-71 is then used to assess the impact of tsunamis.  that can rapidly estimate a near-field tsunami run-up distribution over real topography 97 without substantial loss of accuracy, with respect to high-fidelity models. The main con-98 cept of the TRRF model is that the tsunami run-up distribution can be decomposed into 99 (1) a leading-order contribution being modeled by fault parameters using the Okal and  (Fig. 1). The city of Iquique, one of the important commercial and 118 industrial urban centers in the northern Chile coastal region, is exposed to significant 119 tsunami risk considering its inhabitants (about 184, 000) and critical coastal infrastruc-        -5-manuscript submitted to JGR: Oceans where R T (x) is the tsunami run-up predicted by the TRRF model, R p (x) is the true tsunami  Input: Step 1: Step 3: Step 4: Generate and save earthquake scenarios Step 2: Determine an estimation order Update Figure Table 2. The other four fault parameters vary for three-level val-186 ues (minimum, maximum, and average of values listed in Table 2). The three angles and 187 the earthquake depth are fixed to the values set in step 1. Note that the interval of five 188 fault parameters in Table 2    From now on, the fault parameter of the ith combination (three angles and depth) of the 204 jth iteration of kth estimation order will be represented as F P i,j k .

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To estimate the first-order fault parameter (F P i,j 1 ), the TRRF-INV model gener-

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ates scenarios for each value of the F P 1 in Table 2  Once all fault parameters (F P i,j k ) are estimated, the total error (N RM SE i,j T ) and the minimum number of generated earthquake scenarios (N i,j M IN ) are calculated: where N i,j F P k is the number of earthquake scenarios in the base group to estimate the F P i,j k .

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Then the TRRF-INV model decides whether to stop the iteration based on the two stop 231 conditions: The first stop condition (Eq. 4) is when the total error is not reduced compared where M o is a seismic moment (N m), µ is the rigidity modulus of the Earth's crust (N m −2 ),

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The mean N RM SE t is about 6.82%, which is similar to the error of the TRRF model 307 itself.   In the 200 synthetic-scenario test (Fig. 4), the mean absolute error (M AE) of the 348 epicenter latitude (LAT ) was twice smaller than that of the epicenter longitude (LON ).

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This may be attributed to the orientation of the coastline and the earthquake fault used 350 in this study. We assumed that the coastline was parallel to the north-south direction,  other locations was also found in the case study of the 2014 Iquique tsunami (Fig. 5b). 362 We interpret this large error at Patache as a result of the tsunami-source direction that 363 was mostly oriented toward the Iquique-Pisagua area (Supplementary Table S1). In this

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The maximum water level was interpolated bilinearly onto a regular grid (0.004 • inter-466 vals). The origin was set to (20 • S, 71 • W ) and it was used as a reference point in the Vincenty

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(1975)'s formula to change the coordinate system from a spherical coordinate system to 468 a Cartesian coordinate system.

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To calibrate the TRRF model, we systemically simulated two groups of scenarios.

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First, 75 scenarios were simulated where the fault parameters were selected as follows.