Heat flow data and thermal structure in northeastern Japan
Earth, Planets and Space volume 74, Article number: 155 (2022)
New heat flow data corrected for climate change over Northeastern Japan were obtained using the temperature profile of the borehole of the High Sensitivity Seismograph Network (Hi-net). The obtained spatial distribution of heat flow shows low heat flow on the forearc side, high heat flow along the Ou Backbone Range, and low heat flow in the plains on the back-arc side. However, the distribution is not clearly divided into high and low heat flow along the VF front; for example, the low heat flow extends from near the northern Kitakami Mountains on the forearc side to the Ou Backbone Range crossing the VF, while the high heat flow extends to the central Kitakami Mountains and Sendai plain on the forearc side. In addition, a crustal temperature structure model was developed that considers into account the presence of sedimentary layers, the temperature dependence of thermal conductivity, and differences in heat generation due to lithology. There is a good correlation between this temperature structure and the lower limit of the seismogenic layer, which is between 400 and 450 °C. Compared to previous studies, the crustal thermal structure calculation method assumed is a model whose estimated temperature distribution is sensitive to structural differences; however, a more accurate estimation of the temperature structure is possible if detailed structural information is available. On the other hand, it seems necessary to treat fluid behavior in more detail in areas of high heat flow. However, the estimation of crustal temperature structure, especially in regions with thick sedimentary layers, is considered an improvement over the previous study.
Measurements of heat flow and estimates of subsurface temperature structure based on these measurements are essential for determining the depth of the brittle/ductile transition in the crust, which is considered to be the lower limit of the seismogenic layer of the crust (Sibson 1984), understanding trench and slow earthquakes (e.g., Yoshioka et al. 2013), understanding the recent history of plate tectonic activity (Erkan and Blackwell 2008; Tatsumi et al. 2020), and many other essential applications. A dense seismic observation network has been developed in Japan, and the detailed distribution of seismogenic layers has recently been revealed (e.g., Omuralieva et al. 2012; Yano et al. 2017).
On the other hand, heat flow data around the Japanese archipelago were first presented by Uyeda and Horai (1964), and many measurements were made in the terrestrial and oceanic regions (e.g., Yamano 1995). The distribution of available boreholes has constrained land heat flow measurement in Japan, but many data were obtained in non-geothermal areas. However, there are many areas with low data distribution density. Here we attempt to compensate for this spatial distribution by measuring new heat flow in Northeastern Japan. We investigated temperature profiles of 132 borehole wells (100–200 m depth) in the Northeastern Japan of the Hi-net, seismic network, a uniformly distributed seismic network over land in the Japanese archipelago. Thermal conductivity was measured from the deepest rock cores obtained during borehole drilling or estimated from lithology when a measurement was difficult. From the results of processing the data, taking into account the effects of climate change and other factors, a new heat flow map was created to estimate the subsurface temperature structure.
Northeastern Japan arc is one of the typical island arc–trench systems formed by the subduction of cold plates in ancient times. Northeastern Japan is in contact with the Eurasian plate on the eastern side of the Sea of Japan. To the east is the epicenter of the 2011 off the Pacific coast of Tohoku earthquake, which caused a large resonance slip of over 60 m (Ito et al. 2011), and The Pacific Plate subducts westward at the Japan Trench under the Japanese islands. There are many volcanoes and earthquakes in Northeastern Japan, and these active volcanoes, seismogenic zone, and active faults are distributed almost parallel to the Japan Trench, the boundary of the plates. Active volcanoes are mainly distributed along the Ou Backbone Range, and the eastern edge of their distribution area forms the volcanic front. The distribution of volcanoes on the back-arc side extends to the Sea of Japan side in Northeastern Japan.
The opening of the Yamato Basin on the back-arc side occurred from 21 to 15 Ma, and normal faulting developed in the extensional stress field from the present Japan Sea coast to the forearc from 15 to 13.5 Ma, when the volcanic front also moved in the trench direction (Yoshida et al. 2013). After the opening of the Japan Sea ended around 13.5 Ma, a period of neutral stress field continued (Yoshida et al. 2013). At about 4 Ma, the westward movement of the Pacific Plate increased (Pollitz 1986), followed by strong compression of the entire island arc. It is thought that most of the Miocene normal faults were reactivated, and the volcanic arc was uplifted (Yoshida et al. 2013). These imply tectonic inversion (Sato 1994) (see Fig. 1).
Hi-net borehole temperature logging data
After the disastrous 1995 Kobe earthquake, a new national project has drastically improved Japan's seismic observation system. Many strong-motion, high-sensitivity, and broadband seismographs were installed to construct dense and uniform networks covering the whole of Japan. (Okada et al. 2004). After the 2011 off the Pacific coast of Tohoku Earthquake, a submarine observation network was also constructed, and this integrated ocean–land observation network is called MOWLAS (Aoi et al. 2020). The high-sensitivity seismic observation network consisting of about 700 stations is called Hi-net.
Since the limit of the depth of the epicenter of inland earthquakes in Japan is usually 15–20 km, it was necessary to construct a seismic observation network at intervals of 15–20 km in order to accurately determine the depth of the epicenter of earthquakes of such depth. In order to perform stable and highly sensitive seismic observations by avoiding noise on the ground surface, seismometers are installed at the bottom of a borehole at a depth of more than 100 m at each Hi-net station. Although the majority of the Hi-net stations have boreholes of 100–200 m in depth, deep observation wells were made at some specific sites if necessary. Hi-net borehole wells are cased and full-hole cemented around the casing for long-term stable observation (Okada et al. 2004). Therefore, there is no ingress or egress of groundwater, and good-quality temperature profiles are expected to be obtained.
In Northeastern Japan, Hi-net stations were constructed between 1998 and 2000. In addition, two stations were constructed in 2012 to replace those damaged by the Tohoku earthquake. Of the 133 Hi-net stations in Northeastern Japan, 132 stations conducted thermal logging of each borehole well within a few months of the completion of drilling. For the observation wells with a depth of 100 m to 200 m, the effect of thermal disturbance caused by mud circulation during drilling is considered to be small because the time required for drilling is short, and the temperature difference between the surface and the bottom of the well is slight, generally within 10 °C. In order to test this hypothesis, eight observation wells were re-examined after a certain period. However, it is not easy to conduct temperature logging in Hi-net boreholes with seismometers installed.
Therefore, about six years after the drilling, the temperature logging was conducted by inserting an optical fiber into the borehole. The distributed temperature sensor (DTS) used was a Sumitomo Electric SUT-2. DTS can measure a physical quantity along the fiber length at many multiplexed points. Dakin et al. (1985) were the first to demonstrate that the temperature could be determined from measured Stokes and anti-Stokes Raman scattering ratio. The typical performance of a Raman-based DTS is 1 m spatial resolution and 1 K temperature uncertainty for a 5-min measurement integration period, with a sensing range of 10 km.
However, these figures can be substantially improved if the experimental conditions are alleviated (i.e., shorter range, worse spatial resolution) (Thévenaz 2006). For example, the performance of SUT-2 is 0.5 m spatial resolution and 0.1 K temperature uncertainty for a one-hour measurement integration period, with a sensing range of 2 km. As a result, the difference between the temperature logging data obtained a few months after the end of drilling and the data obtained a few years later was small, and the temperature profiles obtained in these two periods can now be considered to be of good quality with little influence from the temperature disturbance caused by drilling (see Fig. 2).
Rock cores are collected from the deepest 25 m or 30 m section in a typical Hi-net borehole. However, in boreholes drilled to depths of 1,000 m or more, rock cores were collected from multiple sections at intervals of 250 to 500 m. The thermal conductivity of these rock cores was measured using a Kyoto Electronics QTM-500. The thermal conductivity measurement device used in this study, the QTM-500 Rapid Thermal Conductivity Meter, is based on the hot wire method (e.g., Arakawa and Shinohara 1981). The QTM-500 is a one-dimensional (linear) heat wire placed on the surface or inside of a sample to measure the temperature increase inside the sample when a certain amount of heat (electric power) is applied, and the thermal conductivity is calculated (e.g., Tadai et al. 2009).
Rock cores from about 50% of the Hi-net boreholes were shaped, and thermal conductivity was measured using the QTM-500. In addition, for about 50% of the Hi-net boreholes where thermal conductivity measurement by the hot wire method was difficult due to fracturing of the rock core, thermal conductivity was estimated by referring to the columnar map and PS logging results of the well. In the estimation, we referred to Sato et al (1999) and Gueguen and Palciauskas (1994) (see Table 1).
For the thermal conductivity of sedimentary formations, which are particularly difficult to core-shape, data from Hi-net 2000m-class boreholes drilled in the Kanto region were used as a reference, as described below.
Generally, the thermal conductivity of surface soils in plain areas is about 1.2 Wm−1 K−1. However, according to the results of rock core tests in Hi-net boreholes in the Kanto region, the thermal conductivity is about 1.0–1.2 W m−1 K−1, even in Tertiary sedimentary layers when the elastic wave velocity Vp is less than 2.0 km s−1 (Suzuki and Omura 1999). Since PS velocity logging was performed in all Hi-net boreholes during construction, based on the PS velocity data, the thermal conductivity was set as 1.2 W m−1 K−1 for Tertiary sedimentary layers in Northeastern Japan with elastic wave velocity Vp less than 2.0 km s−1 and 1.0 Wm−1 K−1 for Quaternary sedimentary layers.
Terrestrial heat flow
Borehole wells used for heat flow analysis are often deeper than 300 m to avoid thermal disturbance caused by climate change, groundwater flow, and topographic effects. In the case of the Hi-net borehole well, drilling down to the basement rock is desirable to avoid surface ground noise. However, due to the spatial arrangement of the observation points, some wells are constructed in areas with thick sedimentary layers. Furthermore, as mentioned earlier, the Hi-net borehole wells are covered with a casing, and full-hole cementing prevents water inflow into the borehole, so very stable temperature gradient data are expected to be obtained.
In this study, the quality of the temperature logging data were evaluated by the characteristics of the T–D curve, referring to Erkan (2015), who performed heat flow analysis using shallow wells. The data were classified into four classes; A, B, C, and D. Sections up to 10 m in depth were excluded from the evaluation because they are likely to be affected by seasonal variations in surface temperature and artificial ground improvements such as embankments and cuttings.
Temperature log data classified as Class-A are those that show the effects of long-term climate change over the past century in the range of 10 to 30 m below the surface, are largely undisturbed except for temperature inversions, and also show a heat conduction type at depths below 50 m and are undisturbed throughout the entire area. For wells deeper than 100 m, linearity must be obtained in temperature logging data at depths greater than 100 m.
The temperature log data classified as Class-B show the effects of long-term climate change over the past century in the range of 10–30 m from the surface and shows the effects of groundwater flow and other factors in addition to a temperature inversion, but without significant disturbance and also shows a heat conduction type in about 50% of the sections at depths of 50 m or deeper.
The temperature logging data classified as Class-C has poor linearity and is greatly affected by groundwater flow and other factors, but there is no significant disturbance in the deepest 25-m section. The temperature logging data likely strongly influenced by groundwater throughout the section were classified as Class-D. This Class-D data was deemed unsuitable for heat flow analysis. Examples of T–D curves for the four classes are shown in Fig. 3.
The rock cores were collected only in the deepest 25-m or 30-m section. Therefore, the temperature gradient in the deepest 20-m section where the rock core was collected was used to analyze the heat flow. The temperature gradients in the deepest 50 m or 200 m sections where the lithology remains the same were used to analyze the heat flow for the two wells over 1000 m. In determining the temperature gradient, a regression line was obtained using the least-squares method, which was used as the temperature gradient before correction.
Climate change correction
The subsurface temperature field also records climatic changes at the surface. The effects of Pleistocene glaciation over several hundred thousand years extend several thousand meters below the surface, and climate change since the end of the nineteenth century has been particularly significant, affecting depths of 50 to 100 m (Jessop 1990). Therefore, in determining the heat flow, it is necessary to correct the effects of climate change for wells with depths between 100 and 200 m in the Hi-net standard specifications.
The Japan Meteorological Agency (JMA) analyzes that the annual mean temperature in Japan has been rising with various fluctuations and is rising at a rate of 1.28 °C per 100 years in the long term (JMA 2022). However, it is said that there is a difference in the trend of temperature increase between suburban and non-urban areas, known as the heat island phenomenon. Matsumoto (2007) calculated heat flow corrected for the effects of climate change, assuming a uniform 2.0 °C temperature rise over the past 100 years in the Japanese archipelago and considering the temperature rise in urban areas.
This uniform nationwide correction method was insufficient, especially for Hi-net boreholes with many observation points in non-urban areas. Regarding climate change in Japan over the past 100 years, Fujibe (2012) quantitatively assessed background (non-urban) and urban warming trends. According to this, the national average background (non-urban) daily mean temperature was estimated to be 0.88 °C per 100 year, reaching 2.08 °C per 100 year around large cities, where the warming trend increases with increasing population density (Table 2).
According to "Climate Change in Northeastern Japan" (JMA 2016), the temperature in Sendai, the largest city in Northeastern Japan, is 2.4 °C per 100 year, 1.9 °C per 100 year in Aomori, and 1.7 °C per 100 year in Morioka. In the non-urban areas, many areas rely on the records of the past 50 years, with Fukaura at 0.4 °C per 50 year and Miyako at 0.7 °C per 100 year. These results are in general agreement with those of Fujibe (2012).
Based on this model, we estimated the temperature increase over the past 100 years according to the population density around the boreholes, using the Regional Economic Analysis System (https://resas.go.jp/) operated by the Cabinet Office for data on population density as of 2005 (Table 2).
Long-term near-surface temperature changes in subsurface thermal structure vary with lithology. Therefore, in this study, for the seven lithology models listed in Table 1, we evaluated the change in the geothermal gradient after 100 years of continuous increase in surface temperature, according to Jessop (1990). The parameters for the Quaternary sedimentary layers were taken from Miyakoshi and Uchida (2001). Of the seven lithology models, those using granite as the lithology and Quaternary sedimentary layers as the lithology are shown in Figs. 4a–f and 5a–f. Both show the initial temperature distribution and the temperature distribution 100 years after the surface temperature started to rise. For the temperature trend, five cases of 0.88 °C per 100 year, 1.00 °C per 100 year, 1.10 °C per 100 year, 1.60 °C per 100 year, and 2.08 °C per 100 year were prepared for each of the seven lithology models, based on Fujibe (2012). Thus, a total of 35 cases were considered in this study.
The calculation results show that in Japan, the impact of climate change on the subsurface temperature gradient is very large up to a depth of 100 m, and the degree of impact on the temperature gradient due to different rates of temperature increase is also very different.
Three types of temperature profile data for Hi-net boreholes were collected in this study. The first one is two deeper than 200 m depths less affected by the climate change in the recent 100 years described here. Therefore, these two borehole wells are not subject to correction for climate change. Next are the temperature data for standard boreholes with 100 to 200 m depths. There are two sampling intervals for the temperature logging data here, one with a dense sampling interval of 1 m or 0.5 m (9 boreholes) and the other with a coarse sampling interval of 5 m (121 boreholes). For the former nine boreholes, we first tried fitting the observed T–D curve to the T–D curve calculated based on the temperature gradient of the initial conditions and the estimated temperature increase rate. The temperature gradient was arbitrarily assumed in 0.5 K km−1 units, and the fitting temperature gradient was selected by visual inspection.
For the latter 121 boreholes (115 boreholes excluding the 6 Class-D boreholes) that were coarsely sampled at 5-m intervals, a simple correction method was adopted because it was challenging to fit them using the same method as above.
Figures 4g–k and 5g–k show the ratio of the temperature gradient after 100 years from the initial condition for the five sections (60–80 m, 80–100 m, 100–120 m, 130–150 m, 180–200 m) in Figs. 4a–f and 5a–f. The temperature gradient ratios before and after 100 years in Fig. 4g–k for stations where the lithology is granite and Fig. 5g–k for stations where the lithology is Quaternary sedimentary formation were used as climate change correction factors for the measured temperature profiles. The other lithology sites were also classified into the remaining five lithologies listed in Table 1, and the temperature gradient ratios before and after 100 years were determined and used as correction factors.
In the case of the most common 100-m borehole, the average temperature gradient of the 80–100 m section is used for comparison, but the corrected temperature gradient is generally 5–20% larger. The error in the temperature gradient is calculated by multiplying the error in the temperature gradient before correction by the correction factor and is shown in Table 3. The larger the disturbance in the temperature profile due to groundwater and so on, the larger the error in the temperature gradient. The error is about 5% for Class-A boreholes, but for Class-B and Class-C boreholes, the error is about 10% and 10%, respectively (Fig. 6).
As we have discussed, we have attempted to correct for climate change with the model of Fujibe (2012). Here, we examine how the model is consistent with actual surface temperature rise over the past 100 years. Compared to JMA observations for each region in Northeastern Japan, there is a difference of about 0.3 °C, as mentioned above. In addition, a check of the temperature profiles of the Hi-net wells shows no significant temperature rise of more than 3.0 °C, which corresponds to a large city. If we allow an estimated range of temperature rise of up to 0.5 °C, we will attempt to calculate how much error we can expect. The effect of the different rates of temperature rise at the surface on the correction factor depends on the magnitude of the temperature gradient and which depth section was used in the analysis. In the 180–200 m section, the coefficient is less than 1% regardless of the magnitude of the temperature gradient; in the 130–150 m section, the coefficient is up to about 5% for temperature gradients below 25 K km−1 and less than 2% for gradients above 25 K km−1. In the 80–100 m section, which is the most affected, the error in the temperature gradients is estimated to be ± 12% at 20 K km−1, ± 7% at 30 K km−1, ± 5% at 40 K km−1, and ± 4% at 50 K km−1. Errors of this magnitude could be further added to the temperature gradient errors shown in Table 3.
Heat flow map
Heat flow data at 126 stations were obtained by measuring temperature gradient values and thermal conductivities of rock cores. In addition, heat flow data of 65 stations were obtained by measuring the thermal conductivity of rock cores, and 61 stations were obtained by using lithology estimates shown in Table 1. The error in heat flow data is about 11% for Class-A, 15% for Class-B, and 12% for Class-C, due to this error in temperature gradient plus the measurement error in thermal conductivity measurement. A comparison with Matsumoto (2007), who assumed a uniform climate change correction of 2.0 °C increase in 100 years and estimated the thermal conductivity of rock cores at unmeasured sites from the average of surrounding stations, shows that the average value of the two is about 100 mW m−2, which is not significantly different. However, when comparing the heat flow values for each borehole well, the heat flow in this study is 5% larger (Fig. 7). On the other hand, when restricted to boreholes with unmeasured thermal conductivity, the heat flow estimated from thermal conductivity based on Sato et al. (1999) and Gueguen and Palciauskas (1994) (Table 1) is about 14% larger in comparison.
In order to fill in the gaps in the distribution of Hi-net stations, the existing temperature logging data, Database on the Temperature Profiles of Boreholes in Japan (Sakagawa et al. 2004) (hereinafter referred to as DTPBJ), was examined for heat flow values, taking into account the geological conditions. However, because the DTPBJ includes many geothermal wells and hot spring wells in geothermal areas, many of these wells have been temperature logging immediately after drilling or not long enough after the temperature recovery test. The temperature recovery is not sufficient. Therefore, we extracted data only from these vertically drilled borehole wells, which are less affected by groundwater flow and exhibit good heat conductive type temperature profiles. The temperature gradient was determined when examining the heat flow by selecting the temperature profile section showing a straight line at the deep side. For high-temperature locations (above 100 °C), we attempted to correct the temperature dependence of thermal conductivity based on Miao et al. (2014) for granite and Funnell et al. (1996) for other lithologies when using the thermal conductivity of core samples registered in DTPBJ.
Although most of the 5000-m class boreholes drilled for resource exploration were not drilled vertically, Akiyama and Hirai (1997) estimated the vertical temperature gradient in these boreholes, which was adopted in this study. In addition, the government Ministry of International Trade and Industry (MITI) exploratory well Mishima, which is not included in the DTPBJ but was analyzed by Akiyama and Hirai (1997), was also analyzed in the same way as the DTPBJ. These results are shown in Table 4.
Figure 6 is a map of heat flow at the surface. Figure 6a plots the heat flow data for each measurement point, and Fig. 6b is plotted by interpolation using the nearest neighbor method. As shown in Fig. 6a, we obtained heat flow data over a large area of Northeastern Japan. There is a trend of less heat flow in the forearc, and more heat flow in the volcanic regions, and some regions have slightly less heat flow in the back-arc. In the volcanic region of the Ou Backbone Range, the heat flow values are very different despite the close distance between the measurement points, suggesting that the influence of groundwater behavior is significant. The interpolated Fig. 6b shows that high heat flow areas are distributed along the Ou Backbone Range, while low heat flow areas are distributed on the front arc side, especially in the northern and southern parts of the Kitakami Mountains, the eastern part of Abukuma Mountains, and near the Niigata Plain on the back-arc side (see Fig. 6c).
Based on this study's heat flow data, 1-D steady-state conductive geotherms are computed using finite difference approximations (e.g., Beardsmore and Cull 2001). Previous studies that estimated crustal temperatures by one-dimensional heat conduction include Okubo et al. (1998) and Tanaka (2009). The 1-D heat conduction is shown in Eq. (1), where T is the temperature at depth z, λ is the thermal conductivity, and A is the crustal heat generation:
Therefore, we need to know the constituent materials of the subsurface, thermal conductivity, and crustal heat generation. In this study, we adopted a model that incorporates current knowledge of the crustal structure of Northeastern Japan and takes into account the temperature dependence of the thermal conductivity of rocks. The crustal structure model used in this study is explained in section “Structure model”. In addition, how the temperature dependence of thermal conductivity is treated is explained in section “Thermal conductivity”. Finally, the crustal heat generation model is explained in section “Heat generation” (Fig. 9).
In assuming the crustal structure model for Northeastern Japan, we followed the crustal structure model treated by Muto et al. (2013). We consider the lithospheric structure obtained from wide-angle reflection and seismic refraction profiles throughout Northeastern Japan (Iwasaki et al. 2001; Nishisaka et al. 2001; Ito et al. 2004; Takahashi et al. 2004). Following the petrological interpretation of the seismic structure of Northeastern Japan Arc by Nishimoto et al. (2005), we assume that the upper crust is granite, and the lower crust is hornblende-bearing gabbro. The thickness of the upper crust is assumed to be 18 km; according to Matsubara et al. (2017a), the depth of the Moho discontinuity is distributed between 30 and 35 km, so we set the Moho discontinuity at 30 km and calculate the temperature structure from the surface to 30 km (Model A). It has also been noted that some areas on the forearc side of Northeastern Japan have granite in the lower crust (Nishimoto et al. 2008; Ishikawa et al. 2014; Ishikawa 2017). Therefore, instead of a simple horizontal layer structure, we calculate a temperature structure with granite as the lower crust in the region shown in Fig. 9a (Model B).
In addition, there are plains with thick sedimentary layers and areas thickly covered with pyroclastic deposits in Northeastern Japan (e.g., Ozawa and Hirayama 1970; Ikebe et al. 1979; Yamanoi 2005; Kobayashi 1996; Tamanyu 2008). As shown in Table 1, the thermal conductivity of sedimentary layers is about half that of basement rocks. Therefore, to estimate the subsurface temperature structure of these areas, it is necessary to incorporate the sedimentary layers into the subsurface structure model. For this purpose, the shallow and deep layers combined model (SDLCM) (NIED 2019) was used to obtain the depth of the basement rock at each observation point and improve the accuracy of the temperature structure estimation.
Based on the lithologic information from the boreholes, five cases of tectonic models were created for Model A and Model B, respectively (Fig. 9b, c). Case A-1 and B-1 assume that the granite is exposed at the surface. In Case A-2, A-3, B-2, and B-3, where metamorphic and pre-Paleogene sedimentary rocks are exposed, we assume that the near-surface lithology continues up to 5 km below the surface, and granite is assumed below 5 km below the surface. In Case A-4 and Case B-4, the thickness of the Tertiary sedimentary layer is used as the estimated depth of the basement rock at the well location, and the depth below is assumed to be granite. Finally, in Case A-5 and Case B-5, where the bottom of the borehole is Quaternary sedimentary layers, the Quaternary sedimentary layers are assumed to be present up to a depth of 500 m, and the Tertiary sedimentary layers are assumed to be present from there to the estimated depth of the base rock, and the granite is assumed to be present below that.
The thermal conductivity of rocks tends to decrease with increasing temperature (e.g., Cermak and Rybach 1982). Therefore, a model in which a simple linear function represents thermal conductivity and temperature is often used (Royer and Danis 1988; Bodri et al. 1989). On the other hand, to consider the large variability in the measured values, a model with a constant thermal conductivity in the upper crust is also used instead of a simple linear function model (Furukawa and Uyeda 1986; Tanaka 2009).
Miao et al. (2014) measured the thermal diffusivities and specific heat capacities of four types of rocks (granite, granodiorite, mafic rock, and hornblende) from room temperature to 1,173 K using the laser flash method and thermal analyzer simultaneously and then combined them with density data to calculate the thermal conductivity. In this study, we use the results of Miao et al. (2014) for granite and gabbro, which require calculations, especially at high temperatures. For Case A-2 and B-2, the Paleogene sedimentary rocks, the values in Table 1 based on lithological information from the boreholes were used as room temperature thermal conductivity using the formula of Funnell et al. (1996), and the temperature dependence of thermal conductivity was considered. For Case A-3 and B-3 metamorphic rocks, the measured thermal conductivities in Table 3 were used as room-temperature values, and the temperature dependence of thermal conductivity was considered using the Funnell et al. (1996) equation. For Case A-4, A-5, B-4, and B-5, which include Tertiary and Quaternary sedimentary formations, the thermal conductivities in Table 1 are used, and the temperature dependence was not considered here (see Table 5).
Regarding the content of radioactive materials in rocks, which is necessary for estimating crustal heat generation, Minato (2005) conducted a detailed study on the concentration of U, K, and Th in soils in various parts of Japan. The difference between the data for soil and rock is not very large, and it is safe to assume that the relationship between U, K, and Th is reasonably well maintained even when soil is replaced by rock. Therefore, for rocks that make up the upper part of the earth's crust, such as sedimentary layers and igneous rocks, we used this as a reference, and for gabbroic rocks that make up the lower part of the earth's crust, we estimated radiogenic heating based on Beardsmore and Cull (2001) (Table 6).
Two models have been proposed for heat generation in the earth's crust: one that decreases with depth (e.g., Furukawa and Uyeda 1986; Tanaka 2009) and one that varies from layer to layer (e.g., Erkan and Blackwell 2008; Okubo et al. 1998). This study adopts the layer model, defining multiple heating values depending on the crustal structure. Then, based on Eq. (2), the temperature T can be expressed as follows.
Figure 10a shows the crustal structure model calculations in Model A (Case A-1) for seven cases with heat flow ranging from 50 to 200 mW m−2 in 25 mW m−2 increments. In the case of 75 mW m−2, which is the average heat flow, the temperature reaches 300 °C at a depth of about 11 km, which seems reasonable compared to the depth of the seismogenic layer.
For comparison, we also calculated two models from previous studies (Fig. 9d): one is the structural model employed by Tanaka (2009), which assumes a constant thermal conductivity of 2.5 Wm−1 K−1 and a crustal heat generation A(z) that decreases exponentially with depth z:
Here, D = 10 km and heat generation at the surface A(0) = 1.4 μW m−3 (Model C).
The other is a structural model adopted by Okubo et al. (1998), in which the heat generation of the crust is assumed to be 1.5 μW m−3 for the upper crust and 0.15 μW m−3 for the lower crust. Thermal conductivity was estimated to be 2.5 W m−1 K−1 for the upper crust and 2.0 W m−1 K−1 for the lower crust, with lower values on the lower crust side to account for temperature dependence (Model D). Thermal structure calculations were performed for these two models (Fig. 10b and c).
In the shallow area of about 5 km, all three models do not differ much, but Model A tends to have a slightly higher temperature; for example, in the 100 mW m−2 calculation example, Model A is about 30 K warmer than Models C and D at 5 km. In the 200 mW m−2 calculation example, Model A has a temperature about 70 K higher than Models C and D at 5 km. As the heat flow increases, the temperature gradient increases, the temperature dependence of thermal conductivity becomes more pronounced, and the thermal conductivity decreases, further increasing the temperature gradient.
On the low heat flow side, in the case of 50 mW m−2, the attenuation effect of heat flow due to radiogenic heating in the upper crust is significant. As a result, the temperature in the deep underground will be lower. However, as shown in Fig. 11, for example, when there is a thick sedimentary layer at the surface, the temperature gradient in the sedimentary layer increases, and the heat generated in the earth's crust decreases, so the heat flow does not decrease with increasing depth, and the temperature deep underground tends to be higher.
On the other hand, if granite is also present in the lower crust as in Model B, and the heat generation rates of the upper and lower crust are constant at, for example, 2.16 μW m−3, the temperature gradient in the lower crust begins to reverse around 25 km depth when the surface heat flow is 55 mW m−2. Therefore, referring to Furukawa and Uyeda (1986), we set the heat generation in the lower crust, i.e., below a depth of 18 km, to 1.0 μW m−3, which is almost the lower limit. If the surface heat flow is 50 mW m−2, the temperature gradient becomes zero at a depth of 30 km. If the surface heat flow is 45 mW m−2, the temperature gradient reverses at a depth of 23 km. However, at 30 km depth, the temperature is several K lower than the peak at 23 km depth (Fig. 12).
However, the heat flow measured in the relevant area in this study was below 50 mW m−2 in two wells, and the lowest value was around 47 mW m−2. Therefore, although the temperature at 30 km depth will be about 5 K lower than the peak temperature, we decided to allow for this temperature drop in the present calculations based on the assumption that the results will be filtered to average the calculation results from multiple surrounding stations when discussing spatial distribution.
The heat flow values obtained estimate an error of 10–15%. The impact of this error on the estimation of subsurface temperature is estimated. In a typical case A-1 structural model with a heat flow of 50 mW m−2, assuming an error of 5%, the range of estimated temperatures at 5 km below ground would be about ± 6 K, at 10 km below ground about ± 15 K, at 15 km about ± 23 K, and at 20 km below ground about ± 30 K. However, with an error of 15%, the estimated temperature range is about ± 16 K at 5 km below the surface, ± 34 K at 10 km below the surface, ± 50 K at 15 km below the surface, and ± 70 K at 20 km below the surface. Uncertainty is higher at deeper depths, reaching ± 110 K at 30 km. In the case of 75 mW m−2, an error of 5% would result in ± 19 K at 10 km below ground, and an error of 15% would result in ± 50 K. In the case of 100 mW m−2, the error of 5% would be ± 25 K at 10 km below the surface, and the error of 15% would be ± 80 K. Uncertainty tends to increase at shallow depths with high heat flow. Thus, the method of estimating crustal thermal structure assumed in this study is a model in which the estimated temperature distribution is more sensitive to differences in crustal structure than in previous studies.
The partial melting state above the solidus temperature, where the assumption of one-dimensional heat conduction does not hold, is considered as follows. In the upper crust, granitoid have solidus temperatures of 600–700 °C at depths greater than 10 km (Robertson and Wyllie, 1971). The temperature of the lower crustal constituents, such as hornblende and waterless gabbro, is estimated to be 800–900 °C (Tatsumi et al. 1994; Yoshida et al. 2005). Here, following the methods of Okubo et al. (1998) and Nishida and Hashimoto (2007), we assume that the temperature of the upper crustal solidus is 650 °C, the temperature of the lower crustal mafic rocks is 800 °C, and the temperature of the Moho discontinuity (30 km depth) is 900 °C. If the temperature reached 650 °C in the upper crust, the model was designed to monotonically increase over depth to reach 900 °C at a Moho discontinuity depth of 30 km. If the temperature did not reach 650 °C in the upper crust but reached 800 °C in the lower crust, the temperature was assumed to increase to reach 900 °C at a depth of the Moho discontinuity monotonically.
The subsurface temperature was calculated for 126 Hi-net borehole wells, 86 DTPBJ wells, and 1 MITI exploratory test well for 213 locations. Figure 13 shows the temperature distribution at depths of 5 km, 10 km, 15 km, and 20 km, and Fig. 14 shows the depth of the 300 ℃, 400 ℃, and 450 ℃ isotherm, based on Model A and Model B. The depth distribution of isotherms for Model C is shown in Fig. 15. Depths are converted to depths from 0 m above sea level, not surface. Nearest neighbor interpolation was used to create the map. The interpolated grid size was set to 4 min or approximately 7.5 km, and a filter was used to interpolate from the values of multiple observation points within a 50-km radius. Isotherms were created in 100 °C steps based on the values for each grid.
The high-temperature region extends along the central axis of the Ou Backbone Range, and local high-temperature anomalies exist around volcanoes distributed along this axis. Therefore, there are many places where the depth of 650 °C is less than 10 km in these regions. On the other hand, in the coastal area on the forearc side, where low heat flow regions of about 50 mW m−2 exist, a low-temperature structure of about 300 °C to 400 °C is estimated at a depth of 30 km. In the low heat flow region in the southern part of the back-arc, where the thickness of the sedimentary layer is as much as 5 km, the temperature structure is about 300 °C at a depth of 10 km.
Heat flow distribution and characteristics
Compared with the previous study by Tanaka et al. (2004), shown in Fig. 8b, and Sakagawa et al. (2006), shown in Fig. 8c, the spatial distribution of heat flow characteristics shows almost the same trend. Compared to the geothermal gradient distribution shown in Fig. 8a (Tanaka et al. (2004)), the same trend appears to be true. By interpolating the forearc side, where the amount of data was previously small, it can be said that entire Northeastern Japan can now be covered, although the amount of data for the plains in the northern region is relatively small. Along the Ou Backbone Range, where the present volcanic front (VF) is located, many heat flow data estimates above 200 mW m−2. On the forearc side, heat flow is generally low in the area, but some heat flow data are estimated to be around 100 mW m−2 in some parts of the area. In addition, many heat flow data exceeding 200 mW m−2 have been estimated along the Ou Backbone Range.
On the other hand, low heat flow areas can extend to the plains and other areas. Low heat flow areas are distributed on the forearc side, especially in the northern and southern parts of the Kitakami Mountains, the eastern part of the Abukuma Mountains, and near the Niigata Plain on the back-arc side.
Influence of subsurface fluids
Tamanyu (2008) proposed a model of hydrothermal convection related to the thickness of the sedimentary layers in Northeastern Japan and estimated that hydrothermal convection is dominant down to the depth of the Pre-Paleogene basement rocks, from 1 to 3 km in plains and basins, and up to 1 km in volcanic regions. For example, hydrothermal convection systems are thought to be dominant in areas where high heat flow is observed, which exist around volcanoes in the Ou Backbone Range. In this case, the near-surface heat flow is the heat transfer due to heat conduction at depth plus the heat transfer due to fluid at shallow depth.
Therefore, overestimated heat flow values may be used when estimating the temperature structure at depths greater than a few kilometers. Sakagawa et al. (2006), who have conducted many heat flow analyses, especially in geothermal regions, analyzed heat flow due to heat conduction and heat flow due to fluid involvement in many borehole wells and estimated that heat as much as the heat conduction flux is transported to the surface by fluids. Therefore, it should be noted that estimating the temperature structure of the subsurface in areas that exhibit such high heat flow is subject to fluid effects.
On the other hand, it has been pointed out that groundwater flow systems are widespread in the plains (Miyakoshi and Uchida 2001). In these areas, subsurface temperature gradients are complex, with large temperature gradients in the ascending groundwater basins and small temperature gradients in the descending basins (Uchida et al. 2014; Kaneko et al. 2020). On the other hand, most of the D-class wells, which were judged to have powerful groundwater influence, are in the plains with thick sedimentary layers, and their temperature profiles show downward flow type. The temperature profiles of the Hi-net borings showed the influence of surface groundwater in about 10% of the stations, including the C-class wells that were judged to be partially affected. Heat flow in these boreholes is generally estimated to be low. Therefore, more careful analysis that considers groundwater effects may be necessary, especially for borehole wells in geological conditions such as basins and plains where sedimentary layers are thick, and water can easily penetrate.
High heat flow regions and volcanic distribution
In geothermal zones in plains with thick sedimentary layers and around volcanoes, shallow ground structures and groundwater behavior are thought to influence heat flow strongly, and we attempt to interpret the heat flow distribution obtained in this study based on the assumption of the existence of these effects. First, we attempt here to discuss the distribution of high heat flow regions. It is said that in subduction zones, low heat flow is observed on the forearc side, high heat flow on the VF, and moderate heat flow on the back-arc side (e.g., Fukahata and Matsu'ura 2000), and we first examine regions where this pattern and high heat flow distribution are different. Then, we find that there is a region of high heat flow along the eastern side of the Ou Backbone Range.
In the central part of the Kitakami Mountains and near the Sendai Plain, there are areas of high heat flow extending from the VF to the forearc side. Therefore, we will consider the current distribution of volcanoes and the correlation with the past distribution of volcanoes. The position of the VF in Northeastern Japan was about 30–40 km east of its present position at 16 Ma, but it has moved from about 10 km west to east at 10 Ma (Yoshida et al. 2013). Consider the possibility that these past VF movements still influence the thermal structure of the crust. Since 8 Ma, many large calderas have formed along the central axis of the Ou Backbone Range (Yoshida et al. 2013), but only one caldera has been identified on the forearc side of the present VF.
The time required to cool a magma reservoir with a diameter of 10 km is said to be about 1 Ma (Tomiya 2000), so the time scales may not match. On the other hand, there are cases where calderas are assumed to have been active for more than 600,000 years after their formation (Takehara et al. 2017), and hydrothermal reservoirs and low-velocity bodies have been observed beneath calderas formed in the Late Miocene (Sato et al. 2002). It has also been pointed out that magma reservoirs with lifetimes longer than several million years may exist if conditions like continuous fluid supply from deep underground are met (Yoshida et al. 2020). However, the distribution of calderas in Northeastern Japan (Yoshida et al. 2013) shows no evidence of calderas extending over the central Kitakami Mountains and the Sendai Plain. Therefore, the cause of this high heat flow is unrelated to the VF, and we should consider that other factors bring about the high heat flow.
Low heat flow regions
Next, we will discuss the distribution of the low heat flow regime. As discussed in the previous section, we will focus on the differences from the assumed pattern of heat flow distribution in the subduction zone. For example, in the northern part of the Kitakami Mountains, areas of low heat flow are on the Ou backbone Range side of the VF. As mentioned in the previous subsection, the VF existed about 30–40 km east of the present at 16 Ma (Yoshida et al. 2013), but the time when the VF existed west of the present, where low heat flow is expected, goes back to 30 Ma, and it is estimated that it existed near the present Japan Sea coastline at that time (Sato 1994). Therefore, the relationship between the movement of the VF and the existence of a region of low heat flow near the northern Kitakami Mountains, which extend farther to the Ou Backbone Range than the VF, is unclear.
Although heat flow is low in areas where crustal subsidence and sedimentation are in progress (e.g., Fukahata and Matsu'ura 2000), the cause of this is also unknown because the area is not significantly subsided compared to the analysis of crustal deformation in Northeastern Japan over the past 120 years (Nishimura 2012). On the other hand, the Niigata Plain on the back-arc side also has many areas of low heat flow, but these are areas where sedimentation is estimated to be high (Nishimura 2012; Kobayashi 1996), and in these areas, the consistency between low heat flow and crustal activity is recognized to some extent. The impact of this crustal movement and the current tectonic setting that drives it on the distribution of heat flow will need to be examined, including the results of estimating the subsurface thermal structure.
D90 and thermal structure
In order to examine the validity of the calculated temperature structure, we first compare it with the D90 distribution estimated by Omuralieva et al. (2012), shown in Fig. 16, which is an indicator of the lower limit of the seismogenic layer of the crust. There seems to be a good correlation between the temperature structure and the spatial distribution of D90, and the isotherm at a depth of 400 °C and 450 °C is correlated. On the other hand, in the case of Model C (Fig. 15), where isobaths were calculated for comparison, the correlation seems to be at 400 °C or slightly cooler.
Further study of the correlation between Model A + B and D90: among 300 °C, 400 °C, and 450 °C, the 450 °C isothermal depth and the D90 depth seems to be consistent overall. Along the Ou Backbone Range, both isothermal depth and D90 are shallow, but the isothermal depth is slightly different where it is estimated to be shallower. On the forearc side, isothermal depths tend to be consistent in the south near the Kitakami Mountains but slightly different in the north, where isothermal depths tend to be deeper than those of D90. Finally, in the Sendai Plain area, where the D90 is shallower, the isothermal depth is consistent with 450 °C or 400 °C (Fig. 16).
Next, the back-arc side is examined. The Niigata Plain, the epicenter of the Mid Niigata Prefecture Earthquake in 2004, is an area with thick sedimentary layers (Kobayashi 1996). There is a good correlation between temperature and the lower limit of the seismogenic layer in this area, which shows the effect of introducing a detailed crustal structure. On the back-arc side, isothermal depth is consistent with 450 °C near the Niigata Plain, but D90 tends to be a little deeper in areas farther north.
Thus, while regional differences between D90 and the inferred temperature structure may be seen, the relationship between the lower limit of the seismogenic zone and the depth to the brittle–ductile transition in the crust has been extensively investigated in seismically active lithotectonic belts (e.g., Magistrale and Zhou (1996); Albaric et al. 2009; Hauksson and Meier 2019). In addition, some reports suggest that the occurrence of shallow intraplate earthquakes is governed by friction that depends on the temperature and lithology of the upper crust (Maeda et al. 2021). The characteristics of the subsurface temperature structure obtained in this study may provide information on how D90 temperatures vary with depth, lithology, and other factors.
Curie point depth and thermal structure
Next, we compare it with the Curie point temperature distribution by Okubo et al. (1989), shown in Fig. 17. Although both have resolution limitations, there seems to be a good correlation in terms of trends in spatial distribution. However, compared to the estimated temperatures, Model A + Model B (Fig. 14) seems to match 400 °C near the Ou Backbone Range and 300 °C on the back-arc and forearc sides. As mentioned in the previous section, there is a region of low heat flow extending from the northern side of the Kitakami Mountains to the Ou Backbone Range side of the VF, and there is a correlation between this distribution and the Curie point temperature distribution. However, there is no clear correlation between the distribution of high heat flow in the central part of the Kitakami Mountains and the Sendai Plain.
This Curie point temperature distribution is interpreted by Nishida and Hashimoto (2007) as corresponding to 400–450 °C, or about 300 °C, depending on the rock type. However, as with D90, this may need to be carefully considered in terms of the physical conditions of the rock.
Influence of tectonic models
Now that we have mentioned that the rock zone's physical conditions (temperature, structure, and lithology) are essential issues, we will again review the tectonic model of this study. First, the crustal structure is assumed to be a simple horizontal layered structure with an upper crustal thickness of 18 km and a lower crustal thickness of 12 km. However, in many models, the Moho discontinuity is estimated to be deeper just below the Ou Backbone Range and slightly shallower on the frontal and back-arc sides (e.g., Nishimoto et al. 2005; Muto and Ohzono 2012; Matsubara et al. 2017a).
Since the thickness of the upper crust determines the total amount of crustal heat generation, heterogeneity in the upper crust's thickness significantly impacts the lower crust's estimated temperature structure. In addition, the 3D seismic velocity structure shows heterogeneity (e.g., Matsubara et al. 2017b), making it likely that the crustal components are not simple horizontal layers. The model used in this study is that the lower crust near the Kitakami Mountains is composed of granite (Nishimoto et al. 2008; Ishikawa et al. 2014; Ishikawa, 2017). Since the thermal conductivity and amount of radiative heat generation vary depending on the type of rock, it will be necessary to construct a 3-D structure that considers these characteristics. The existence of high heat-flow regions on the forearc side and low heat-flow regions near the VF may be explained to some extent by the heterogeneity of heat generation in the upper and lower crust.
In addition, Northeastern Japan is an area where tectonic inversion is in progress (Sato 1994), and as Fukahata and Matsu'ura (2000) point out, the influence of the active crustal movement of uplifts such as uplifts and sedimentation needs to be taken into account.
However, this method, which considers the detailed structure of the crust, tends to estimate temperatures on the low side for low heat fluxes and on the high side for high fluxes, compared to previous studies. A further improvement of this method would be to consider heat transfer by fluids. For a more accurate estimation, it may be helpful to use an approach proposed by Sakagawa et al. (2006) to elaborately model the heat flux, which is the sum of heat conduction in the rock mass and heat transport by the fluid, as observed heat flow at the surface. In the future, it will be necessary to collaborate with groundwater models, for example, to separate the heat flux from the surface to 1 to 2 km, where the influence of fluid is significant, from the heat conduction below the base rock conduction is dominant.
For example, a factor other than structure is the behavior of fluids deep in the crust. Nakajima and Hasegawa (2003) proposed a model in which an S-wave reflection surface exists on the east side of the volcanic front, and water is supplied from the lower crust. The effect on the thermal structure of the movement of such fluids from the lower crust to the upper crust, such as the cause of the high heat-flow regions that exist east of the VF and on the forearc side, would need to be considered.
Finally, the relationship between deep structure and temperature structure, i.e., the possibility that the temperature structure of the mantle wedge may affect the inferred thermal structure, is discussed. Compared to the hot finger model (Tamura et al. 2002), in which particularly hot regions of the mantle wedge are distributed at regular intervals, the spatial distribution of regions hotter than the surroundings appears to be in good agreement. However, a quantitative comparison may be difficult since this study uses a simplified model for calculating thermal structure above the solidus temperature.
The lower temperatures, especially on the forearc side, may also be consistent with the model inferred by Wada and Wang (2009) and Wada et al. (2011) that the slab and the mantle are fully decoupled until a depth of 70–80 km, but fully coupled at greater depths. Using shear-wave splitting analysis, Uchida et al. (2020) found a distinct lack of anisotropy in the forearc mantle wedge, indicating that the forearc mantle wedge is decoupled from the slab and does not participate in the viscous flow. While the correlation between the location of the 70-km slab isobath (Fig. 16) and the low-temperature regions in the estimated temperature distribution (Fig. 14) is certainly good, the low-temperature regions in the northern Kitakami Mountains and the high-temperature regions in the central Kitakami Mountains may become consistent if we assume some regional variation in the depth at which these mantle wedges become uncoupled to the slab, for example.
Suppose these issues can be overcome, such as addressing the behavior of groundwater in the shallow part of the crustal structure model used to estimate thermal structure in this study and the behavior of fluids rising from deeper parts of the crust. In that case, it may be possible to increase the accuracy required for comparison with D90 and improve the accuracy of temperature estimates to the Moho discontinuity.
New heat flow data covering Northeastern Japan, corrected for climate change, were obtained using borehole temperature profiles of the NIED Hi-net. The obtained spatial distribution of heat flow shows low heat flow on the forearc side, high heat flow along the Ou Backbone Range, and low heat flow in the plains on the back-arc side. However, the distribution is not clearly divided into high and low heat flow along the VF front; for example, the low heat flow extends from near the northern Kitakami Mountains on the forearc side to the Ou Backbone Range crossing the VF, while the high heat flow extends to the central Kitakami Mountains and Sendai plain on the forearc side. In addition, the crustal temperature structure was obtained by using a crustal structure model that takes into account the temperature dependence of thermal conductivity and the difference in heat generation due to lithology, using a crustal structure model that takes into account sedimentary layers rather than a uniform structure model with exposed bedrock at the surface.
Good correlation was observed with D90 and Curie point depth distribution, with D90 ranging from 400 to 450 °C, Curie point depth around 400 °C near the Ou Backbone Range, and a strong correlation around 300 °C on the anterior and back-arc sides. Compared to previous studies, the crustal thermal structure calculation method assumed is a model whose estimated temperature distribution is sensitive to structural differences; however, a more accurate estimation of the temperature structure is possible if detailed structural information is available.
On the other hand, it seems necessary to treat fluid behavior in more detail in areas of high heat flow. However, the estimation of crustal temperature structure, especially in regions with thick sedimentary layers, is considered an improvement over the previous study. We hope that this study will be useful in developing initial models for future complex analyses of crustal thermal structure.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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The comments from two anonymous reviewers were very helpful in revising the manuscript. The authors are very grateful to Keiji Kasahara, Kazushige Obara, Katsuhiko Shiomi, Youichi Asano, Akira Yamamoto, and Kentaro Omura for their support of this work. Some figures were drawn using the Generic Mapping Tools software package (Wessel and Smith 1998). The plate models by Iwasaki et al. (2015) were constructed from topography and bathymetry data by the Geospatial Information Authority of Japan (250-m digital map), Japan Oceanographic Data Center (500 m mesh bathymetry data, J-EGG500, http://www.jodc.go.jp/jodcweb/JDOSS/infoJEGG_j.html) and Geographic Information Network of Alaska, University of Alaska (Lindquist et al. 2004).
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Matsumoto, T., Yamada, R. & Iizuka, S. Heat flow data and thermal structure in northeastern Japan. Earth Planets Space 74, 155 (2022). https://doi.org/10.1186/s40623-022-01704-4