Stress Field Interactions Between Overlapping Shield Volcanoes: Borehole Breakout Evidence From the Island of Hawai'i, USA

Knowledge of the in situ stress state of the Earth's crust plays a key role in understanding geological processes including plate tectonics, earthquakes, slope failure, and igneous emplacement. In this paper, we determine the in situ stress orientation from the PTA2 borehole on the island of Hawai'i, drilled into a lava flow dominated sequence between Mauna Kea and Mauna Loa. High‐resolution acoustic images were collected from the open hole interval 886 m to 1,567 m. Based on identification of 371 borehole breakouts for a total length of 310 m, the mean orientation of the minimum horizontal principal stress is N106° and remains constant across different volcanic rock fabrics. Changes in borehole breakout shape are linked to the different strength of volcanic facies and intra‐facies. The orientation of the present‐day stress field at Mauna Kea deviates from the plate forces and regional tectonic stress field. We interpret the compressive stress regime at the PTA2 site as resulting from the competing gravitational fields of the large topographic highs of Mauna Kea and Mauna Loa. Our study reveals that the mass accumulation associated with shield volcano growth imparts significant local variations to the subsurface stress state on volcanic islands consisting of overlapping shield volcanoes. The results have significant implications for stress accumulation leading to brittle failure and flank collapse, along with potentially influencing magma accumulation and ascent pathways during volcanic island evolution. This study provides the first insights into the orientation of the present‐day stress field between the major island forming shield volcanoes of Hawai'i.


Introduction
The determination of the present-day stress field in the Earth's crust is fundamental for investigations of the mechanical behavior of rocks, fluid flow at depth, and in revealing mechanisms that cause tectonic plates to move, fault, or rupture (Amadei & Stephansson, 1997;Engelder, 1993;Zang & Stephansson, 2010;Zoback, 2007). In general, three orders of stress patterns are present in the Earth's crust: first order (plate tectonic scale), second order (regional scale), and third order (local scale) (Zoback, 1992). The third order (local scale) of stress patterns is controlled by basin geometry, topography, local inclusions, density contrasts, and active faults (Heidbach et al., 2007;Zoback, 1992) and can show significant deviations from regional and plate stress patterns (e.g., Bell, 1996aBell, , 1996bPierdominici & Heidbach, 2012;Tingay et al., 2006). The present-day stress field is described by four main stress indicators: earthquake focal mechanisms, wellbore breakouts and drilling-induced fractures, in situ stress measurements (including over-coring, hydraulic fracturing, and borehole slotter), and young geologic data (from fault-slip analysis and volcanic vent alignments) (e.g., Heidbach et al., 2016).
The island of Hawai'i is located within the Pacific Ocean and comprises one of the best studied and monitored volcanoes on the planet (Barnard, 1995;Poland et al., 2018;Tilling et al., 2014). Available stress data for the island of Hawai'i are derived mainly from focal mechanism solutions of earthquakes and geological field analysis of recent faulting. These extensive data sets reveal the respective role of rift zone intrusions, surface exposures, flank sliding/collapse, and lithospheric flexure mainly linked to the two active volcanoes Mauna Loa and Kīlauea (e.g., Borgia & Treves, 1992;Cannon et al., 2007;Klein, 2016;Le Corvec & Walter, 2009;McGovern, 2007;Moore et al., 1994). Volcanic lineaments and faulting on topographic ridges on Mauna Kea volcano are very poorly developed, with shield-stage rift zones overlain by post-shield volcanic strata (e.g., Cannon et al., 2007). In contrast to the extensive surface and deep seismic data sets, subsurface measurements documenting the stress state of the island of Hawai'i are restricted to the HSDP borehole, located near Hilo on the eastern flank of the island. To date no subsurface measurements have been presented from the central areas of the island, and therefore, the present-day stress field and the potential influences of the competing large shield volcanoes have remained unknown until now. Within this contribution, we determine the orientation of the present-day stress field from borehole analysis in the center of the island of Hawai'i between the large Mauna Loa and Mauna Kea shield volcanoes.
The Humu'ula Groundwater Research Project (HGRP) drilled two boreholes in order to obtain a complete data set of fully cored volcanic rocks with associated borehole measurements and to characterize the groundwater resources in the saddle region (Jerram et al., 2019). The PTA2 borehole was drilled in the saddle region between Mauna Kea and Mauna Loa and offers a unique opportunity to study the previously untested subsurface of central Hawai'i. Within this study, high-resolution borehole images acquired by an acoustic borehole imager are used to detect and interpret borehole breakout features which are utilized to reconstruct the present-day stress state in the borehole. We identify linkages between borehole breakout magnitude and different volcanic rock properties, including porosity and rock strength.
Our analysis provides the first subsurface evidence to suggest that the competing gravitational loads of two large overlapping shield volcanoes form the primary control on the orientation of the present-day stress field. The subsurface stress indicators from the PTA2 borehole on the island of Hawai'i show an orientation of maximum horizontal principal stress about north-south that differs from the northwest-southeast orientation of the large-scale Pacific plate stress field (Torsvik et al., 2017). Knowledge of the shallow stress field may impact future borehole planning and aquifer/geothermal resource management and may also give important information for understanding the influence of stress field evolution on ocean island development.

Geological and Tectonic Setting
The Hawaiian volcanic chain was created as the Pacific tectonic plate moved over the Hawaiian hotspot (Fiske & Jackson, 1972;Sherrod et al., 2007;Wilson, 1963;Figure 1a). Hawai'i Island's volcanoes are the most recent expression of this process that has created the 6,000 km long Hawaiian Ridge-Emperor Seamount chain over a period of about 70 million years (Appleman, 1987;Clague & Dalrymple, 1987;Sharp & Clague, 2006;Watson, 1999). The island of Hawai'i is the closest to the present-day mantle plume and consequently is a volcanically active region comprising the youngest part of the island (%3C0.4 Ma; Figure 1b). It is composed of five volcanoes on land, of which three (Kīlauea, Mauna Loa, and Hualālai) are still considered to be active. Offshore, the still growing Lō'ihi seamount is the only known pre-shield stage volcano in the chain. Mauna Kea is one of the five shield volcanoes on the island of Hawai'i, and it is in a dormant phase having last erupted approximately 4,000 ka (Porter, 1987).
Mauna Kea's subaerial edifice was formed in two main stages: first, a shield stage dominated by tholeiitic basalts was emplaced and, secondly, a post-shield stage with tholeiitic and alkali basalts (Frey et al., 1990(Frey et al., , 1991Wolfe et al., 1997). The post-shield lavas are subaerially exposed with two main lava units: (i) the tholeiitic, transitional-alkalic basalts of the Hāmākua volcanics (250-65 ka) (Frey et al., 1990(Frey et al., , 1991Wolfe et al., 1997) and (ii) Laupāhoehoe volcanics (66-4 ka). The latter include mainly hawaiite and less abundant mugearite and benmoreite (West et al., 1988;Wolfe et al., 1997) for the most recent volcanic flows (Frey et al., 1990). Volcanic lineaments on Mauna Kea are scattered and poorly developed or not present (Cannon et al., 2007;Sherrod et al., 2007). The shield stage rift zones of Mauna Kea are thought to be buried by the Mauna Kea post-shield volcanic lineaments (Cannon et al., 2007), and therefore, no fissure vents, open cracks, and normal faults along the rift zone axes are clearly present at the surface. The location and orientation of the Mauna Kea ridge is still debated (Figure 2) (Holcomb et al., 2000;Moore & Clague, 1992;Morgan et al., 2010;Peterson & Moore, 1987). However, recent geophysical surveys on Mauna Kea's east flank have shown evidence of a buried rift system (Park et al., 2009;Thomas, 2016). The Mauna Kea volcano is also affected by a little seismic activity. The relocated earthquakes beneath Mauna Kea by Wolfe et al. (2004) show a hypocenter depth between 15 and 50 km with a prevailing compressive stress field and a radial distribution of P-axis orientation (Pritchard et al., 2007;Wolfe et al., 2004). In contrast the island of Hawai'i is dominated by strong and intense seismicity due to the Kīlauea and Mauna Loa active volcanoes. Forty-two earthquakes have been located at a depth greater than 5 km recorded by the National Earthquake Information Center from 1929 to 2018 with M w ≥ 5.0 (NEIC; https://earthquake.usgs.gov/contactus/golden/neic.php), which shows that the area is dominated by compressive and strike-slip regimes ( Figure 1c; Table S1). The area shows variable P-axis azimuths with a preferred northwestern orientation in contrast with the orientation of maximum horizontal principal stress from the borehole analysis. Focal mechanism solutions show a complex system with a mixture of normal, strike-slip, and reverse faulting, reflecting the influence from both magmatic and tectonic activities. The P-axes azimuths show a southeast orientation close to the south flank of Kīlauea and to the southeast flank of Mauna Loa, a west orientation close to the summit zone of Mauna Loa, and in the strike orientation of the East Rift Zone at Kīlauea's summit caldera. The seismicity above 15 km is located under the caldera and active rift zones, and it is mainly related to dike emplacement and magmatic activity (e.g., Klein, 2016;Lin & Okubo, 2016, and reference therein). The deeper seismicity is mainly associated with flexure and subsidence under Mauna Kea and Mauna Loa volcano load (e.g., Klein & Koyanagi, 1989;Moore, 1970;Pritchard et al., 2007;Walcott, 1976;Wolfe et al., 2004). The complexity of the tectonic and volcanic setting of the island of Hawai'i, at different depths and at different volcanic centers, reflects the variability of stress and strain states (e.g., Klein, 2016;Lin & Okubo, 2016, and reference therein). In the show the locations of some other deep boreholes drilled on the eastern part of the island. In brackets, the year and the depth of drillings. Seismicity and the focal mechanism solutions are scaled according to the magnitude; the numbers for each event reference details for each event are presented in Table S1. center part of the island of Hawai'i between Mauna Loa and Mauna Kea volcanoes, no seismic event has been recorded at shallow depths (see, e.g., Klein, 2016). Clear geological surface evidences for stress indicators are also lacking in this area (Cannon et al., 2007). The World Stress Map catalogue of the island of Hawai'i shows few focal mechanism solutions but again with none from the center of the island (see the inset of Figure 12a). The analysis of borehole breakouts from the PTA2 borehole within this study enables an appraisal of the present-day stress field at shallow depths within the center of the island of Hawai'i for the first time.

Drilling Activity on Island of Hawai'i
By the end of the twentieth century, several deep (1 km) borehole studies on the subsurface geology of the island of Hawai'i had been completed (Tilling et al., 2014). Between 1989 and 1991, three scientific boreholes (SOH 1, SOH 2, and SOH 4) were drilled into Kīlauea's Lower East Rift Zone (LERZ) reaching depths between 1,700 and 2,000 m. In 1993 a 1,056 m borehole and from 1999 to 2007 a 3,520 m borehole were  Peterson and Moore (1987), Fornari (1987), and Moore and Chadwick (1995); (b) and (c) modified from Holcomb et al. (2000); (d) modified from Morgan et al. (2010). Legend: Active and buried rift zones in thick solid and dashed gray lines, respectively; the volcano boundaries in dashed black lines; exposed caldera in solid black triangle, inferred buried caldera in black and white triangle; black lines are the observed faults; location of PTA2 borehole in black star. SWRZ: Mauna Loa's southwest rift zone; NWRZ: Mauna Loa's northwest rift zone; ERZ: Kīlauea's east rift zone; FZ: fault zone; the bathymetry is from Eakins et al. (2003). drilled as part of the Hawai'i Scientific Drilling Project (HSDP; see hawaii.icdp-online.org) partially funded by National Science Foundation of USA (NSF) and the International Continental Scientific Drilling Program (ICDP) with the main objective to characterize the chemistry of lavas generated by the mantle plume during Mauna Kea's evolution and to get information about the state of the stress field present within the volcanic shield. The borehole breakout analysis, performed in the deeper HSDP hole, allowed to determine a north-south and east-west orientation of maximum and minimum horizontal principal stresses (S H and S h ), respectively (Morin & Wilkens, 2005).
More recently, the PTA2 borehole was drilled in Pōhakuloa Training Area (PTA) on the southwestern flank of the Mauna Kea volcano in 2013 within the Humu'ula saddle region, between the Mauna Kea and Mauna Loa volcanoes (see Figure 1c). PTA2 was drilled as part of the Humu'ula Groundwater Research Project (HGRP) with the primary objective of testing for groundwater resources potential. The PTA2 borehole provided a 1,794 m deep fully cored section through the volcanic sequence ( Figure 3) revealing spectacular detail of the subaerial lava-dominated volcanic facies (Jerram et al., 2019). The PTA2 borehole sampled the shield stage strata (from approximately 300 m to the bottom) and the post-shield sequence, including Hamakua and Laupāhoehoe lavas (0 to approximately 300 m; Figure 3a). The stratigraphic section is dominated by basaltic lava deposits (including 'a'ā, transitional, and pāhoehoe facies; HGRP website; Jerram et al., 2019) with subsidiary occurrences of ash, breccia, and volcanoclastic layers, as well as thick cinder deposites and some identified intrusive layers ( Figure 3b).
A suite of downhole logging measurements in the PTA2 hole was performed in June 2016 by the Operational Support Group at GFZ German Research Centre for Geoscience (Jerram et al., 2019) and included total natural gamma ray, spectral gamma ray, magnetic susceptibility, sonic velocity, dipmeter with four-arm caliper, and the ABI43 acoustic borehole imager ( Figure 3c). The downhole geophysical measurements provide a unique opportunity to measure and determine the in situ geophysical and structural properties of the Mauna Kea volcanic rocks. Downhole logging has investigated the open hole section between 886 and 1,567 m. Total natural gamma radiation was also measured in the cased upper hole section from 0 to 886 m. The lowermost section between 1,567 and 1,764 m was not accessible for wireline tools. All logs (except the acoustic image log) were depth synchronized by gamma ray correlation. The acoustic images were depth corrected by matching the caliper and the magnetic field intensity of the acoustic imager with those of the dipmeter tool (which beforehand was GR depth-matched).

Method: Acoustic Borehole Imaging
The measuring principle of an acoustic borehole imager (ABI) (Zemanek et al., 1969) consists of a piezo-electric acoustic transducer which emits an ultrasonic pulse (1.2 MHz) to the borehole wall where the pulse is being reflected and received by the same transducer. A rotating acoustic mirror in the beam path directs the pulse sequentially along the circumference covering the entire 360°of the borehole wall. The spatial orientations of tool and borehole are determined by built-in triaxial accelerometers and magnetometers. The acoustic borehole imager tool delivers two types of information: a Acoustic two-way travel time (TT) is the time between transmission of the sonic pulse and reception of the reflected pulse at the transducer. The TT image yields information on the borehole shape (acoustic caliper). b Acoustic amplitude (AMPL) delivers information on the acoustic reflectivity of the borehole wall resulting from the acoustic impedance contrast between borehole fluid and wall. The AMPL image depends on the roughness and shape of the borehole wall and its acoustic properties.
These TT and AMPL acoustic images are visualized in 360°images of the borehole wall versus depth and are presented in colors that code their value range. In the TT image, the bright colors indicate short time period (fast) for the impulse to go from the transducer and back to the receiver; the dark colors represent long time period (slow), which means widened size of the borehole. In the AMPL image, bright colors (high amplitude) indicate a strong signal (good reflection and strong contrast), and dark colors (low amplitude) indicate weak to missing signals (scattered or absorbed impulse). In both acoustic images, therefore, features such as open fractures, voids, washouts, and breakouts are in dark colors (low amplitude and slow travel time). In this study, the ABI43 tool has been used (Table S2), and all recorded acoustic images have been oriented with respect to the magnetic north, filtered and edited for noise from the data records by interpolating the bad signals, scaled and calibrated for the borehole size (96 mm), and finally corrected where the tool was decentralized. These processing steps were necessary to avoid distortion, misinterpretation, and incorrect geometry (e.g., strike, dip, and width) of the features. The processing allows us to enhance data quality in order to recognize very small features that would otherwise have been overlooked. Image logs are a powerful tool to identify geological features such as thin beds, volcanic facies, sedimentary sequences, slumps, conglomerates, bedding planes, foliations, tectonic features, such as fractures and faults, and drilling-induced features as borehole breakouts and drilling-induced fractures. Here, we focus only on borehole breakout features identified and processed with the logging data software WellCAD5.1 ALT company (www.alt.lu).

Borehole Breakouts
When drilling a borehole into the Earth's crust, which is under a nonuniform in situ stress condition, rock failure can occur around the borehole where the stress exceeds the rock strength (Haimson & Herrick, 1985;Zang & Stephansson, 2010;Zoback et al., 1985). The zones of broken and spalled-off rock material in the wellbore walls generate bidirectional stress-induced borehole enlargements widely known as borehole breakouts (e.g., Babcock, 1978;Bell & Gough, 1979;Plumb & Hickman, 1985). The stress concentration around a vertical borehole, drilled parallel to the vertical principal stress (S v ), is described by the Kirsch equations (Kirsch, 1898). The maximum compressive stress on the borehole circumference occurs parallel to the minimum horizontal principal stress axis (S h ); the maximum tangential tensile stress occurs parallel to the maximum horizontal principal stress axis (S H ) ( Figure 4a). Therefore, the borehole breakouts develop parallel to the S h , because maximum compressive stress concentration is built up at the borehole wall in this direction (Figure 4a; Bell & Gough, 1979;Plumb & Hickman, 1985;Zoback et al., 1985).
Borehole breakout enlargements form due to compressive shear failure of the borehole wall, which generates shear yield, destroying cohesion and weakening the rock (Bell & Gough, 1979). Intersecting conjugate shear planes develop, ultimately causing pieces of the borehole wall to spall off ( Figure 4; Bell & Gough, 1979). The determination of borehole breakouts, together with other features (such as natural and drilling-induced fractures), and their spatial distribution, frequency, and orientation are fundamental for reconstructing the present-day stress field. In acoustic image logs in subvertical wells (%3C10°deviation), borehole breakouts appear with low AMPLs and slow TTs and hence show as pair of dark stripes on opposing sides of the wellbore wall ( Figure 4a). Borehole breakouts bridge the gap between near-surface stress indicators from geological data and deep stress indicators from earthquake focal mechanisms at greater depth (Zoback et al., 1989). The present-day stress field orientation by borehole breakouts forms an essential part of the World Stress Map Project (WSM; Heidbach et al., 2018;Zoback, 1992). The borehole breakouts contribute approximately 20% of the WSM database, and their contribution is growing (Heidbach et al., 2016;Tingay et al., 2006).

Quality Data Control: Artifacts in the Image Log
High-resolution image logs also display some features related to drilling operations such as vertical drag lines, drill bit marks, stick and pull zones, and horizontal striping (e.g., García-Carballido et al., 2010;Lofts & Bourke, 1999). These features can alter the image quality (signal to noise ratio) and lead to misinterpretations. The PTA2 acoustic images contain drilling-induced artifacts. These artifacts arise from mechanical wear during drilling, tripping, and back-reaming activities. These superficial marks are visible especially in the upper part of the wellbore due to the frequent round trips (Figure 5a). Subvertical scratches appearing also in the image log are interpreted as drilling-caused marks induced by moving of the drill string ( Figure 5b).
The image log is affected in some zones by measurement artifacts such as horizontal striping due to momentary interruptions of data acquisition reducing the quality of the image, especially in the uppermost and lowermost sections of the image log ( Figure 5c). The first class of artifacts of the PTA2 image log, which are most common, is the so-called "stick and pull zones" (Lofts & Bourke, 1999). The presence of stick and pull zones reduces the image quality of the log and arise from drag effects acting on upward tool travel.
Even if stress-induced structures would be present, they would be concealed and blurred making them extremely difficult to identify, classify, and measure. The tool sticking is also easily identified from the acceleration curve where the frequency and the amplitude significantly change (gray curve in Figure 5d). The second group includes the borehole wall artifacts, which are caused by irregularities in the wellbore such as roughness, mud cake, spiral hole, and washout ( Figure 5e).

Borehole Breakout Orientation
The ABI interval was logged from 886 to 1,567 m (Figure 3c), and a total of 371 borehole breakouts was identified in the acoustic images ( Figure 6). The breakouts occur in 310 m of the 681 m long logged section (Figures 7a and 7b) representing 45% of the entire section ( Figure 8a). The analysis exhibits a constant azimuth of S h mean = 105.9°(st.dev. = 13°) along the entire logged interval crossing all lithological units with no change in orientation (Figure 7 and Tables S3 and S4).
The borehole breakouts have been divided into two groups. Borehole breakouts with high confidence and well-defined extent are assigned a good quality (Q = 1) and defined as major breakouts. Borehole breakouts with lower confidence have been ranked as poor quality (Q = 2) and called minor breakouts. The Q2 group includes breakouts with small size in width, length, and depth and also includes poorly developed examples termed "incipient-breakouts." The distribution of these two groups has been analyzed for cumulative lengths and number versus the borehole lithology ( Figure 8). One hundred and forty-seven Q1 borehole breakouts (brown dots in Figure 7d) with a cumulative length of 123.15 m were recognized representing approximately 18% of the entire logged interval (Figure 8a). Most of Q1 breakouts are focused in pāhoehoe and 'a'ā lavas and in the intrusion intervals ( Figure 8). Two hundred and twenty-four Q2 borehole breakouts (blue dots in Figure 7d) have been distinguished with a cumulative length of 187 m (Figure 7d). The Q2 breakouts represent about 27.5% of the entire logged interval (Figure 8a), and they are developed dominantly within pāhoehoe lava facies (Figure 8b).

Borehole Breakout Geometry
The analysis of the horizontal cross-sectional shape of the borehole breakout shows different geometries of wellbore failures. The borehole breakout shapes were categorized in four groups based on their degree of symmetry (symmetric implies breakouts are 180°apart), width, and depth of the breakouts (Figure 9a
The analysis of the acoustic image of PTA2 wellbore reveals that the breakouts geometry (orientation, width, and depth) can occasionally take different shapes (Figure 9b). Most of the borehole breakouts show a symmetrical shape, and they have very good development in depth and width (Figure 9b (v)). The asymmetric breakout shapes are shown in Figure 9b (vi-viii). Some breakouts display slightly different orientation of one side of the breakout shifted by α (orientation of S h1 ≠ orientation of S h2 ) in combination with different borehole breakouts widths (θ 2 %3E%3E θ 1 ; Figure 9b (vi)); other zones exhibit dissimilar breakout shape in width (θ 2 %3E θ 1 ) and depth of elongation (d 1 ≠ d 2 ) as in Figure 9b (vii) and, finally, only an initial borehole breakout formation on one side of the borehole (Figure 9b (viii)).
In addition, in Figure 9b, we compare the breakouts identified in the AMPL image with the acoustic caliper (Cal min , Cal max ) calculated from the TT and the two calipers measured by the four-arm caliper tool Cal C 1 and Cal C 2 . The latter is useful for the identification of breakout when the diameter difference exceeds the bit size by more than 10% (Plumb & Hickman, 1985;Reinecker et al., 2016). The four-arm caliper tool cannot detect enlargements when the radial extension of the breakout is poorly developed into the formation (Figure 9b (vi)) and when the enlargements are only in incipient stage (Figure 9b (viii)). In both figures, the calipers Cal C 1 and Cal C 2 show the same size of the borehole diameter (bit size). Therefore, the number of borehole breakouts would be significantly lower than that detected by the acoustic borehole imager tool. Small rotations observed along the wellbore likely are related to the local variation in stress due to different rheology of the rocks linked to the rock strength.
The acoustic image analysis has also shown different stages of borehole breakout evolution. The first stage in the breakout formation starts by initiation of subvertical thin fractures (Figure 10a) because the already failed rock material has not yet spalled off from the borehole wall. Such features, called incipient-breakout, could be misinterpreted as drilling induced fractures; therefore, special attention was taken to identify them. The azimuth of these incipient borehole breakouts is consistent with the azimuth of the well-developed

Journal of Geophysical Research: Solid Earth
borehole breakouts (Barton & Moos, 2010;Trice, 1999). The cross sections (Figures 10a-10c) are still almost circular although in the travel time and amplitude image logs, the incipient breakouts are present (Figures 9a and 9b). Over time, more fractures will form, propagate, and merge causing chips of rock to spall off and develop into borehole breakouts, eventually also showing the typical borehole breakout cross section (Figures 10e and 10f).

Borehole Breakout Volcanic Facies Dependence
Borehole breakout shapes are related to rock type and are affected by range of different shapes (Figures 9 and  10). Within intervals of uniform facies, more mature borehole breakout development is often observed (i) symmetrical shape with a symmetrical pair of similar deep (d 1 = d 2 ) extended and shaped "breakout-ears" on opposite sites (orientation S h1 = orientation S h2 ); (ii) the breakout-ear on one side is not parallel with the opposite side's borehole breakout-ear direction but shifted by an angle α (orientation S h1 ≠ orientation S h2 ); (iii) asymmetric shape of the two borehole breakout-ear with different breakout widths (θ 1 %3E θ 2 ) and/or with different extension depth (d 1 ≠ d 2 ); (iv) well-developed breakout on one side and absent and/or only initially staged borehole breakout on the opposite side (θ 1 %3E%3E θ 2 and/or d 1 %3E%3E d 2 ). Combination of these four different features can also take place. Gray area shows the breakouts (zones of rock failure and spall off); the dashed line is the bit size of the borehole. (b) The above mentioned examples of breakout shapes in horizontal cross sections have been identified in the acoustic image logs of the PTA2 borehole. Cal min and Cal max = acoustic borehole calipers from TT image log (blue and red, respectively), Cal C 1 and Cal C 2 = mechanical calipers from four-arm caliper tool (green and purple, respectively); (v) good example of breakout development; (vi) different orientation and width (θ 2 %3E%3E θ 1 ); (vii) different width (θ 2 %3E θ 1 ) and depth of elongation (d 1 ≠ d 2 ); (viii) unequal initial borehole breakout formation, where the western side is more developed than the other in both the amplitude image and cross section.

Journal of Geophysical Research: Solid Earth
within the strongest intra-facies such as lava flow interiors ( Figure 11). Within intervals having uniform facies, more mature development (e.g., more prominent enlargement in radial depth, greater width, or length of the enlargement) of the borehole breakouts appear to correspond to intra-facies intervals with greater strength (freshest and higher Vp) and density (lower porosity) such as the interiors of lava flow facies and intrusions (Figure 11). In the representative pāhoehoe facies example, the breakout shape evolves from an incipient stage (Figure 11a; 1,220.0-1,221.9 m (i), 1,224.0-1,225.7 m (iv), and 1,227.4-1,128.5 m (vii)) to a juvenile step (Figure 11a; 1,221.9-1,223.0 m (ii) and 1,225.7-1,226.5 m (v)) until it reaches the mature stage (Figure 11a; 1,223.0-1,224.0 m (iii) and 1,226.5-1,227.4 m (vi)). The three stages of breakouts reflect the different physical properties of the pāhoehoe lava. Less evolved breakouts appear only in zones where the pāhoehoe lava has a vesicular texture, as shown in the amplitude image and confirmed from core (low amplitude values; Figure 11a (i), (iv), and (vii)). In contrast, mature breakout stages are present in layers with high amplitude values in the image log indicating that it corresponds with the dense inner part of the lava flow (Figure 11a (iii) and (vi)).
Similar development stages are identified in 'a'ā and sheet intrusion facies. In the 'a'ā lavas, breakouts are best developed in intervals with high contrast in the amplitude (Figure 11b). In contrast, the enlargements are not present or very poorly developed in the 'a'ā intra-facies with less contrast in the amplitude image ( Figure 11b). Enlargements linked with the sheet intrusions which are characterized by extremely high impedance values and are prominent and very well shaped, (e.g., Figure 11c).

Interpretation and Discussion
The present-day stress field inside the island of Hawai'i likely results from the interference between several contributors happening at different depths: plate tectonic forces, lithospheric flexure, topographic loading, density contrasts, magma emplacement, and edifice deformation and failure (e.g., Fiske & Jackson, 1972;Le Corvec & McGovern, 2018;McGuire & Pullen,1989;Pritchard et al., 2007). Most commonly, only surface stresses constrained by neotectonics indicators and deep stresses constrained by focal mechanisms are investigated (NEIC, Wolfe et al., 2004).
The main orientation of the present-day stress field recorded on the island of Hawai'i shows high variability. The orientation of the P-axis azimuths indicates a complex system dominated by normal, strike-slip, and reverse faulting. This system is associated with the influence of both magmatic and tectonic activities (e.g., Klein, 2016;Lin & Okubo, 2016 and reference therein) and with flexure and subsidence under Mauna Kea and Mauna Loa volcano load (e.g., Klein & Koyanagi, 1989;Moore, 1970;Pritchard et al., 2007;Walcott, 1976;Wolfe et al., 2004). Within the central part of the island of Hawai'i, however, determining the present-day stress state is more challenging, because geological and tectonic surface structures are poorly visible and seismicity is dominantly located at depths greater than 15 km around Mauna Kea (Figure 1c, Wolfe et al., 2004).
Borehole breakouts within PTA2 therefore represent a unique opportunity for constraining the present-day stress states in the central part of the island of Hawai'i (Millett et al., 2018;Morin & Wilkens, 2005). The borehole breakouts observed in the acoustic image log indicate an orientation of the minimum (S h ) and maximum (S H ) horizontal principal stresses of N106°and N16°, respectively. These orientations remain consistent throughout the 681 m of open hole, showing that the measured stress orientation is robust and acts throughout a significant section of the upper crust in this area. In the broad scale, this orientation is rotated 100°from that of the Pacific Plate (Torsvik et al., 2017). However, it is known that active stress orientations measured in other parts on the island of Hawai'i also differ locally, as documented by the active rift zones (Figures 2 and 12a). For instance, (1) S h is nearly oriented N-S in the eastern rift zone of Kīlauea (e.g., Wolfe et al., 2004), whereas (2) S h is oriented NNW-SSE and WNW-ESE on the northeastern and southern rift zones, respectively, of Mauna Loa volcano as documented mainly by focal mechanism solutions and orientations of the dike emplacement (Klein, 2016;Walter & Amelung, 2006, and reference therein;Wolfe et al., 2004). Such complex stress orientation pattern strongly suggests that the stress orientation measured from borehole breakouts within PTA2 results dominantly from local effects.
A key observation is that the orientation of the maximum horizontal principal stress S H measured within PTA2, which is located on the SW flank of Mauna Kea volcano, is parallel to an axis linking the summits 10.1029/2020JB019768

Journal of Geophysical Research: Solid Earth
of Mauna Loa and Mauna Kea (Figure 12b). Both volcanoes exhibit substantial topography (4,207 m for Mauna Kea and 4,169 m for Mauna Loa). It is well known that topography and its compensation at depth can produce significant stress perturbations away from simple burial and tectonic stresses (Artyushkov, 1973;Hergert et al., 2015;Liu & Zoback, 1992;McGuire & Pullen, 1989). The local gravitational stresses associated with a high conical edifice can produce radial S H stress trajectories, which can overprint the regional stress regime (e.g., Acocella & Neri, 2009;Chadwick & Dieterich, 1995;Delcamp et al., 2008;Dieterich, 1988;Kervyn et al., 2009;McGuire & Pullen, 1989). The stress orientation measured within the PTA2 borehole is consistent with the interference between the gravitational stress fields induced by the two large volcanic loads, which essentially restrict or buttress each other, leading to a focusing of compressional stresses in the saddle region. Similar scenarios have been modeled for irregular topographic loading in nonvolcanic settings (Pan et al., 1995). How these stress states evolve with greater burial and at what point they become aligned to the more regional stress field remains a subject for future modeling.
What is clear here is that the stress state in areas comprising multiple major volcanic edifices in close proximity to each other will have a significant influence on the shallow stress state, which may influence edifice stability and shallow magma emplacement (e.g., Galland et al., 2018;Kervyn et al., 2009;Le Corvec & McGovern, 2018).
The stress orientation measured within the PTA2 borehole is very similar to that measured within the HSDP deep hole, which comprised the first determination of the present-day stress field orientation on the island of Hawai'i by breakout analysis in the late '90s (Morin & Wilkens, 2005). In this borehole, located far east of Mauna Kea volcano and north of Kīlauea Volcano, Morin and Wilkens (2005) revealed that the S h and S H are also orientated east-west and north-south, respectively. We argue that such orientation similarity between the stress fields estimated in PTA2 and HSDP is not related to a regional trend but instead relate to separate mechanisms. Morin and Wilkens (2005) interpreted the orientation of the stress field in the HSDP borehole as a consequence of the combination of increased north-south stresses due to the emergence of the Kīlauea Volcano and reduced east-west stresses due to gravitational instabilities in the onshore and offshore slopes of Mauna Kea volcano. Thus, even if stress orientations measured in PTA2 and HSDP are very similar, they likely result from very distinct origins.
It is well known that local stresses due to topographic loads have first-order effects on magma propagation through the crust (Galland et al., 2018;Hyndman & Alt, 1987;Kervyn et al., 2009;Muller et al., 2001, and references therein). Based on the observed present-day stress state at the PTA2 borehole, shallow dike emplacement would be expected to be dominantly parallel to an axis between Mauna Loa and Mauna Kea. However, an important condition is that Mauna Kea and Mauna Loa volcanoes did not build up at the same time. The topographic load associated with Mauna Loa has become progressively stronger as the edifice built up. Therefore, the stress states in the central part of the island of Hawai'i must have significantly evolved through time: A first state of stress due to the gravitational load of older Mauna Kea has likely been progressively affected/rotated by the growth of the younger Mauna Loa volcano. Thus, the timing of volcanic edifice buildup is crucial for interpreting the structure of paleo-rift systems and dyke swarms and vice versa. For instance, previous studies have identified a region of positive gravimetric anomaly (Flanigan & Long, 1987;Flinders et al., 2013) between Mauna Kea and Mauna Loa volcanoes, interpreted as an east-west dike swarm, that is, an orientation parallel to, and incompatible with, the present minimum orientation S h measured in PTA2. A hypothesis is that this dike system was emplaced in a state of stress that was not affected by the gravitational stress induced by the Mauna Loa edifice, that is, prior to buildup of Mauna Loa volcano.
Although the borehole breakout orientation is constant in the borehole, the shape and size of the enlargements change within PTA2. A correlation exists between the shape and size of the borehole breakouts with volcanic facies. Within the same lithology, a variation in breakout development has been observed and correlated to contrasts in both the amplitude image and volcanic intra-facies ( Figure 11). Pāhoehoe and 'a'ā lava flows contain a clear inner layering linked to intra-facies development of individual flow units (Self et al., 1998). In general terms, pāhoehoe lava flows commonly comprise an upper vesicular zone (UVZ) or upper crust, a dense poorly vesicular interior, and a lower vesicular zone (LVZ) or lower flow crust at the base (Katz & Cashman, 2003) although variations such as spongey pāhoehoe occur (Walker, 1989;Wilmoth & Walker, 1993). 'a'ā lava flows show instead auto-brecciated upper and lower crusts separated by a dense poorly vesicular interior which may display strained and irregular vesicles alongside vesicle bands (Katz & Cashman, 2003). These different intra-facies can be clearly recognized in the acoustic amplitude images.

Journal of Geophysical Research: Solid Earth
Low contrast in the amplitude image has been interpreted as layers with vesicles or breccia and can be calibrated by core observations. High amplitude values reflect a lower presence of vesicles/breccia (lower porosity) and also lower percentages of clays, a common feature linked to alteration at lava flow margins. Intrusions often show high amplitude values associated with well-developed breakouts (Figure 11c).
The intra-facies variations are confirmed by cross-checking the acoustic image intervals with the core, and the relative strength is inferred based on numerous literature studies which confirm that strength of volcanic rocks decreases both with increasing porosity (Al-Harthi et al., 1999;Heap et al., 2014) and alteration (Planke et al., 1999;Schiffman et al., 2006). These results give clear evidence for the anisotropic accumulation of stress within the PTA2 borehole. Stronger, more coherent and less compressible facies and intra-facies are capable of storing higher stresses in a precritical stress state than the weaker facies and intra-facies. This observation is consistent with the observations of Schiffman et al. (2006) from the HSDP borehole where predicted UCS for different facies was linked to slope stability of the island of Hawai'i. Our observations further demonstrate that the highly anisotropic nature of strength within layered lava flow dominated sequences may promote differential slip when exposed to applied topographic loads or variable remote stresses. Therefore, the tendency for slip along flow boundaries and associated edifice stability may be significantly influenced by the stacking pattern of evolving lava fields, the geometry of subsurface intrusions, and the orientation of both relative to evolving applied stresses such as topographic loading through time. This study therefore provides the basis for a quantitative investigation into the stress magnitudes and anisotropy of the island of Hawai'i utilizing petrophysical testing of the PTA2 core.

Conclusions
The contemporary stress field of the southwestern flank on Mauna Kea volcano has been determined from borehole breakout analysis of the PTA2 borehole drilled in the saddle region of the island of Hawai'i. The location of the PTA2 borehole enables unique insights into the stress field in an area where only limited other stress indicators, such as faulting and focal mechanisms, are available. Our study reveals how the shallow subsurface stress state within composite volcanic islands evolves during edifice growth with implications for the improved understanding of slope stability, magma ascent, and earthquake monitoring on the island of Hawai'i and in similar settings.
Based on this analysis of the PTA2 breakout data, we conclude the following: 1. This study provides the first documentation of the subsurface in situ stress state between the major island forming shield volcanoes of Mauna Loa and Mauna Kea. 2. The borehole breakout analysis shows a clear and consistent orientation along the PTA2 borehole with a mean orientation of N106°with very low standard deviation for a total length of 310 m within seven main zones of breakouts. This corresponds to a maximum horizontal stress (S H ) orientation of N16°. 3. The orientation of the present-day stress field at Mauna Kea volcano deviates significantly from that of the plate forces and regional tectonic stress field which give a dominant NW-SE orientation of S H . The orientation of the local stress field within the saddle region is dominantly controlled by the competing gravitational effects of the two large topographic masses of Mauna Loa and Mauna Kea volcanoes. 4. Our study suggests that the incremental growth of the younger Mauna Loa imparted an equivalently incremental stress addition to the southern flank of Mauna Kea. Given the important role of in situ stresses on magma propagation, this temporal change likely influenced the transport of magma in the area between the shield volcanos through time. 5. The variability of breakout shape and extent is associated with the different strengths of volcanic facies and intra-facies. Strong lava flow interiors and intrusions are capable of focusing greater stress accumulations than weaker lava flow margins. These findings have important implications for how applied stress is stored and dissipated in volcanic edifices and may have important implications for slope stability through time.