The structural complexity of volcanic islands and their difficult accessibility make geophysical imaging problematic. Moreover, geophysical modeling generally suffers from nonuniqueness in its solutions. This study uses two geophysical techniques to overcome these problems and reduce modeling errors. Despite the accessibility limitations, geophysical modeling techniques of potential data have been used extensively in different geologic settings to provide reliable results on structures and geometries (Green, 1975; Guillen and Menichetti, 1984; Camacho et al., 1997; Li and Oldenburg, 1998; Camacho et al., 2000; Boulanger and Chouteau, 2001; Montesinos et al., 2006; Cella wt al., 2007; Camacho et al., 2011; Marcotte et al., 2014; Barnoud et al., 2016). Figure 1 shows the location and topography of the Hawaiian Island arch system.

Geophysical and structural measurements are used extensively to delineate the three-dimensional (3-D) shape of granitoid plutons (Miller and Tauch, 1989; Vigneresse, 1995a, b; Eguíluz et al., 1999) in different areas. Most previous studies include horizontal map views of intrusions in their results. However, scientific studies assume the widespread concept of the inverted teardrop when considering pluton 3-D geometries (Vigneresse, 1995b) based on structural extrapolations to depth. Most field-based studies use extrapolations to depth without direct evidence to obtain a reasonable approximation when geophysical techniques are employed.

Aeromagnetic datasets are widely used to estimate the Curie point depth (CPD) and assess geothermal resources (Chiozzi et al., 2005; Trifonova et al., 2009; Hsieh et al., 2014). The CPD is considered at the surface at a high temperature of ∼540°C, as measured in situ from holes drilled through the crust and into the still-molten lens of tholeiitic basalt in Kilauea (Zablocki and Tilling, 1976). The CPD surface indicates the bottom of the magnetic layer; this is where paramagnetic minerals are formed from ferromagnetic minerals when they reach the Curie point temperature (Nagata, 1961) or the depth at which nonmagnetic rocks are formed from magnetic rocks (Ravat et al., 2007). Iron sulfides and iron–titanium oxide are the most common ferromagnetic minerals (Rajaram, 2007).

Castro and Brown (1987) have used high-resolution sampling of the 1950 and 1972 flows in Kilauea to identify the intraflow variations of very young basalt flows. The paleomagnetic directions of these samples are different from the direction of Hawaii’s geomagnetic field. This shallow inclination anomaly was attributed to the recording mechanism of subaerial basalts (Castro and Brown, 1987); however, it has since been identified as the nondipole field effect (Cox, 1975). Another paleomagnetic study has identified the lavas in the main part of the Pohue Bay flow and those of the Hawaiian cones to have similar paleomagnetic properties with relatively similar ages (Jurado-Chichay et al., 1993). That study could have identified both younger lava flows, which later utilized the main tube, and an earlier subset of cones, which were formed before the Pohue Bay eruption.

Magnetic data have been analyzed extensively to estimate both the depth to the magnetic basement (Spector and Grant, 1970; Hahn et al., 1976; Garcia-Abdeslem and Ness, 1994) and the Curie isotherm (Blakely, 1988; Okubo and Matsunaga, 1994). According to Spector and Grant (1970), the depth factor controls the shape of the readily averaged power spectrum. Their statement has resulted in a wide interpretation of the average two-dimensional (2-D) power spectrum of magnetic data. Moreover, the depth to the source can be calculated from the slope of the log radially averaged power spectrum.

The thermal structure of the crust in different geologic environments has been widely investigated using magnetic data (Spector and Grant, 1970; Bhattacharyya B. K. and Leu L.-K., 1975, 1977; Byerly and Stolt, 1977; Okubo et al., 1985; Blakely, 1995; Tanaka et al., 1999; Chiozzi et al., 2005; Ross et al., 2006; Trifonova et al., 2009; Gabriel et al., 2011, 2012; Bansal et al., 2013, 2016; Hsieh et al., 2014; Nwankwo and Shehu, 2015; Nwankwo and Abayomi, 2017); the resulting geomagnetic anomalies above the CPD have been used to delineate magnetic structures (Bhattacharyya and Leu, 1975a, b; Byerly and Stolt, 1977; Blakely and Hassanzadeh, 1981; Blakely, 1988; Chiozzi et al., 2005; Trifonova et al., 2009; Hsieh et al., 2014; Idárraga-García and Vargas, 2018; Mohamed Al Deep, 2021).

Flinders et al. (2013) used land and marine gravity data and a 3-D gravity model to calculate the average densities, volumes, and percentages of olivine in the intrusive materials and cumulate cores below the volcanoes in Hawaii. They used an isosurface density of 2.85 g cm⁻³ to delineate intrusive material, which equated to over 60% of dikes with a density of 2.95 g cm⁻³. Furthermore, they defined cumulate cores using an isosurface density of 3.00 g cm⁻³, which corresponded to ∼35% olivine (density: 3.2–3.3 g cm⁻³) in the intrusive complex (density: 2.85 g cm⁻³).

The Hawaiian Islands were formed during the past 70 Ma as the Pacific lithospheric plate moved north and then west relative to a melting anomaly. This phenomenon is represented by the hotspot hypothesis, which accounts for the formation of a volcanic chain on the ocean floor. Wilson (1963a, c) proposed that the islands of Hawaii were formed when the seafloor moved over lava sources in the asthenosphere; they limited this theory to the volcanoes and the ridge of the Hawaiian Islands. Subsequently, Wilson’s theory was expanded by Christofferson (1968) to include the Emperor Seamounts. Morgan (1972a, b) suggested that the Hawaiian hotspot and others are thermal plumes of material rising from the deep mantle. Clague and Dalrymple (1987) tested and validated this hypothesis based on a study of the geologic evolution of the Hawaiian–Emperor volcanic chain. In terms of geology, tholeiitic basalts account for >95% of the islands’ rocks (Clague and Darlrymple, 1989).

Geophysical data collected from the ground and from the airborne were commonly employed in groundwater investigations and subsurface geology (e.g., Meneisy and Al Deep, 2020; Mohamed and Abu El Ella, 2021; Al Deep et al., 2021). On the other hand, Global data from the Earth Gravitational Model and the Earth Magnetic Anomaly Grid have been widely used for crustal studies and the depth to the bottom of the magnetic layer (e.g., Idárraga-García and Vargas, 2018; Mohamed and Al Deep, 2021), whereas gravity data from the Gravity Recovery and Climate Experiment mission have been successfully applied for estimating mass transport and distribution in the Earth’s fluid (e.g., Mohamed et al., 2017; Mohamed, 2019; Mohamed, 2020a; Mohamed, 2020b; Mohamed, 2020c; Taha et al., 2021; Mohamed and Gonçalvès, 2021; Mohamed et al., 2021; Mohamed et al., 2022).

The current study aims to characterize the morphology of the magmatic chamber beneath Hawaii Island using gravity and magnetic potential fields. Delineating the geometrical border of the magmatic chamber beneath the island of Hawaii and estimating the CPD, geothermal gradient, and heat flow of the area require the techniques of gravity inversion and spectral analysis of magnetic data. Our method of estimating the CPD to determine the maximum depth to the magnetized rocks calculates the depth to the upper surface of the magma chamber indirectly. Additionally, a two-layer 2-D geological model using the contrast in density between the average density of the solidified rocks and the magma layer is applied using gravity modeling techniques.

Hawaii Island comprises five major shield volcanoes (Figure 2): Mauna Kea (MK), Kohala (Ko), Kilauea (Ki), Mauna Loa (ML), and Hualalai (Hu) (Langenheim and Clague, 1987). Except for some minimal erosion to the northern sides of Ko and MK, these volcanoes have suffered little erosion (Langenheim and Clague, 1987). They progress in age from the southeast end (with its still-active volcanoes) to the northwest end (with its volcanoes dating from 75 to 80 Ma) (Clague and Dalrymple, 1987).

The ML volcano is the largest on Earth at 97-km long, 48-km wide, and an estimated volume of 70–80 million km³ (Robinson and Eakins, 2006). Its shield-shaped dome rises to 4,167 m above sea level (Figures 1, 2), and its slopes are dotted with a few cinder cones. The caldera of Mokuaweoweo is located on the summit (Macdonald, 1977). ML formed over a period of ∼0.5 million year. During recent years, lava younger than 1,000 year has poured from fissures and a cone on the volcano’s floor and rim, filling depressions and covering about 40% of its surface area (Lockwood and Lipman, 1987). A few weak explosions have occurred. The surface of ML originates mostly from the Holocene (Stearns and Macdonald, 1946; Lipman and Swenson, 1984). Stearns and Macdonald (1946) divided the volcano’s rocks into Pliocene Ninole basalt, Pleistocene Kahuku basalt, and Pleistocene and Holocene Kau basalt (the most recent).

At 4,205 m above sea level, MK is Hawaii’s highest volcano (Figures 1, 2). There have been no eruptions over the past 3,600 years (Porter, 1979a). The configurations of cinder cones indicate the location of less-defined southerly, easterly, and westerly rifts. The volcano’s rocks were divided into two volcanic series by Stearns and Macdonald (1946). The older (Hamakua) series forms a major part of the mountain and represents the shield stage and part of the post-shield stage. The upper part of the mountain (above 3,353 m) comprises a plateau resulting from the Laupahoehoe series filling of a caldera in the Hamakua volcanic series, which represents the rest of the post-shield stage. Porter (1979a, 1979b) redefined the volcano’s two rocks to include glacial deposits; additionally, they were elevated to a group ranking of volcanic and glacial formations.

The last eruptions of the Hu volcano in 1800–1801 occurred from five separate vents (Moore et al., 1987) (Figures 1, 2). The volcano has an approximate diameter of 27 km and a well-defined NW-striking rift zone; its less-well-defined N- and SE-trending rift zones are characterized by widespread cinders and spatter cones (Langenheim and Clague, 1987). Its subaerial surface is represented by the Pleistocene Waawaa Trachyte Member, with short flows of hawaiite and a few flows of alkali basalt lava (Moore et al., 1987). According to detailed mapping and C-14 dating, the volcano’s Holocene lava flows have been divided into four groups: 10–5, 5–3, 3–1, and <1 ka (Moore et al., 1987).

Based on K–Ar analysis, Ko is the oldest Pleistocene (McDougall and Swanson, 1972) and longest inactive volcano in the islands (Lipman, 1980) (Figures 1, 2). It was formed over northwesterly and southwesterly rifts and a weak southwesterly rift (Langenheim and Clague, 1987). Its last eruption was ∼60,000 years ago, and it is considered to be extinct. The volcano’s rocks represent two volcanic series (Stearns and Macdonald, 1946): the older Pololu series (Pololu basalt) (Langenheim and Clague, 1987) of shield-stage tholeiitic basalt and caldera-filling postshield-stage alkalic basalt (Stearns and Macdonald, 1946) and the younger Hawi series (Hawi Volcanics) (Langenheim and Clague, 1987) of differentiated alkalic lava of the postshield stage (Stearns and Macdonald, 1946).

The Ki volcano has an area of 2,500 km² and rests on the southeast slope of ML (Figures 1, 2). Lava flows from ML pass over the slopes of Ki. The Ki volcano is the youngest in Hawaii and remains very active (Clague and Dalrymple, 1987). Around 70% of its surface is younger than 500 years, and about 90% is younger than 1,100 years (Holcomb, 1987). At the base of a fault escarpment on its mobile south flank, Ki’s older rocks of Hilina basalt are between 100 and 30 kyr old (Easton, 1987). The most recent Puna basalts of the Pleistocene and Holocene (Easton, 1987) represent the younger rocks and are separated from the older ones by Pahala ash.

The land and airborne potential field data used in this study are described below.

The geothermal gradient ( dt/dz ) from the Earth’s surface to the CPD was estimated using Eq. (15) (Tanaka et al., 1999): d t / d z = 540 ° C / Z b (15)

The heat flow ( q ) was calculated using Eq. 16 (Okubo et al., 1985): q = h ( d t / d z ) = h ( 540 ° C / Z b ) (16)

This study used h = 2.5 W/m°C as the value for igneous rocks (Springer, 1999). As can be seen in Table 1, the dt/dz varied from 43.5 to 581.1 °C km⁻¹. Figure 11 presents the estimated heat flow, which ranges between 108.8 and 1,453 mW/m² close to the volcanic eruption zone of ML. As geological constraints strongly influence CPDs (Ross et al., 2006), in the volcanic zones, the CPDs are shallower than 10 km (Obande et al., 2014). According to Table 1 and Figure 11, Hawaii Island has high geothermal potential energy proximal to the volcanic eruption zones with shallower CPDs as well as high geothermal gradient and heat flows. The data in Table 1 show window no. 213 to have the lowest heat flow, while the flow is highest in window no. 141.

Investigating the morphology of the magmatic chamber beneath Hawaii Island as an example of an island arc system enhances the current understanding of plate tectonics theory. However, the growth and movement directions of these magmatic diapirs require a time-lapse investigation. Herein, we utilized the available potential data to better understand the morphology of the magmatic chamber, estimate the CPD, and calculate the heat flow.

This study successfully applied airborne geophysical data to characterize the morphology of the magmatic chamber beneath Hawaii Island and estimate the depths to the deeper sources; these varied from 7.8 km below the flight height to shallower sources estimated to be 1.3 km deep. The Curie point is located from shallow depths (<1 km) at and proximal to the ML volcano to 12 km close to the northeastern part of the MK volcano region below the ground surface.

The results of the gravity data inversion revealed the existence of very steep vertical rising magmatic plumes, reflecting the dense intrusive material of basaltic and ultramafic rocks underlying the volcanoes. The results corresponded well with those calculated using the magnetic method. The depth to the top of the second (magma) layer varied from 500 m to about 10 km. An inverse relation was identified between the heat flow and the CPD, whereby a decrease in heat flow corresponded with an increase in the CPD. The highest value of 1,453 mW/m² occurred at the shallowest CPD (0.93 km) in window no. 141, while the lowest value of 108.8 mW/m² was correlated with the highest CPD (12.4 km) in window no. 213. According to Jessop et al. (1976), these anomalous geothermal conditions are related to heat flows of between 80 and 100 mW/m².

The results of this study are in good agreement with the previous 3-D gravity models used by Kauahikaua et al. (2000), who studied the magmatic structures within basaltic volcanoes and defined the structures related to seismic hazards and landslides on the island of Hawaii. Their results revealed the existence of dense cumulates and intrusions beneath the summits of every volcano.

Information on the magmatic properties of subsurface rocks was provided by Hildenbrand et al. (1993), who applied the spectral depth technique to aeromagnetic data. Two shallow magnetic zones were identified at a depth of 1 km. Additionally, using the spectral inversion of the magnetic data, they defined a deep magnetic horizon at 10.5 km below the flight height. The results of the current study correspond well with those of Hildenbrand et al. (1993), as our interpretation revealed shallow and deep magnetic sources to be located at 1.3 and 8 km below the flight height, respectively. Based on the CPD estimations, the bottom of the magnetized layer varied between 0.93 and 12.4 km in depth, while the gravity inversion technique indicated a depth of 0.5–10 km below the ground surface.

The existence of large magmatic plumes of dense cumulates and intrusions beneath the summits of the MK, ML, and Ki active volcanoes in this study was confirmed by the presence of higher-velocity regions near the active volcanoes containing dense intrusive materials, such as olivine cumulates (Thurber, 1984; Hill and Zucca, 1987; Okubo et al., 1997). However, a 3-D P-wave velocity model run by Park et al. (2007) for the southeastern part of Hawaii Island produced higher crustal seismic velocity values of 7.0–7.4 km/s. These higher values indicate the dominance of dense olivine cumulates mixed with extrusive and intrusive basaltic rocks in the high-velocity regions underlying the summits and rift regions of the active areas of Ki and ML. In the study of Park et al. (2007), the lower-velocity regions south of the Hilina and along the Kao’iki fault zones were attributed to thick accumulations of volcaniclastic sediments.

Using more than one geophysical dataset provides adequate confidence in the calculated results to overcome the problem of nonuniqueness. The calculated upper surface of the magma chamber delineated about five diapirs, three of which (ML, MK, and Ki) were grouped in one large plume of dense basic and ultrabasic materials. Compared with other studies, the integrated approach presented herein provides an in-depth understanding of the geometry of the magmatic chamber using an indirect CPD estimation to calculate the depth to the chamber’s upper surface. Finally, the new gravity model for Hawaii Island, which incorporates advanced software, corresponds well with the results of the magnetic data.

Estimates the depth to the bottom of the magnetized rocks based on calculating the Curie point depth beneath Hawaii Island.

Characterizes the morphology of the magmatic chamber beneath Hawaii Island using the gravity inversion technique.

Estimates the geothermal gradient and heat flow associated with the active volcanoes of Hawaii Island.