### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[1] Earthquake hypocenters from global datasets commonly have regional biases in their locations due to the use of a one-dimensional velocity model in their location. To analyze this effect, we group intermediate-depth earthquakes into forty-four 500-km-long sections of subduction zone. We relocate earthquakes in each group relative to one another and in a three-dimensional global velocity model. Hypocenters shift up to 25 km regionally when these effects are included; most earthquakes in circum-Pacific subduction zones are pulled toward the Pacific. Location uncertainties from the relative relocations are reduced to one-fifth of those from single-event locations; Wadati-Benioff zone thicknesses are reduced to two-thirds of their original thickness. These biases alter estimates of depth to slab beneath arc volcanoes up to 50 km, and alter measurements such as the volume of mantle wedge available for water storage or melt generation, and the size of the thrust zone on which large earthquakes can occur.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[2] Plate geometries are frequently based on seismicity and rely on the accuracy of hypocenters in global earthquake catalogs. Regional and local catalogs provide more accurate locations, but exist for relatively few regions. Within subduction zones, intermediate depth earthquakes define the Wadati-Benioff zone (WBZ) and slab geometries, which constrain geodynamical models. At shallower depths hypocenters provide information on the locations of transform faults at mid-ocean ridges and normal faults at the outer rises of trenches. Accurate earthquake locations are also important in the study of earthquake hazards; knowing the locations of large earthquakes makes it possible to relate seismicity to surface features.

[3] In subduction zones four main factors may degrade the accuracy of global datasets. The first is that all hypocenters have random errors due to inexact arrival times, inexact velocity models and incomplete arrival data. These errors cause earthquake locations to scatter around the actual structure that they define; such errors can be assessed statistically [e.g., *Pavlis and Hokanson*, 1985; *Thurber*, 1986; *Gomberg et al.*, 1990; *Pavlis*, 1992]. In particular, random errors cause WBZ seismicity to appear wider than its actual distribution. This causes slab surfaces based on seismicity to be interpreted too shallowly when the surfaces are interpreted as the top of the WBZ. Such biases can be corrected by incorporating hypocenter uncertainties [*Syracuse and Abers*, 2006]. Relative relocation methods minimize these effects [e.g., *Jordan and Sverdrup*, 1981; *Poupinet et al.*, 1984; *Got et al.*, 1994; *Waldhauser and Ellsworth*, 2000], reducing relative scatter among earthquakes within a localized region by assuming that a portion of the time delays to a particular station is due to velocity structure common to their similar raypaths.

[4] A second factor is the station geometry surrounding the earthquake, both on the local and global scale. Locally, networks above subduction zones often include only land stations, limiting azimuthal coverage, particularly at island arcs. Networks restricted to the forearc may result in hypocenters that are located too deeply and close to the trench [*McLaren and Frohlich*, 1985]. Expanding station coverage through the backarc improves locations, as well as including teleseismic arrivals from a variety of azimuths. The global station distribution, however is also largely limited to land stations and heterogeneous, with more stations above cold cratons than hot oceanic mantle, leading to potential error in teleseismically located hypocenters.

[5] A third factor is the bias caused by high velocity slabs. Earthquakes that occur at shallow depths (<50 km) in a subduction zone produce signals that can travel long distances within a high velocity slab, causing hypocenters to shift up to 40 km in the direction of the slab dip [*Sorrells et al.*, 1971; *Jacob*, 1972; *Fujita et al.*, 1981]. This effect is smaller for deeper earthquakes since the rays travel a comparatively shorter distance within the slab [*McLaren and Frohlich*, 1985].

[6] A fourth contributing factor is the accuracy of the global velocity model used in earthquake location. Generally, earthquakes are located in one-dimensional (1D) global velocity models that do not take into account three-dimensional (3D) velocity variability. This may lead to systematic biases in earthquake locations within some regions which may vary globally, such as found by *Smith and Ekström* [1996] and *Antolik et al.* [2001] for explosion epicenters. Relative relocation methods are unable to independently remove these biases [*Wolfe*, 2002], necessitating a combined approach to reduce both relative scatter of earthquakes within a region and remove far-field velocity model biases.

[7] In this study, we focus on the effect of random scatter and of large-scale 3D earth structure on global earthquake locations for intermediate depth earthquakes in subduction zones. Relative relocations are determined in a 1D velocity model and in a model corrected for 3D earth structure for earthquakes in most subduction zones. The effect on slab geometries and the depth of the slab beneath arc volcanoes is analyzed, providing a comprehensive and systematic survey of WBZ seismicity. Globally, the median difference between the 1D and 3D locations for earthquakes within a section of subduction zone is usually less than 10 km, but can be as much as 25 km.

### 2. Data

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[8] This study uses arrival times from 43 years (1964–2007) of the International Seismic Centre (ISC) catalog. Arcs longer than 500 km are separated into 500 km sections, following the *Syracuse and Abers* [2006] delineations. The ISC database is subsetted to include only earthquakes within 250 km of the projection with depths between 50–400 km that have at least 10 arrivals, including at least one *S* arrival. On average, each earthquake included has 116 *P* arrivals, 11 *S* arrivals and 8 *pP* arrivals. Gaps in the volcanic arc, arcs with fewer than 100 intermediate depth earthquakes, and areas where the arc does not overly WBZ seismicity are omitted. For each of the resulting 44 sections of arc, a line is projected through the center of the section in the downdip direction. For uniformity and ease of computation, the resulting catalog is further subsetted to a final size of about 300 earthquakes for each arc section, retaining the earthquakes with the most arrivals. The number of earthquakes used varies from 210 in Kermadec to 310 in Bali – Lombok.

### 3. Methods

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[9] Earthquakes within each of the 44 arc sections are relocated with and without travel time corrections based on 3D earth structure using the relative relocation method of *Jordan and Sverdrup* [1981]. This method divides each hypocenter in two parts – a hypocentroid and a cluster vector. The hypocentroid is nominally the mean location of the population. The cluster vector is the perturbation of each hypocenter from the hypocentroid, and usually has smaller uncertainties because systematic path effects are removed [*Jordan and Sverdrup*, 1981]. *P* arrivals are assigned an uncertainty of 0.75 s, while *S* and *pP* arrivals are assigned an uncertainty of 1.5 s. *P* arrivals are eliminated if residuals relative to the cluster vector exceed 2 s or residuals relative to the overall location exceed 4 s. For *S* and *pP* arrivals, these limits are 3 s and 6 s, respectively. These limits are doubled in the first of three iterations. If a relocated earthquake has moved more than 200 km from its original location and has no *S* arrivals that are within the residual limit, the earthquake is removed from the relative relocation, minimizing effects of poorly located outliers and reducing hypocentroid uncertainties by up to 300%.

[10] To account for 3D Earth structure, arrival time corrections are calculated for each hypocenter following the method of *Antolik et al.* [2001] using the crustal thickness model Crust 2.0 [*Bassin et al.*, 2000] and the mantle *P* and *S* model J362D28 [*Antolik et al.*, 2003]. Crust 2.0 describes the crust on a 2° by 2° grid by classifying each grid cell as a crustal type, specified by a 7-layer model of *P* and *S* wave velocities, densities and thicknesses, including ice, water and sediment. Crustal corrections are calculated as the differences in travel times between Crust 2.0 and PREM [*Dziewonski and Anderson*, 1981] for *P*, *S*, and *pP* arrivals with earthquake-station distances of 20° to 98°. J362D28 describes mantle *P* and *S* velocities as perturbations to PREM through a set of 362 spherical splines that extend to 3000 km depth with a horizontal resolution equivalent to that of spherical harmonic degree 18 (∼1000 km). Mantle corrections are calculated as travel time deviations from PREM, added to the crustal corrections, applied to the iasp91 travel times [*Kennett and Engdahl*, 1991], and relative relocations are calculated. Differences between PREM and iasp91 should affect the corrected locations minimally since they are the same for all azimuths, and vertical differences between the models are absorbed into origin time variations to first order. This procedure is applied iteratively, updating corrections if hypocenters move an average of 10 km or more per cluster. These locations are referred to as the corrected locations. For comparison, each group of earthquakes are also relocated with the same method but no 3D or crustal corrections; these are referred to as “uncorrected”. Finally, single-event locations are recalculated for each earthquake, using uncorrected arrival times and the same data sorting and statistical treatment as the relative locations. These are referred to as “single-event locations”.

[11] Biases are calculated by comparing the difference in location between the corrected (3D) and uncorrected (1D) locations. For each arc section, bias vectors are defined as the median difference in location in the vertical, along arc, and across arc directions. Horizontal shifts are calculated as the square root of the sum of the squares of the shifts in the along arc and across arc directions. Shifts in depths are considered positive if using the corrected arrival times increased hypocenter depth.

### 4. Results

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[12] Biases in earthquake location and associated uncertainties for each arc section are shown in Table S1 in the auxiliary material. In most cases the standard error in the location of the hypocentroid is less than 1 km in all directions, and the median standard error (2-sigma) in the hypocenters is 3.2 km. For single-event locations, the median standard error is 16.0 km, or five times that of the relative relocations. For comparison the median 1-sigma standard error in the hypocenters relocations by *Engdahl et al.* [1998], who use a 1D velocity model for location, is 6.1 km; their error estimation method differs.

[13] The average WBZ width is narrower from the relative relocations than from the ISC hypocenters and the single-event hypocenters (Table S1 and Figure 1). The width of each WBZ is approximated as four times the standard deviation in the width normal to the corresponding digitized slab surface from *Syracuse and Abers* [2006]. To account for possible differences in slab shapes indicated by different datasets, a linear trend is fitted to describe variations with depth between any particular set of hypocenters and the digitized slab surfaces, and WBZ width is calculated relative to the digitized slab surface corrected for that trend. The corrected and uncorrected locations from this study both result in an average WBZ thickness of 35 km. The single-event and ISC locations result in an average thickness of 53 km (Figure 2), showing that relative relocations reduce scatter in WBZ locations. Average WBZ thickness calculated from *Engdahl et al.* [1998] is also 35 km; the additional phase analysis carried out in that study provides similar improvement over single-event methods. However actual WBZ thickness still must be less in many cases, as evidenced by the correlation between reported formal errors and WBZ width [*Syracuse and Abers*, 2006].

[14] The median magnitude of the biases associated with the 3D velocity model is 4.7 km horizontally and 1.5 km vertically; the small vertical shifts reflect the inclusion of *pP* phases. Horizontal shifts vary from less than 2 km in the Lesser Antilles to 25 km in Kermadec (Figure 3). The 3D velocity model correction decreases hypocenter depths by as much as 6 km (in parts of Indonesia) and increases hypocenter depths by up to 8 km (in the Kuriles). On average, individual earthquakes are biased by 0.35 km south, 1.54 km east and 0.43 km in depth in a 1D velocity model, with a maximum bias in Kermadec of 4.71 km north, 25.14 km east and 2.02 km in depth.

[15] The direction of the biases systematically varies between circum-Pacific subduction zones (Figure 3). In general, a 1D velocity model underestimates travel times to seismically slow regions, such as the western United States and western South America, and overestimates travel times to seismically fast cratonic regions such as the eastern United States and Australia. Correcting arrival times for 3D Earth structure shifts hypocenters away from seismically fast continental regions and toward slower regions, such as the center of the Pacific.

[16] Comparison to relocated seismicity using local datasets from Nicaragua, Alaska, and Honshu show that adding 3D corrections makes hypocentral locations more similar to those based on local data at 100–200 km depth (Figure S1), reducing offsets between local and corrected teleseismic locations by 15% on average. However between 50 and 100 km depth and below 200 km, discrepancies are larger, possibly due to shortcomings of many local networks. *McLaren and Frohlich* [1985] and *Hauksson* [1985] show strong coupling between slab velocity and earthquake locations below 200 km. Narrow station aperture, such as in the Central Aleutians [*Kisslinger*, 1993] also limits the accuracy of intermediate depth hypocenters from local networks.

### 5. Discussion

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

[17] Since most slabs dip away from the central Pacific and applying 3D corrections moves intermediate depth hypocenters toward the central Pacific, most slabs probably lie trenchward of where they do based on intermediate depth seismicity from standard catalogs. These biases are similar in all depth ranges within individual arc sections, so the slab geometries can be assumed to remain unchanged, while the absolute position of the slab is shifted uniformly throughout the 50–400 km depth range. Since the trench remains fixed, the portion of the slab between the trench and 50 km depth must be steeper. Therefore, measurements such as the volume of the mantle wedge and the location of the slab relative to the arc show small systematic bias.

[18] These regional biases affect previous measurements of the depth the slab beneath arc volcanoes, *H* [*England et al.*, 2004; *Syracuse and Abers*, 2006]. To calculate the effect on *H*, an average two-dimensional cross section is calculated for each section of arc interpolated from the slab surface contours from *Syracuse and Abers* [2006]. Each contour is shifted by the corresponding bias in the vertical and across-arc direction and *H* is recalculated (Table S1).

[19] The magnitudes of the *H* corrections average 10 km, ranging from less than 2 km in the Lesser Antilles to 45 km in Kermadec. The magnitude and sign of corrections depends mainly on the size of the regional bias and direction and dip of the slab. For slabs dipping away from the center of the Pacific, correcting for the regional bias increases *H*, since circum-Pacific hypocenters are pulled toward the center of the Pacific. The few slabs dipping toward the central Pacific (Solomons, Vanuatu, etc.) show the opposite trend. For the majority of WBZs that dip away from the Pacific, standard catalogs that locate earthquakes in 1D models bias dips too shallow and effectively mislocate earthquakes toward the mantle wedge by an average of 6 km.

[20] Previous studies have found that *H* varies up to 65–70 km among different subduction zones [*England et al.*, 2004; *Syracuse and Abers*, 2006]. The majority of this variation among different arcs is indeed due to real structure, as correcting for hypocenter biases reduces the overall global variation in *H* by about 15 km, or about 20%. There is no correlation between the bias correction to *H* and the value of *H* (Figure S2), although the slab with the largest *H*, Vanuatu, is most affected. As a result, reported correlations between *H* and subduction parameters [*England et al.*, 2004; *Syracuse and Abers*, 2006] change minimally.

[21] The effects of these biases extend to other features of subduction geometry. For example, the volume of mantle wedge trenchward of the arc places an upper bound on water storage in hydrous minerals in the forearc [*Hyndman and Peacock*, 2003], and the vertical distance to the slab below arc crust constrains the size of the region available for melting [*Plank and Langmuir*, 1988]. Consider the volume of the region trenchward of the arc, below 50 km depth (a nominal upper-plate thickness) and above the slab. The volume of this region is changed by an average of 30% by accounting for hypocenter biases, with the volume reduced by more than half in Vanuatu. These biases also affect measurements of the size of the thrust zone, which can affect estimates of the maximum magnitude earthquake possible on a section of fault. Assuming a planar slab between the trench and 50 km depth, and a thrust zone extending along the plate interface between 10 km depth and 50 km depth [*Dixon and Moore*, 2007], the length of the thrust zone changes 5% on average by accounting for hypocenter biases, and is reduced by 24% in Kermadec.

[22] In summary, by accounting for 3D Earth velocity structure, global earthquake datasets can be corrected for the biases associated with using an oversimplified 1D velocity model. In the case of intermediate depth earthquakes within subduction zones these corrections can exceed 20 km horizontally and change previous measurements of *H* up to 50 km. These changes are significant and detectable, but they do not eliminate the observed global variations in *H* between arcs.

### Supporting Information

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methods
- 4. Results
- 5. Discussion
- Acknowledgments
- References
- Supporting Information

Auxiliary material for this article contains comparisons of uncorrected and corrected teleseismic locations to several local catalogs and the effect of accounting for regional location biases on depth the slab, referred to as H, and a table showing regional biases and associated statistics for each arc section.

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