## Abstract

We examine how the choice of ground‐motion‐to‐intensity conversion equations (GMICEs) in earthquake early warning (EEW) systems affects resulting alert regions. We find that existing GMICEs can underestimate observed shaking at short rupture distances or overestimate the extent of low‐intensity shaking. Updated GMICEs that remove these biases would improve the accuracy of alert regions for the ShakeAlert EEW system for the West Coast of the United States. ShakeAlert uses ground‐motion prediction equations (GMPEs), which calculate spatial distributions of peak ground acceleration (PGA) and peak ground velocity (PGV) from earthquake source estimates, combined with GMICEs to translate GMPE output into modified Mercalli intensity (MMI). We find significant epistemic uncertainty in alert distances; near‐source MMI estimates from different GMICEs can differ by over 1 MMI unit, and MMI extents used for public EEW alerts can differ by hundreds of kilometers for larger magnitude earthquakes (**M** ∼6.5+). We use a catalog of “Did You Feel It?” shaking reports to evaluate how well GMICEs predict observed shaking. Our preferred GMICE is the one that computes MMI using PGV for high intensities and transitions to using PGA for nondamaging intensities. These results motivate updating GMICE relationships more generally, including in ShakeMap applications.

## Introduction

The impacts of earthquake shaking on people and the built environment are quantified through macroseismic intensity scales like modified Mercalli intensity (MMI; Dengler and Dewey, 1998; Worden *et al.*, 2012). MMI is a key metric used in post‐earthquake rapid response, including in products such as ShakeMap ground‐shaking distribution maps (Wald *et al.*, 2022) and Prompt Assessment of Global Earthquakes for Response (PAGER) rapid‐loss estimates (Wald *et al.*, 2010). Shaking intensity is also the main ground‐motion metric used to define alert regions in many earthquake early warning (EEW) systems, including the ShakeAlert EEW system for the West Coast of the United States (Given *et al.*, 2018; Kohler *et al.*, 2020). In ShakeAlert, a location is issued an alert if that location is expected to experience shaking exceeding a given MMI alert threshold (Kohler *et al.*, 2020).

Rapid and accurate shaking intensity distribution estimations are thus key components to EEW alert success. ShakeAlert aims to estimate median‐expected intensity distributions (Given *et al.*, 2018), for which users select different MMI alert thresholds based on their alert performance needs (Saunders *et al.*, 2022). ShakeAlert provides two types of shaking distribution estimates as alert products: the contour product, a symmetric, simplified set of coordinates defining the extent of specific MMI levels used as alert thresholds; and the grid product, a map‐based distribution of MMI estimates in a 0.2° × 0.2° grid dependent on site conditions such as $VS30$ (Thakoor *et al.*, 2019). Both products employ two types of ground‐motion models in their procedures: ground‐motion prediction equations (GMPEs), which calculate spatial distributions of peak ground acceleration (PGA) and peak ground velocity (PGV) from estimates of the earthquake source (magnitude and rupture distance); and ground‐motion‐to‐intensity conversion equations (GMICEs), which translate PGA and PGV into MMI.

Here, we investigate which existing GMICE (from Worden *et al.*, 2012) developed specifically for the United States should be used in ShakeAlert in combination with the Next Generation Attenuation‐West2 Project (NGA‐West2) GMPEs (Bozorgnia *et al.*, 2014) used in ShakeMap (Worden *et al.*, 2020) and anticipated to be implemented in ShakeAlert. Current ShakeAlert operations use different GMICEs for its contour and grid alert products, both of which differ from the GMICE used in ShakeMap, and all three are different from the GMICE preferred in the original GMICE regression in Worden *et al.* (2012). Reconciling these ground‐motion modeling procedures and GMICEs using observations will bring consistency to these alert products.

Using the GMICEs presented in Worden *et al.* (2012) in comparison to shaking intensity observations derived from “Did You Feel It?” (DYFI) reports (Wald *et al.*, 2011), we determine which of these GMICEs gives the best performance. We find that the different GMICEs produce different MMI estimates given the same ground‐motion inputs, which causes significant alert region differences at the MMI levels used for public alerts in ShakeAlert (MMI 4.5, 3.5, and 2.5; Kohler *et al.*, 2020). The preferred GMICE favors MMI computed in terms of PGV for higher intensities and transitions to PGA at lower intensities and includes magnitude and distance terms. Although these ground‐motion model adjustments in ShakeAlert produce different alert distances compared to current procedures, these models match median‐observed DYFI intensity distributions much better than current operations.

## GMICEs

MMI categories are defined by how people experience shaking as well as the severity of damage in a region (Dengler and Dewey, 1998). Notably, these definitions do not include instrumental ground‐motion metrics such as PGA and PGV, which makes it difficult to directly convert between ground‐motion metrics and MMI. The empirical GMICEs in Worden *et al.* (2012) regress collocated PGA and PGV observations from seismic stations against intensities derived from DYFI reports. In the DYFI system, individual reports are aggregated by region (such as $1\u2009\u2009km2$ areas), and the resulting intensity, called a community decimal intensity (CDI) value, is calibrated to correspond to the MMI scale (Dengler and Dewey, 1998; Wald *et al.*, 2011).

Inherent uncertainty and variability in both DYFI intensities and their correlation with instrumental ground motions give rise to different forms of a relationship between the two. Worden *et al.* (2012) present several versions of a GMICE developed for California (reproduced in Table 1). In its simplest form (equation [eq.] 3), a single ground‐motion metric, either PGA or PGV, is used to convert to MMI. Additional terms considering magnitude (M) and hypocentral distance (*R*) are included in eq. (6). Finally, Worden *et al.* (2012) tested several options to combine the MMI computed in terms of PGA ($MMIPGA$) with the MMI computed in terms of PGV ($MMIPGV$) to form a single MMI estimate. These combinations included: a weighted average determined through an additional regression (eq. 9); a simple average of $MMIPGA$ and $MMIPGV$ (eq. 10); and the use of $MMIPGV$ at higher intensities with a transition to using $MMIPGA$ at lower intensities (Wald *et al.*, 1999; “eq. 11”).

Worden *et al.* (2012) found similar variability between these relationships, and, because of this, different applications ended up using different GMICEs. The GMICE preferred by Worden *et al.* (2012) is the eq. (9) combination using $MMIPGA$and $MMIPGV$ from eq. (6) (“eq.s 6 + 9” in Table 1). ShakeMap procedures for U.S. West Coast earthquakes prefer eq. (6) using PGV due to the reversibility between MMI and an individual ground‐motion metric (Worden *et al.*, 2020). In its current operations, ShakeAlert uses eq.s (6) + (10) for the grid product, whereas the contour product uses essentially eq.s (3) + (10) but in a “reverse” approach. Whereas the “forward” implementation computes MMI from the GMPE‐predicted PGA and PGV at a given distance, the “reverse” calculation uses eq. (3) to compute PGA and PGV at a given MMI value, determines the distances for each PGA and PGV from the GMPEs, and averages these distances together. These different procedures stemmed from earlier ShakeAlert operations that employed GMPE and GMICE functions (Thakoor *et al.*, 2019); current operations implement precomputed look‐up tables.

## Examining the Variation in MMI Due to GMICE Choice

We demonstrate the variation in the GMICE relations for three example magnitudes of **M** 4.0, 5.0, and 7.0 (Fig. 1) by computing PGA and PGV with distance using an equally weighted average of the NGA‐West2 shallow crustal GMPEs (Bozorgnia *et al.*, 2014) with the ground‐motion modeling assumptions used in ShakeAlert. These assumptions include: an 8 km source depth; strike‐slip rupture mechanism; a 5 MPa stress drop; no additional event terms; Joyner–Boore distance to the fault, if available, otherwise to the epicenter (Joyner and Boore, 1981); a $VS30$ of 500 m/s (used in the ShakeAlert contour product); and median‐expected ground motions (Thakoor *et al.*, 2019; Saunders *et al.*, 2022; see supplemental material available to this article for additional context). We then use these input ground motions and compute MMI with distance using the GMICEs in Table 1. We also include the eq.s (3) + (10) “reverse” procedure used in the current ShakeAlert contour product for comparison.

In the distance range for which the GMICE regressions are best constrained (∼20–200 km), different GMICEs produce similar MMIs (Fig. 1). However, for **M** 5.0+ earthquakes and at near‐source distances, MMIs computed for a given distance can vary by up to ∼1 MMI unit. Eq. (6) generally produces lower MMIs than eq. (3), and combinations using eq. (9) produce lower MMIs than eq. (10). For larger magnitudes and at far distances, $MMIPGV$ produces higher MMIs compared to $MMIPGA$, and eq. (3) produces more extreme MMIs than eq. (6). The MMI computed for a given distance can vary by ∼1.5 MMI units at distances greater than 200–400 km—distances beyond where the models were originally constrained (Worden *et al.*, 2012; Bozorgnia *et al.*, 2014).

Public EEW alerts in ShakeAlert are sent to distances corresponding to MMI 4.5+, 3.5+, and 2.5+ (Kohler *et al.*, 2020) and can vary significantly due to GMICE choice alone. This variability increases with magnitude. For an **M** 5.0 earthquake, alert distances vary by 8, 11, and 44 km for the MMI 4.5+, 3.5+, and 2.5+ alert thresholds, respectively. For **M** 6.0, these public alert distances vary by 10, 36, and 162 km, respectively. And for **M** 7.0, the alert distances vary by 36, 206, and 595 km, respectively. For **M** 7.0 and higher, nearly the entire range of the possible MMI 2.5 alert distances involves extrapolation of the GMPEs and GMICEs.

In addition, these examples highlight differences in resulting MMI levels and alert distances caused by the GMICE implementations in the current ShakeAlert contour product (eq.s 3 + 10 “reverse”) and grid product (eq.s 6 + 10). This means that depending on the alert product used, current ShakeAlert operations can yield different MMI distributions, affecting which locations are alerted during an earthquake. This also suggests a high uncertainty in the reversibility between ground‐motion metrics and intensities.

## Determining a Preferred GMICE to Use with the NGA‐West2 GMPEs in ShakeAlert

Our goal is to determine an appropriate GMICE to use in ShakeAlert in conjunction with the NGA‐West2 GMPEs, which were found to better match seismic station PGA and PGV observations compared to current ShakeAlert GMPEs (Böse *et al.*, 2023; Chatterjee *et al.*, 2023). We find the GMICE (Table 1) that best models the median‐observed MMI given DYFI intensity observations because these are considered ground truths for shaking intensity model development in the United States (Worden *et al.*, 2012).

### Methods

We gather DYFI CDI observations from all **M** 4.5+ earthquakes (through 2023) that have at least 100 DYFI reports and have occurred in and around the state of California, defined by the boundary used for seismic hazard analysis for the state (Field *et al.*, 2014; U.S. Geological Survey [USGS], 2017). This totals 210 earthquakes with over 273,000 CDI observations (aggregated into $1\u2009\u2009km2$ regions) from over 679,000 individual DYFI reports (Fig. 2). Although the vast majority of these events occurred after the DYFI system launched in 1999, this catalog includes significant earthquakes from before 1999 with retrospectively submitted DYFI reports, such as the 1989 **M** 6.9 Loma Prieta and 1994 **M** 6.7 Northridge earthquakes.

For each CDI location, we compute MMI using each candidate GMICE (Table 1), using as input the average PGA and average PGV from the NGA‐West2 shallow crustal GMPEs, following the procedures in the previous section. We consider the $VS30$ estimate at the CDI location in the GMPE calculation (Heath *et al.*, 2020). The input source parameters consider the U.S. Geological Survey (USGS) Comprehensive Catalog (ComCat) magnitude and hypocenter for each earthquake (USGS, 2017), with ShakeMap fault rupture information for the **M** 6.0+ earthquakes, if available.

We compute residuals between the modeled MMI values and the DYFI CDI observations, and determine average residuals, aggregating into magnitude and distance bins. For a given magnitude category, we compute the mean and standard deviation of these intensity residuals in 20 km distance bins, weighted by the number of DYFI reports aggregated per CDI observation (to a maximum weight of 5). Although ShakeMap procedures require at least three DYFI reports per location to incorporate CDI observations, we used all available DYFI CDIs to not significantly reduce the number of CDI observations in our analysis. However, we only calculate residuals for distance bins containing at least 10 CDI observations aggregated using at least three DYFI reports per observation.

### Results

The different GMICEs show a variety of mean residual behavior across the different magnitude categories (Fig. 3); however, there are some cases where this behavior is consistent. Although we considered all DYFI CDIs out to a distance of 800 km, 500–520 km was the farthest distance bin that contained sufficient CDI observations to meet our criteria for evaluating the residuals. All GMICEs systematically underestimate MMI for **M** < 5.5 at distances of 100+ km. This is because the lack of MMI 1 (not‐felt) and MMI 2 (few‐felt) reports in the DYFI system biases the average CDI values for those distances (Boatwright and Phillips, 2017). All GMICEs tend to significantly underestimate intensities at distances of <100 km for earthquakes in the 6.5 ≤ **M** < 7.0 category (seven earthquakes) due to this category containing intensity observations from the very damaging 1989 **M** 6.9 Loma Prieta and 1994 **M** 6.7 Northridge earthquakes; very high intensities (MMI ≥ 8) are difficult to model with median‐expected ground motions (Fig. 1). Similarly, all GMICEs tend to significantly overestimate intensities at distances of <100 km for earthquakes in the 6.0 ≤ **M** < 6.5 category (eight earthquakes) because most of these observations are from the 2014 **M** 6.0 South Napa earthquake, which produced lower‐than‐expected shaking at distances beyond the immediate epicentral area (>20 km).

In terms of the GMICEs tested, MMIs computed using eq. (3) tend to show larger residuals compared to corresponding MMIs computed using eq. (6). In addition, the intensity residuals for $MMIPGA$ tend to have the opposite behavior compared to $MMIPGV$. $MMIPGA$ (eq. 3) overestimates MMI in the near field but underestimates MMI at larger distances. Adding the distance and magnitude terms in $MMIPGA$ (eq. 6) improves residuals except for increased underestimation of near‐source MMI for **M** > 6.5. $MMIPGV$ (eq. 3) can significantly overestimate MMI, especially for **M** > 6.0. Adding magnitude and distance terms to $MMIPGV$ (eq. 6) improves residuals but still overestimates MMI for **M** > 6.0 at large distances. Combining $MMIPGA$ and $MMIPGV$ using eq. (9) or eq. (10) yields very similar residuals when using the same initial GMICE (e.g., eq.s 6 + 9 and eq.s 6 + 10). All GMICE combinations that use eq. (9) or eq. (10) tend to overestimate MMI for **M** > 6.0 earthquakes at larger distances, likely due to the MMI overestimation from $MMIPGV$.

Our preferred GMICE is the eq. (6) + (11) GMICE combination, which favors $MMIPGV$ for higher intensities and transitions to $MMIPGA$ for lower intensities (Table 1). This combination produces mean residuals that are close to zero and are unbiased across the most magnitude and distance bins compared to the other GMICEs tested with the NGA‐West2 GMPEs. Over all events, this GMICE has mean MMIs of 0.1 ± 0.1 MMI units larger than the corresponding DYFI CDI observations, which is within the uncertainty range of the DYFI CDI observations (∼0.3 MMI units; Wald *et al.*, 2011). We found similar results considering just the earthquakes with at least 500 and 1000 DYFI reports per earthquake (Figs. S1, S2). We also compared additional GMICEs (Caprio *et al.*, 2015; Gallahue and Abrahamson, 2023) and intensity prediction equations (Allen *et al.*, 2012; Atkinson *et al.*, 2014) and found that the preferred relationship was still the eq. (6) + (11) of Worden *et al.* (2012) (Fig. S3).

## Discussion

By examining the behavior of MMI with distance, we found that different GMICEs are not as transferable as suggested in Worden *et al.* (2012), which focused mainly on comparisons between MMI and peak ground‐motion metrics. Our results suggest that PGA or PGV alone cannot accurately model MMI for all magnitude and distance ranges, which has implications for ShakeMap. In ShakeMap procedures, a background MMI distribution map is computed using GMPEs and GMICEs, for which adjustments are made in locations with station and DYFI observations (Wald *et al.*, 2022). Our results suggest that ShakeMap’s use of $MMIPGV$ could overestimate the extent of nondamaging but likely‐felt intensities in locations that do not have DYFI CDIs available for adjustments, particularly for **M** ≥ 6.0 earthquakes (Figs. 1b, 4a). Although this will not affect PAGER loss estimates, which focus on damaging intensities (Wald *et al.*, 2010), this can affect the interpretation of EEW alert performance when comparing alert regions against ShakeMaps. Ultimately, revisiting the GMICE relationships and performing new regressions with updated datasets will best improve MMI distribution estimates in the United States (Gallahue and Abrahamson, 2023).

Given the observed differences in MMI predictions when using different GMICEs, the updated GMPE and GMICE combination in ShakeAlert proposed in this study would change alert performance compared to the current system (Fig. S4). To investigate this, we compare DYFI CDI distributions to modeled MMI with distance for a set of example earthquakes (Fig. 4), highlighting: the current ShakeAlert contour product GMPE and GMICE; the current ShakeAlert grid product GMPE and GMICE; the NGA‐West2 GMPEs using the ShakeMap GMICE; and the NGA‐West2 GMPEs using our preferred GMICE (and proposed update to ShakeAlert). These MMI with distance curves use the ComCat magnitude and epicenter alongside the typical assumptions used in ShakeAlert. Although these comparisons represent idealized alert distance curves, they are still informative for determining expected alert performance changes should the ground‐motion model updates be implemented into ShakeAlert.

At smaller magnitudes (**M** <∼5; Fig. 4e,f), current ShakeAlert GMPEs and GMICEs tend to underpredict median‐observed shaking. Transitioning to the proposed updates will expand the sizes of the MMI 3.5+ and 2.5+ public alert regions for earthquakes in this magnitude range. At moderate magnitudes (**M** ∼5.5; Fig. 4d), the different GMPEs and GMICEs produce similar MMI distributions; therefore, we do not expect significant changes in alert performance. We see the greatest divergence between the models at larger distances and lower MMI levels. At larger magnitudes (**M** > 6; Fig. 4a–c), the current ShakeAlert contour product GMPE and GMICE tend to overestimate MMI relative to median CDI observations, whereas the proposed updates more closely match median CDI observations. This means that the proposed updates will decrease the size of the alert regions for the ShakeAlert contour product in these magnitude ranges, though changes relative to the current ShakeAlert grid product will be slight.

Our proposed GMPE and GMICE updates bring ShakeAlert EEW alert regions closer to the stated objectives of modeling median‐observed shaking (Given *et al.*, 2018). However, there remains uncertainty about the transition between felt and not‐felt shaking intensities due to the dearth of low‐MMI reports in DYFI (Boatwright and Phillips, 2017; Figs. 2d, 4). Accurately modeling this transition is key for evaluating alert performance and determining alerting strategies that aim to minimize missed alerts at significant shaking levels while keeping alerts within locations of likely‐felt shaking (Minson *et al.*, 2019, 2021; Saunders *et al.*, 2022). This uncertainty particularly impacts alert regions using MMI 2.5, the lowest public alert threshold in ShakeAlert.

The necessity of an MMI 2.5 alert threshold for ShakeAlert is uncertain as many locations that experience potentially damaging shaking will receive timely warnings from the MMI 3.5 alert threshold (Saunders *et al.*, 2022; Thompson *et al.*, 2023). The choice to use an MMI 2.5 alert threshold for public alerts was made in response to the significant magnitude underestimation by ShakeAlert during the 2019 **M** 7.1 Ridgecrest earthquake (Cochran and Husker, 2019; Chung *et al.*, 2020). Adjustments to the ShakeAlert EEW algorithms in light of these performance issues have made significant magnitude underestimation less likely with the current system (Böse *et al.*, 2023). This, combined with the poor observational constraints on the extent of lower MMIs as well as lower MMI locations containing high percentages of people who do not feel shaking (Sbarra *et al.*, 2014), indicates that the MMI 2.5 alert threshold in ShakeAlert should be reevaluated.

## Summary

MMI is defined primarily by the impacts of shaking on the built environment and by people’s experiences of shaking, not by instrumental ground‐motion parameters such as PGA and PGV. Although there are empirical GMICEs for the United States that convert instrumental ground motions to MMI, these models produce significant variation between their resulting MMI with distance curves. For applications like ShakeAlert that use GMICEs in their procedures, this high epistemic uncertainty in GMICEs impacts alert distances and therefore EEW alert performance, particularly for larger magnitudes and at the lower MMI thresholds used for public alerts. By comparing MMIs computed using the different GMICEs presented in Worden *et al.* (2012) with an updated catalog of DYFI intensity observations, we determined which existing GMICE best models the median‐observed intensity from DYFI ground truths. The preferred GMICE considers MMI computed in terms of PGV for higher intensities and transitions to MMI computed in terms of PGA for lower intensities. Notably, our preferred GMICE is not the one that is currently used in USGS applications such as ShakeAlert or ShakeMap, indicating that updated GMICE regressions should be considered.

## Data and Resources

Earthquake source information and “Did You Feel It?” (DYFI) intensity observations were obtained from the U.S. Geological Survey (USGS, 2017). All analyses and figures were created using Python (https://python.org, last accessed January 2024). The supplemental material contains additional details about ShakeAlert’s ground‐motion modeling procedures and additional figures.

## Declaration of Competing Interests

The authors acknowledge that there are no conflicts of interest recorded.

## Acknowledgments

The authors thank Gail Atkinson, Bruce Worden, an anonymous reviewer, and the U.S. Geological Survey (USGS) internal review officials for comments that improved this article. This work benefited greatly from discussions with members of the ShakeAlert Ground‐Motion Modeling Working Group as well as other members of the ShakeAlert community. This research was supported by the USGS Earthquake Hazards Program through the ShakeAlert Project, under Grant Number G21AC10561 to Caltech and Grant Number G21AC10532 to ETH Zürich.

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