Predicting the Temperature Field of Hot Dry Rocks by the Seismic Inversion Method

Abstract

Hot dry rocks, as clean and abundant sources of new energy, are crucial in the restructuring of energy. Predicting the temperature field of hot dry rocks is of great significance for trapping the target areas of hot dry rocks. How to use limited logging data to predict the temperature field within a work area is a difficulty faced in hot dry rock exploration. We propose a method to predict the hot dry rock temperature field (using seismic inversion results). The relationship between porosity and transverse wave velocity was established with petrophysical modeling. The difference in porosity calculated from the density and transverse wave velocity was incorporated in the seismic inversion results to find the thermal expansion and predict the temperature field. We applied the method to predict the temperature of hot dry rocks in the Gonghe Basin. The results showed that the temperature in the northeast work area was higher than in the southwest area at the same depth, and a depth of 150 °C of the hot dry rock reservoir was shallower. The thermal storage cover was analyzed from the geological stratigraphic data of the Gonghe Basin. The thermal storage cover in the northeastern part was thicker than in the southwestern part and had better thermal insulation, which is consistent with the prediction of the temperature field.

1. Introduction

Hot dry rock systems are clean and renewable energy resources (despite the absence of geothermal fluids) [1]. The water injected into injection wells for power generation is not entrained with a large number of impurities dissolved from the formation when recovered because of the short circulation time in the hot dry rock reservoir. Therefore, hot dry rock power generation can achieve a theoretically low water loss rate and has a broad development prospect.

As an important part of hot dry rock target area determination, traditional temperature field prediction is customarily obtained by interpolation between geothermal wells. However, the depth (generally > 3000 m) of the hot dry rock reservoirs and high drilling cost lead to few logging data. This makes it difficult to predict the temperature field. The prediction of the temperature field of hot dry rock by seismic inversion can play an alternative role in the exploration and development of hot dry rock.

Seismic exploration assumes that elastic waves travel in a constant temperature medium [2,3]. Studying the temperature-sensitivity of seismic properties of seismic waves is the basis for predicting the temperature field by seismic inversion. Yun et al. (2001) analyzed the relationship between the elastic modulus of dry rock under the influence of temperature and pressure by combining the study on the physical properties and laws of rocks under the reservoir conditions of the Daqing oil field and the relevant experimental data by Phillips et al., and fitted a multi-parameter dry rock elastic modulus equation [4]. Du et al. (2003) performed physical properties measurements on granite samples before and after high temperature to indirectly calculate the elastic modulus and inferred that the rock properties change more drastically after high temperature than the mechanical properties [5,6]. Punturo et al. (2005) studied the effect of pressure and temperature on the thermal expansion of rocks and looked at the relationship between pressure and temperature required to prevent fractures from thermal expansion [7]. Jaya et al. (2010) studied fluid viscosity and fractures in rocks at high temperatures and concluded that seismic wave attenuation increases at high temperatures due to the high viscosity of the fluid and the generation of fractures [8]. Wang et al. (2013) measured the longitudinal wave velocity of granite at different temperatures and performed triaxial compression tests to analyze the effect of thermal expansion of the rock [9]. Poletto et al. (2018) derived from rock physics model simulations that the seismic longitudinal and transverse wave velocities are almost constant until the melt temperature is reached without considering the change in porosity [10]. Wu et al. (2021) investigated the variation pattern of longitudinal wave velocity after repeated thermal shocks on hot dry rock samples and analyzed the thermal damage of granite [11]. Wu et al. (2021) studied the variation of physical properties of granite at different temperatures and cooling methods and analyzed the sensitivity of granite density, longitudinal wave velocity, and thermal conductivity to thermal damage [12]. Zou et al. (2022) introduced temperature into the Gassmann equation and predicted the effect of fluid on the physical properties of rocks considering the effect of temperature [13]. The current research on temperature-sensitivity of seismic properties is mainly laboratory experiments and simulations, while there are few studies for the prediction of actual temperature fields.

In this paper, a temperature field prediction method is proposed. The method relies on transverse wave velocity and density in order to capture the porosity anomalies due to thermal expansion and assumes no significant change in the lithology of the hot dry rock. The temperature field prediction process is shown in Figure 1. Firstly, petrophysical experiments were conducted to analyze the temperature-sensitive properties of the hot dry rock. Petrophysical modeling was also performed by analyzing the logging data to find the relationship between transverse wave velocity and porosity. Considering that simultaneous inversion can provide a variety of temperature-sensitive properties, including longitudinal and transverse wave velocities and density, it was used to invert the seismic data [14,15]. The temperature field was predicted by combining the petrophysical analysis with the seismic inversion results. The proposed method was tested to predict the temperature field of the hot dry rock in the Gonghe Basin. Seismic inversion was used to predict the hot dry rock temperature field in the work area where only single-well data were available and inter-well interpolation was not possible.

2. Geology Background

The Gonghe Basin is located at the intersection of the Qinling, Kunlun, and Qilian Mountains, as well as the Songpan-Ganzi orogenic belt (Figure 2). Because of the thick Quaternary sedimentary layers in the Gonghe Basin, which serve as an important channel for heat transfer to the shallow substratum, the deep major fractures cannot be seen more obviously from the surface. The Quaternary strata completely cover the surface of the Gonghe Basin. The sedimentary cover of the basin consists of Paleoproterozoic-Neoproterozoic terrains. The upper part of the basement of the Gonghe Basin is mainly composed of Middle to Late Triassic granites, Middle Triassic Gulangdi Formation, and Early to Middle Triassic Longwu River Formation, while the lower part of the basement is mainly composed of Indo-Chinese intrusive rocks. These intrusive rocks, as good carriers of geothermal energy, play an important role in the formation of geothermal resources in the Gonghe Basin [16,17]. Yu et al. constructed a three-dimensional geological structure model based on the lithological catalogs of 16 boreholes in the Chabcha geothermal field (Figure 2) and classified the strata into Quaternary aquifer, Neoproterozoic thermal reservoir, and hot dry rock thermal reservoir (Figure 3) according to the type of reservoirs [18,19]. The stratigraphic column is shown in Figure 4 [16].

Four diorite (LY) samples and two granodiorite (GH) samples from the Gonghe Basin were analyzed by X-ray diffraction (XRD) by Lei. The results are shown in

Table 1. XRD test results of granite samples from the Gonghe Basin (%) [20].

Rock Sample	Quartz	Orthoclase	Plagioclase	Dark Mica	Muscovite Mica	Calcite	Hornblende	Clay
LY-1	24	40	31	2	1	0	2	0
LY-2	25	38	30	1	3	0	0	3
LY-3	22	42	28	3	2	2	1	1
LY-4	27	35	32	1	3	1	1	0
GH-5	25	8	37	3	0	0	22	5
GH-6	30	9	35	5	0	0	15	6

[20].

It can be found that the diorite granite of the Gonghe Basin is mainly composed of quartz (22–27%), feldspar (67–71%), and mica, where the ratio of orthoclase to plagioclase can be seen to be about 4:3, while the granodiorite of the Gonghe Basin has more hornblende and clay as the main components compared to the diorite granite.

Lei also performed thin-section analyses of the rock samples (Figure 5). The identification results show that the rock composition is mainly orthoclase, quartz, plagioclase, hornblende, and mica. It is consistent with the XRD results.

In addition, Lei determined the density, porosity, and permeability of granodiorite samples, and the test results showed that the density of granite in the Gonghe Basin area is about 2.524–2.694 g/cm³, the porosity is basically less than 4.59%, and the permeability is less than 0.7 mD [20].

3. Petrophysical Analysis

To analyze the temperature-sensitive properties of hot dry rock, we measured petrophysical properties at different temperatures for granite samples from the Gonghe Basin and performed petrophysical modeling of the hot dry rock system.

3.1. Petrophysical Analysis of Temperature Sensitive Properties

The change of the physical properties of rocks with temperature is the basis for temperature predictions.

We conducted longitudinal and transverse wave velocity tests from 20 to 220 °C for four granite outcrop rock samples collected from the Gonghe Basin (Figure 6).

The measurement results show that although there are relative differences in the longitudinal and transverse wave velocities of granite samples from different areas of the Gonghe Basin, the trends of changes with temperature rise are basically the same:

(1) Below 140 °C, the longitudinal and transverse wave velocities of granite fluctuate within a certain range, with the amplitude of the longitudinal wave velocity fluctuating up and down within 500 m/s and the transverse wave fluctuating within 700 m/s.

(2) At 140 °C, the transverse wave velocities of all four samples reached a peak of 3200 m/s–3700 m/s. Compared with the transverse wave velocities, the longitudinal wave velocities still maintained the original fluctuation without any obvious trend of change.

(3) At 140–160 °C, the longitudinal and transverse wave velocities decreased very significantly, with the decrease in the longitudinal wave velocity ranging from 800 m/s to 2200 m/s and the decrease in the transverse wave velocity ranging from 300 m/s to 1200 m/s.

Also, considering that the investigated temperature range is still far from the granite melting temperature and the transition temperature from α-quartz to β-quartz, the longitudinal and transverse wave velocity change is assumed as only dependent on the change in porosity [21].

In summary, it can be seen that the fluctuation ratio of the transverse wave speed with temperature is more evident than that of the longitudinal wave velocity in the range of 20–140 °C. At 140 °C, the transverse wave will reach an extreme value, while the longitudinal wave does not change significantly, and at 140 °C–160 °C, the decrease ratio of the longitudinal wave speed is more obvious than that of the transverse wave speed. In general, the transverse wave velocity is more sensitive to temperature change than the longitudinal wave velocity, which is relatively easy to be found in the inversion results. In addition, the longitudinal and transverse wave velocities of the four rock samples decreased significantly from 140 °C to 160 °C, which can be used as a reference for temperature field prediction. Although the temperature at which a large decrease in longitudinal wave velocity generally occurs in subsurface rocks may change due to factors such as stratigraphic pressure, different granite compositions, and the fact that seismic wave frequencies are very different from laboratory acoustic frequencies, it can still be inferred that there is a critical temperature for granite in the Gonghe Basin. When the rock reaches this temperature, a massive decrease in transverse wave velocity occurs.

3.2. Analysis of Petrophysical Modeling

The change in density of rocks of the same lithology tends to be negatively correlated with the change in porosity without considering the change in temperature. Moreover, the change of transverse wave velocity in rocks is also negatively correlated with the change in porosity. Thus, the transverse wave velocity is positively correlated with the change in density. However, comparing Figure 7a,b, it can be found that at 3600 m, the change of transverse wave velocity and density shows a negative correlation without any change in lithology. We suggest that this is due to the thermal expansion decrease in the matrix density and the closure of the pore space. Thus, the transverse wave velocity and density change show a negative correlation. Under these conditions, the density can no longer reflect the change in porosity, while the transverse wave velocity can account for the change in porosity trend.

Considering that the hot dry rock lithology is mainly granodiorite, the petrophysical modeling of granodiorite was performed. The modeling process is shown in Figure 8: based on the XRD results, the rock matrix model was predicted using the V-R-H model [22]. Pore space was added using the K-T model [23]. The equivalent fluid substitution was performed using Batzle–Wang formula and Gassmann equation to obtain a saturated rock model [24,25]. The rock matrix components are shown in

Table 2. The rock matrix components of petrophysical modeling (%).

Quartz	Orthoclase	Plagioclase	Dark Mica	Hornblende	Clay
30	9	35	5	15	6

. In order to find the relationship between transverse wave velocity and the porosity of granodiorite, petrophysical modeling was carried out in the porosity range of 0–5% (Figure 9). The predicted results are fitted to obtain the approximate relationship between transverse wave velocity and porosity:

$$\phi =-0.000135925V_S+0.495825$$

(1)

We calculated porosity with Equations (1) and (2). Petrophysical modeling was performed according to Figure 8. The predicted transverse wave velocity (red) of porosity calculated with Equation (2) compared with the measured transverse wave velocity (blue) was obtained (Figure 7c). The predicted transverse wave velocity (red) of porosity calculated by Equation (1) compared with the measured transverse wave velocity (blue) is obtained (Figure 7d). It can be found that the transverse wave velocity is more strictly correlated to porosity in the case of thermal expansion of the rock than the density.

$$\phi =\frac{{\rho }_{\mathrm{martix}}-{\rho }_{\mathrm{logging}}}{{\rho }_{\mathrm{martix}}-{\rho }_{\mathrm{pore}\mathrm{fluid}}}$$

(2)

4. Simultaneous Inversion

4.1. Estimation of Hot Dry Rock Parameters

The accuracy of the seismic pre-stack inversion is affected by the quality of the seismic data, so the seismic tract set needs to be optimized before performing the inversion. The pre-stack CRP data are loaded (Figure 10).

The signal-to-noise ratio is an important indicator of seismic data quality, which is generally defined as the ratio of effective signal to noise. Seismic noise can be mainly classified into random noise and regular noise.

Super-gather is an effective means to suppress random noise without fixed rules. Its data from multiple adjacent CRP points are combined together by merging to enhance the effective signal, which can improve the signal-to-noise ratio. The larger the number of combined traces, the better the denoising effect, but too large the number of combined traces may also suppress the constructive features. The number of combined traces in the Xline direction and Inline direction is set to 5 traces each, and super-gather is performed (Figure 10b).

The interface between the top surface of the granite and sedimentary rocks is a strong reflection interface, which often generates strong multiples; Radon transform converts the signal in the time-space domain to the Radon domain, separates and removes the multiple waves by the difference of energy groups between primary waves and multiple waves, and then inverts them to time-space domain to obtain the primary wave data after the multiple waves are suppressed. Figure 10c shows the seismic profile after the Radon transform suppressed multiple waves.

The residual static correction picks up the correction quantity directly in the correlation curve by the multiple overlay feature. It selects the static correction volume by making each recorded trace achieve the best similarity to the stack trace, flattening the trace gather. Figure 10d shows the seismic profile after performing the residual static correction.

The Zoeppritz equation and its approximation equation are based on the incident angle when the seismic wave arrives at the interface. Since there is a nonlinear relationship between the offset and angle, it is necessary to convert the offset gather into the incident angle gather for simultaneous seismic inversion. From 2°–44° with 3° per trace, 15 traces were extracted to obtain Figure 10e.

Seismic wavelet is an important link between seismic data and stratigraphic interpretation. The extraction of statistical wavelets is based on the assumption that the seismic wavelet is time-invariant. Moreover, assuming that the reflection coefficients are white noise, the autocorrelation of the seismic records can be used to obtain the autocorrelation of the wavelet and thus the amplitude spectrum of the wavelet. The wavelength should be set so that the seismic sampling rate is an integer multiple of the half-wavelength, and the extraction time window of the wavelet should be set to 2–5 times the wavelet length [26]. The wavelet wavelength is set to 200 ms, and the time window is 1500–2500 ms to extract the wavelet and obtain Figure 11.

Well-seismic calibration is an important method used to establish time-depth relationships. It can relate the seismic data in the time domain to the logging data in the depth domain. Since the granite is in block form with no obvious reflection layers, the seismic data are first stacked to enhance the stratigraphic characteristics. Synthetic logs are generated from the longitudinal and density curves of the logs, and the upper top surface of the granite is used as the main calibration target, and the well-seismic calibration is performed with the post-stack data by combining the work area information (Figure 12a). The time-depth conversion relationship of granite stratigraphy in the work area is obtained (Figure 12b).

The stratigraphic model was established from the work area stratigraphic data, and the logging curves were interpolated to the whole model by extrapolation to obtain the initial inversion models of longitudinal wave velocity, transverse wave velocity, density, longitudinal impedance, and transverse impedance in Figure 13.

Simultaneous inversions were carried out. We compare the logging curve with the inversion curve. The inversion parameters are adjusted to reduce the error to provide quality control of the inversion. The inversion quality control is shown in Figure 14. The inversion results were used to build a 3D model, using Xline 229 of the logged wells as the profile (Figure 15).

4.2. Analysis of Inversion Results

By analyzing the inversion results (Figure 15), it is concluded that the longitudinal wave velocity has more obvious laminarity at 1300 ms–1660 ms, and the variation of 1660 ms is complicated without an obvious pattern. The laminarity of the transverse wave velocity can be seen more obviously, except that the variation pattern is not obvious from 1660 ms to 2000 ms. The laminarity characteristic of density is very obvious. The longitudinal impedance and transverse impedance are calculated from the longitudinal and transverse wave velocity and density, so the obvious laminarity of density makes the laminarity of longitudinal and transverse wave impedance in 1660 ms–2000 ms due to the longitudinal and transverse wave velocity, but below 2000 ms, the original obvious laminarity becomes less obvious, which reflects that the relationship between longitudinal and transverse wave velocity and density is sometimes negatively correlated.

In the case that the deep granite is not obviously laminated lithologically, but the inversion results can show more obvious laminations, it is thought that it is likely to be caused by external factors. Considering that the distribution of temperature and pressure in the subsurface is also mainly related to depth, it is likely that this laminar feature is due to temperature and pressure.

5. Discussion

5.1. Discussion on Experimental Analysis of Petrophysical Experiments and Logging Data

Seismic exploration can provide valuable information for the exploration of geothermal reservoirs, which requires a study of the temperature-sensitive properties of seismic. Theoretical studies show that the longitudinal and transverse wave velocities of rocks with porosity unaffected by temperature changes are almost constant until the melt temperature is reached without pressure, and there is a significant decrease in longitudinal wave velocity after the melt temperature is reached. Since the rock can be approximated as a fluid after melting, the transverse wave velocity decreases to zero. Whereas, the longitudinal and transverse wave velocities will first increase with the temperature when considering the formation pressure. After reaching the melting temperature, the wave velocity variation approximates to the no-pressure case. Therefore, for strata that have not reached the melting temperature, the variation of the longitudinal and transverse wave velocities of rocks is theoretically mainly influenced by the formation pressure [8,10].

In practical situations, however, the longitudinal wave velocity of subsurface rocks is strongly influenced by the porosity in addition to the lithology. In turn, porosity is influenced by both temperature and formation pressure. The porosity decreases with the increase in the formation pressure and, thus, the longitudinal wave velocity becomes larger with the increase in the formation depth. When the temperature increases, the change in porosity is influenced by two aspects. On the one hand, the minerals in the rock will close the original pore space by the thermal expansion with the increased temperature. On the other hand, the different coefficients of thermal expansion of the different minerals contained in the rock will lead to fractures due to uneven expansion when the temperature increases, thus leading to an increase in porosity. This is verified by the variation of transverse wave velocity with temperature in the petrophysical experiment in Figure 6. Furthermore, according to a large number of petrophysical experimental data, in granite, in a certain temperature range, the wave velocity generally increases slightly with the increase in the temperature. It starts to decrease slowly after reaching the peak. At about 500 °C with the transition from α- quartz to β-quartz, the wave velocity starts to decrease significantly. Granite wave velocity peaks in different regions have some deviations [27,28].

In the Gonghe Basin, the temperature at a depth of 4000 m is around 200 °C. Since the temperature of quartz transformation or rock fusion is not reached, the shift of longitudinal and transverse wave velocity with temperature is mainly due to the variation of porosity with temperature. However, there are many reasons for the change in porosity. How to bring out the effect of temperature on porosity becomes the key to performing temperature field prediction.

Changes in porosity due to other effects, such as formation pressure, often do not cause changes in the density of the matrix, so porosity tends to be negatively correlated with the density of the rock. In contrast, the porosity caused by the thermal expansion of the rock triggered by an increase in temperature becomes smaller due to the density of the matrix becoming smaller during thermal expansion. Thus, porosity is positively correlated with wave velocity and negatively correlated with the transverse wave. Petrophysical experiments have found that the physical properties that are lithologically similar are related to the temperature. The negative correlation between transverse wave velocity and density can be used to predict the temperature of a hot dry rock system. In addition, the physical property temperature test of granite samples proved that the variation of rock porosity with temperature is a closure–rupture–closure–rupture cycle. Its transverse wave velocity also shows fluctuations within a certain range, so it cannot be predicted quantitatively only based on the density and transverse wave relationship. Isotherms need to be drawn based on the trends of transverse waves and density. The temperature field prediction is extrapolated from the logged well temperature data.

Analysis of the logging temperature curves reveals that after passing through the superficial Quaternary overburden, the temperature curves can be approximated as three linear curves: above 1360 m, 1360–3500 m, and below 3500 m (Figure 16) [16]. Among them, the temperature is 100 °C at 1360 m for the stratification of granite and sedimentary rocks, while there is no obvious rock stratification at 3500 m. From the analysis above, it is judged that the specific heat capacity of the rock decreases due to the thermal expansion of the pore space caused by the temperature, and the temperature here is 180 °C. Comparison by GR-1 logging temperature curve shows that the curve trend also basically matches the linear distribution of the three sections [16]. The first inflection point occurs at the granite-sedimentary rock interface with a temperature of about 105 °C. A second inflection point appears at about 180 °C.

5.2. Combining Seismic Inversion Results for Temperature Field Prediction

Comparing the inversion results of density and transverse waves to obtain Figure 17 for analysis, it can be found that in most of the formations, the variation of transverse wave velocity and density are positively correlated. However, at 3500 m (180 °C)–3700 m (190°C) (2000–2050 ms) after logging, there are obvious laminar anomalies of decreasing density and increasing transverse wave velocity to a peak. The peak transverse wave velocity of the granite in the Gonghe Basin is approximately at the same temperature, and there is a significant decrease in wave velocity afterward, as found by the granite physical properties tests. Combining the inflection point of the temperature curve at 180 °C in the logging curve and the fact that the transverse velocity reaches its maximum, it is believed that the thermal expansion of the hot dry rock reaches its peak at this temperature, resulting in the closure of the pore space. The fluid accumulates here and cannot infiltrate, thus changing the thermal conductivity. As the temperature increases further, the thermal expansion causes the rock to rupture and the transverse wave velocity to decrease. Due to the high underground pressure, the porosity resulting from rock rupture is less than that of the petrophysical experiments. Thus, the decrease in the transverse wave velocity is not so obvious. Although 180 °C–190 °C is slightly higher than the 140 °C–160 °C interval in the petrophysical experiments, considering that the actual hot dry rock reservoir received other factors such as formation pressure, and there is no obvious anomaly from the logging temperature curve before 180 °C, we believe that the drop in transverse wave velocity occurring around 180 °C–190 °C is caused by rock fracture due to thermal expansion, just as the sudden drop in temperature at 140–160 °C in petrophysical experiments. A comprehensive analysis of the petrophysical experimental results and the temperature profiles of the two wells can conclude that the temperature at which wave velocity decreases occur in the hot dry rock reservoir in the Gonghe Basin is around 180 °C–190 °C.

According to the inference prediction of the logging temperature curve above, the upper and lower interfaces of this formation are 180 °C and 190 °C isotherms, respectively.

The thermal expansion due to high temperature can cause a large deviation of the porosity derived from the density of Equation (2) from the actual porosity. From Equation (1), the inverse transverse wave data can be converted into porosity data. Taking the Xline 229 profile as an example, the porosity derived from the transverse wave is subtracted from the porosity calculated by the inverse density, and the thermal expansion trend of granite can be obtained (Figure 18).

Observing Figure 18, it can be seen that the thermal expansion trend has obvious laminar characteristics, and in the transverse direction, the laminar extension trend is basically consistent with the previously predicted 180 °C and 190 °C isotherm trends. In the longitudinal direction, the trend of each layer is also basically the same, which is consistent with the temperature field distribution characteristics. Considering that the similar rock properties have the same trend with temperature but the values still differ. Therefore, the isotherm of thermal expansion change cannot be used as the isotherm directly. The extreme value of the thermal expansion trend in the vertical direction should be used as the temperature field isotherm. Extrapolate the logging temperature curve (Figure 19).

To further explore the distribution of the temperature field in three-dimensional space, the profile Inline 206 was analyzed in the same steps to obtain the temperature field data and then plotted the three-dimensional temperature field profile together with the Xline 229 temperature field data (Figure 20).

Combining with the location map of the work area (Figure 2d) to predict the temperature field distribution in the work area, it is found that the temperature of the hot dry rock in the work area is higher in the northeast than in the southwest at the same depth. It is thus judged that the 150 °C hot dry rock reservoir depth in the northeast is shallower than that in the southwest. From Figure 2b, it can be found that in the Chabchai area, the thermal storage cover of hot dry rock is mainly the Quaternary aquifer and the Neoproterozoic aquifer. Among them, the thickness variation of the Neoproterozoic aquifer is relatively gentle and can be regarded as almost constant in thickness in terms of the size of the work area, thus the variation of this layer of thermal storage of hot dry rock is mainly provided by the Quaternary aquifer. Furthermore, the interface between the Quaternary aquifer and the Neoproterozoic aquifer can be regarded as almost flat, so the thickness variation of the Quaternary aquifer is mainly related to the elevation of the ground surface. In addition, when the thermal storage cover is well insulated, the temperature at the bottom of the cover will be higher [29]. Combining Figure 2c and Figure 3, we can find that the northeast part of GH-01 logging and seismic work area is mountainous with obvious elevation increase, while the southwest part is subject to river erosion and has a lower elevation. It can be inferred that the Quaternary thermal storage cover in the northeast part of the work area is thicker than the southwest part and has better insulation performance, thus the temperature in the northeast part is also higher compared with the southwest part, which is consistent with the predicted results of temperature field. In addition, in the horizontal direction, the variation of the bottom depth is more obvious. We suggest that the change from hydrothermal to hot dry rock leads to a change of specific heat capacity and thermal conductivity of the rocks, due to less fluid, and thus to temperature difference.

6. Conclusions

A method to predict the temperature field distribution of hot dry rock is proposed that incorporates the physical properties of granite outcrop rock samples, logging data, and the integrated analysis of pre-stacked seismic inversion.

(1) Through petrophysical experiments, it was found that the porosity of hot dry rock under the influence of thermal expansion at high temperatures undergoes a change in the closure–rupture–closure–rupture cycle. Thus, the fluctuation law of transverse wave velocity influenced by temperature was found.

(2) The relationship between transverse wave velocity and porosity was fitted by petrophysical modeling and the analysis of logging data. The method of calculating porosity from density (Equation (2)) is based on a constant density of the rock matrix. The calculated porosity is biased by temperature due to the presence of thermal expansion in hot dry rocks. The porosity calculated from the transverse wave velocity (Equation (1)) is more consistent with the actual porosity. By subtracting the porosity calculated by transverse wave velocity from the porosity calculated by density, the trend of thermal expansion of the hot dry rocks can be obtained. Thus, the temperature can be predicted. The temperature field can be predicted by combining the results of transverse wave velocity and density obtained from the seismic inversion.

(3) The method is used to predict the temperature field of hot dry rocks in the Gonghe Basin. The results show that the northeastern part of the work area has a higher temperature at the same depth than that of the southwestern part. The northeast part is mountainous and has a significantly higher elevation. The thermal insulating cover is significantly thicker than that in the southwest. This is consistent with the predicted results of the temperature field.

The proposed method shows that seismic inversion can lead to the inference of the temperature field even if logging data are scarce.