Comparative study of estimating the Curie point depth and heat flow using potential magnetic data

1 Introduction

The measurements of heat flow (HF) are typically taken in boreholes that are widely spaced and unevenly distributed. Furthermore, subsurface and surface temperature variations, such as groundwater flow and long-term surface temperature variations, may affect HF measurements. In regions where HF measurements are not available, geochemical or geophysical methods can be used to infer the temperature at given depths indirectly. Geochemical methods comprise helium isotope ratios [1] and silica concentration [2] in hot springs. Geophysical approaches involve magnetics, magnetotellurics (MT), and seismic velocity estimates from tomographic studies. However, MT and seismic methods do not provide direct temperature estimates, but rather indirect evidence for lower electrical resistivity or seismic P-wave and S-wave velocities that may indicate higher HF. However, the magnetic method can be used to estimate the Curie point depth (CPD) by determining the bottom of the magnetic sources [3,4,5,6,7,8,9,10]. However, using the CPD to determine HF is still problematic because the bottom of the magnetic sources may reflect mineralogical variations rather than temperature. As a result, the bottom depth estimation from magnetic interpretation methods is not accurate [7,11,12]. In addition, the CPD may be affected by the Curie temperature of the magnetic minerals [13].

There are several methods for determining the depth to the bottom of magnetic sources, and these approaches are classified into two different categories [7]. The spectral method is the most widely used technique, in which the depth is estimated by determining the spectrum due to either an isolated magnetic anomaly using one-dimensional (analysis done along a profile) spectral methods [4] or the two-dimensional (2D) (analysis done on a grid of data) azimuthally averaged power spectrum (power spectrum method) of a region of magnetic data [3,5,6,7,14,15]. When considering the power spectrum methods, there are several techniques to determine a top and bottom of a magnetic susceptibility (magnetization distribution) source including the centroid method, forward modeling, spectral peaks, and fractal methods [15,16,17]. These methods assume different magnetization distributions which include random sources for the spectral peak and forward modeling techniques, statistical magnetization ensembles for the centroid method and fractal sources for the fractal methods [15,16,17]. All of these methods have been extensively used; however, Maus and Dimri [18] have demonstrated that these methods have limited depth information when they are not used correctly. The other techniques of determining the magnetic source depth is the forward modeling or inversion of the isolated magnetic anomalies [19,20,21]), or three-dimensional (3D) inversion of magnetic data [22,12]. However, the spectral and modeling methods are robust when the estimated depths are constrained and must be validated by other geological and geophysical results [11].

To apply either the spectral and/or the modeling methods, it has been common to process the magnetic data due to the dipolar nature of the data. This is done by applying the reduction to the north magnetic pole operator (RTP) or the reduction to the equator operator (for low latitude data) to the total magnetic intensity data (TMI) to correct the shape and the location of magnetic anomalies above their causative bodies. However, this process had been shown to be unnecessary to determine the CPD [23]. Okubo et al. [24] and Zhou and Thybo [25] have shown, from numerical experiments, that there are insignificant differences between the depths to the bottom of the magnetic sources obtained using RTP versus not using this method. Thus, several studies have estimated the CPD directly from the TMI data [26,27,28] and other studies have used RTP magnetic data [29,30,31,32,33,34,35,36,37].

Magnetic anomalies either from TMI or RTP data are usually produced by a combination of shallow and deep crustal magnetic sources, or shorter and longer wavelengths [38]. Usually, estimating the CPD is related to the deeper magnetic sources; the CPD estimated without removing the shorter wavelength anomalies may affect the final CPD especially for the spectral methods. Several studies using spectral methods have not removed the shorter wavelength magnetic anomalies [27,28,37], while other studies have attempted to remove the shorter wavelength anomalies [29,30,33,36,39,40]. The removal of the shorter wavelength anomalies depends on a variety of factors including the geological setting of the region and the amount of noise in the data. Our study area consists of a thin (maximum of 2 km) sedimentary layer over portions of the peninsula and no sedimentary cover over other parts [41]. Since the Sinai Peninsula does not have a thick sedimentary layer, removing the shortwave length anomalies may enhance imaging the CPD.

The present study compares the estimated CPD and HF values, which resulted from the application of the spectral analysis technique to the TMI and RTP data. Additionally, the effect of the wavelength filtering on the estimation of the CPD was tested. We used ground TMI data, which is described below, from the Sinai Peninsula to validate the above effects.

2 Geologic and thermal setting of Sinai Peninsula

The Sinai Peninsula has a land area of about 61,000 km² and is bounded by the Suez Gulf and the Aqaba Gulf-Dead Sea Fault System [42] (Figure 1). The active boundaries of the Sinai Peninsula and the rock distribution patterns from the Precambrian to Recent have been governed by alternating series of compressional and extensional events [43,44]. The Neoproterozoic basement complex of granite, schists, and gneisses was formed during the closure of the Mozambique ocean with the accretion of Arabian-Nubian craton terranes [43,45,46]. Lying above the basement complex is a series of Cambrian to Recent sedimentary units that were formed by a series of compressional and extensional tectonic events. These tectonic events include the opening of the Tethys Ocean in the early Mesozoic era, the Syrian Arc system that produced compression structures in the Late Cretaceous to Early Tertiary [47], the extensional tectonic in the opening of the Gulf of Suez (Late Oligocene to Early Miocene), and the Gulf of Aqaba (Pliocene) [44,48].

Figure 1

Geologic map of the Sinai Peninsula from Egyptian Geological Survey and Mining Authority (EGSMA) [49].

Several detailed geological and tectonic studies of the Sinai Peninsula have been undertaken since the discovery of oil and mineral resources [42,50,51,52,53,54,55]. The Sinai Peninsula, in general, consists of Paleozoic, Mesozoic, and Tertiary sediments overlying Proterozoic metamorphic and igneous lithologies (Figure 1). Near 29°N, there is a narrow region of Paleozoic sediments (Carboniferous to Lower Cretaceous) that overlie the Neoproterozoic basement rocks. The northern and central portions of the Sinai Peninsula are covered by Mesozoic and Tertiary sediments (marl, chalk, limestone, and shale) with a thickness of approximately 2,000 m [50,56,57].

Of importance in this work are the previous geothermal studies in the Sinai Peninsula. Extensional tectonic events since the Late Oligocene thinned the crust, and a series of mostly olivine diabase reached the surface or near surface and formed intermittent lava flow, sills, and dykes [58]. Thermal activity related to this rifting is manifested by hot springs (Ras Sidr, Oyun Mousa, Hammam Pharaoun and Hammam Mousa) with temperatures varying from 35 to 72°C. These springs are clustered along the eastern shore of the Suez Gulf [58]. For example, the Miocene groundwater aquifer at Oyun Mousa is located at a depth of around 300 m, making it ideal for extraction. Meanwhile, the aquifer is deeper and thicker at Hammam Faraun hot spring. At the hot spring area, the hot water is circulated at great depths and seeps to the surface through fault planes [59].

3 Data and methodology

3.1 Data

A regional ground based magnetic survey was conducted on the Sinai Peninsula between 1991 and 1998 as part of an Egyptian development and exploration project. The data were collected with spacing between 3 and 5 km in accessible areas, whereas the station interval increases within the higher terrains. Therefore, the aliased power fraction expected from the survey is less than 1% [60], indicating that the data are of high quality and suitable for achieving the objective of this study. Two proton precession magnetometers (Geometrics G856 and a Scintrex ENVI) were used to collect the data [61]. The Geometrics magnetometer with an accuracy of 1 nT was used when collecting the field data, while the Scintrex magnetometer with an accuracy of 0.1 nT was used as a base station to account for the diurnal variations. International Geomagnetic Reference field (IGRF) correction was applied to remove the effect of the main magnetic field. Then, the magnetic data were diurnally processed and gridded, using a spacing of 1,000 m to produce a total field magnetic map (Figure 2a).

Figure 2

Magnetic maps of the Sinai Peninsula: (a) total magnetic intensity, the sporadic black circles throughout the map refer to the magnetic stations, (b) reduced to the north magnetic pole, (c) 20 km LP filtered map of the TMI data, and (d and e) LP maps of RTP using 40 and 20 km, respectively. The centers of the analyzed regions are depicted as solid white circles and topped by white numbers from 1 to 14 in (a). All maps are superimposed by the triangle of the exposed basement rocks and other major structural elements.

3.2 Methodology

The spectral analysis of magnetic anomaly data is fundamental in CPD estimation. Spector and Grant [3] described the basics of the 2D spectral analysis method, in which the depth to the top of the magnetized rectangular prisms (Z _t) is estimated from the slope of the log power spectrum. Bhattacharyya and Leu [4,62] further calculated the depth of the centroid of the magnetic source bodies (Z ₀). Okubo et al. [24] developed an approach for estimating the bottom depth of the magnetic bodies (Z _b) using the spectral analysis method of Spector and Grant [3].

Tanaka et al. [7] proposed an approach assuming that: (1) the layer extends infinitely in all horizontal directions, (2) the depth to the top of the magnetic source is much smaller than the magnetic source dimensions, and (3) the magnetization M (x, y) is a random function of x and y. Blakely [63] introduced the power density spectra of the total field anomaly data ∅ Δ T :

∅ Δ T ( k x , k y ) = ∅ M ( k x , k y ) × F ( k x , k y ) ,

(1) F ( k x , k y ) = 4 π 2 C m 2 ∣ θ m ∣ 2 ∣ θ f ∣ 2 e − 2 ∣ k ∣ Z t ( 1 − e − ∣ k ∣ ( Z b − Z t ) ) 2 ,

where ∅ M is the power–density spectra of the magnetization, C _m is a proportionality constant, θ _m and θ _f are factors for magnetization direction and geomagnetic field direction, respectively. Z _b and Z _t are basal and top depths of the magnetic source, respectively.

By expressing all terms except ∣ θ m ∣ 2 and ∣ θ f ∣ 2 that are radially symmetric and the radial averages of θ _m and θ _f are constant, the equation (1) can be simplified. If M (x, y) is completely random and uncorrelated, and ∅ M (k _x , k _y ) is constant, the radial average of ∅ Δ T is:

(2) ∅ Δ T ( ∣ k ∣ ) = A e − 2 ∣ k ∣ Z t ( 1 − e − ∣ k ∣ ( Z b − Z t ) ) 2 ,

where A is a constant and k is a wavenumber.

For the wavelengths of less than about twice the thickness of a layer, equation (2) can be rewritten as:

(3) ln [ ∅ Δ T ( ∣ k ∣ ) 1 / 2 ] = ln B − ∣ k ∣ Z t ,

where B is a constant.

The depth to the top of a magnetic source (Z _t) could be estimated by fitting a straight line through the intermediate to high wavenumber part of the radially averaged power spectrum. Also, equation (2) can be rewritten as,

(4) ∅ Δ T ( ∣ k ∣ ) 1 / 2 = C e − ∣ k ∣ Z 0 ( e − ∣ k ∣ ( Z t − Z 0 ) − e − ∣ k ∣ ( Z b − Z 0 ) ) ,

where C is a constant.

For long wavelengths, equation (4) can be rewritten as,

(5) ∅ Δ T ( ∣ k ∣ ) 1 / 2 = C e − ∣ k ∣ Z 0 ( e − k ( − d ) − e − ∣ k ∣ ( d ) ) ≈ C e − ∣ k ∣ Z 0 2 ∣ k ∣ d ,

where d is the thickness of the magnetic source. From equation (5), it can be concluded that:

(6) ln { [ ∅ Δ T ∣ k ∣ 1 / 2 ] / ∣ k ∣ } = ln D − ∣ k ∣ Z 0 ,

where D is a constant.

Similarly, the depth to the centroid of the magnetic source Z ₀ can be estimated from the straight line fitted with the lowest-wavenumber part of the radially averaged power spectrum curve.

Okubo et al. [24] and Tanaka et al. [7] developed a formula that combines the depths of the top and centroid to yield the basal depth of the magnetic source as shown below:

(7) Z b = 2 Z o − Z t .

The depth to the bottom of the magnetic source (Z _b) is assumed to be the CPD [4,24], where the ferromagnetic minerals are transformed to paramagnetic minerals (at a temperature of approximately 580°C [853°K]).

In this work, the effect of the RTP transformation and wavelength filtering on estimating CPD was investigated. The TMI data were reduced to the north magnetic pole. Then, LP wavelength filtering was applied to both the TMI and RTP magnetic data. The study area was divided into 14 overlapping regions, each with dimensions of 100 km × 100 km, taking into account the relationship between the window size and the thermal regime of the area. In high HF areas, the window size should be small enough to estimate the HF where the CPD is expected to be shallow. In contrast, in low HF areas, it should be large enough to estimate deeper CPDs [15]. Several window sizes were tested by applying the power spectrum method, and the appropriate length was selected based on the criteria of the minimal block size that does not cut off the spectral peak [11]. The windows with sufficient widths were used to detect the deepest possible magnetic source which may be mineralogical or related to HF. The overlapped length is 50 km, and the central point of a region is used to represent Z _b of that region. The top of a magnetic source (Z _t) is first assessed by fitting a straight line through the intermediate to high wavenumber portions of the power density spectral curve, while the depth to the centroid (Z ₀) of a magnetic source is obtained from the lower wavenumbers of power density spectra. The basal depth of a magnetic source (CPD) is then estimated by substituting into equation (7).

Additionally, the geothermal gradient (GG) between the Earth’s surface and the CPD (Z _b) can be estimated using (Tanaka et al. [7]; Stampolidis and Tsokas [64]; Maden [31]):

(8) G G = 580 ° C / Z b ,

where 580°C is the Curie temperature for magnetite [65].

From the estimated GG and Z _b, the HF (Q) can be estimated [7,66]:

(9) Q = λ ( 580 ° C / Z b ) ,

where λ is the coefficient of thermal conductivity.

Classical techniques of statistics, such as correlation coefficient (CC), residual sum of squares (RSS), and the root mean square error (RMSE), can be applied to describe the similarity between the estimated CPDs derived from different magnetic data sets. The CC in the simplest form (Pearson product, equation (10)) was used to find how strong a relationship is between data. It has a value between 1 and –1, where the larger the number, the stronger the relation.

(10) C C = ∑ ( x i − x ¯ ) ( y i − y ¯ ) ( x i − x ¯ ) 2 ( y i − y ¯ ) 2 ,

where, x i is x variable data (the CPDs estimated from a specific type of magnetic data), y i is the corresponding y variable data (the CPDs estimated from another magnetic data form), and x ¯ and y ¯ are the mean CPD values derived from both the datasets.

The RSS (equation (11)) is a formula for calculating the difference between data and an estimation model (linear regression). A small RSS indicates a close fit of the model to the data.

(11) RSS = ∑ i = 1 n ( y i − x i ) 2 ,

where, x _i and y _i are the corresponding CPDs estimated from two different magnetic data.

Finally, the RMSE or variance (equation (12)) is frequently used to measure the differences between the measured and predicted values.

(12) RMSE = ∑ i = 1 N ( x i − y i ) 2 / N 1 / 2 ,

where x _i and y _i are the corresponding CPDs estimated from two different magnetic data.

A flowchart (Figure 3) was created to summarize the applied research methodology and how the data were analyzed.

Figure 3

A flowchart summarizing the applied research methodology.

4 Results and interpretation

Magnetic anomalies are commonly caused by the presence of magnetic minerals (usually magnetite) in the rocks from the surface to lower crustal depths and/or the local geothermal gradient. The depth depends on the HF in the region as magnetic minerals lose their ability to induce a magnetic field at the CPD. Longer wavelength anomalies are commonly related to deeper magnetic bodies or the CPD, while the shorter wavelength anomalies are correlated to the near-surface geologic structures. Within the Sinai Peninsula, the majority of the central and northern portions of the peninsula are covered by nonmagnetic Paleozoic and younger sedimentary rocks and thus, the TMI map basically reflects magnetic mineralogy variations within the Proterozoic basement rocks (Figure 2a). To remove the dipolar effect of the Earth’s magnetic field, the TMI data were reduced to the north magnetic pole using the RTP transformation with declination and inclination angles of 3 and 42°, respectively, as shown in Figure 2b. Examining the RTP map (Figure 2b) and based on the size and orientation of the magnetic anomalies, the Sinai Peninsula is broken into two geologic districts with the two regions being separated by the Themed Fault (Figure 1) at approximately 30°N, which was formed during the orogeny that formed the Syrian Arc [47]. The southern half contains anomalies that have high amplitudes and short wavelengths that primarily trend east-west (Mediterranean trend), northeast (Aqaba trend), and northwest (Suez trend). These anomalies are mostly correlated with the exposures of the Proterozoic igneous and metamorphic rocks. Moreover, the circular patterns of several of the RTP anomalies are related to the strike slip faulting, which is associated with the formation of the Gulf of Aqaba [67]. Conversely, the northern portions of the TMI and RTP maps have an east-trending of the long wavelength magnetic minima that is related to the Raqabet El-Naam shear zone [68].

To investigate the effects of removing shallow magnetic sources on the determination of a CPD, LP wavelength filtering was applied to the TMI and RTP magnetic data. A LP filter was applied to the TMI data where all anomalies with wavelengths less than 20 km were removed (Figure 2c). Then, LP wavelength filters were applied to the RTP data where all anomalies with wavelengths less than 40 and 20 km were removed (Figure 2d and e, respectively). These LP wavelength filters effectively smooth the TMI and RTP maps by removing the effects of the shallow magnetic sources, most notably in the region that has extensively exposed or shallow Precambrian basement rocks. However, excessive filtering may have a great effect on the CPD calculation, hence determining the threshold cut-off wavelength value should be controlled by the geologic context of the study area.

All the TMI, RTP, and LP wavelength filtered magnetic maps were divided into 14 overlapped square regions to estimate the CPD, GG, and HF, using the method of Okubo et al. [24]. The top of a magnetic source is determined from the plot of the radially averaged power density spectra [ln(ɸ_∆T (|k|)^1/2)], where a straight line is fitted through part of intermediate to high wavenumbers (commonly within the range of 0.11–0.34 rad/m). Similarly, the centroid depth of a magnetic source is determined, where [ln(ɸ_∆T (|k|)^1/2)/|k|] is plotted, and a straight line is fitted through the portions of lower wavenumbers (commonly within the range of 0.001–0.06 rad/m). The basal depth of the magnetic source is then calculated using equation (7). The challenging issue of using the spectral methods is determining which selective wavenumbers (within the same window) can be considered for estimating the top and centroid depths, as the segments of different slopes yielding different depths [11]. Each window in each magnetic data set has its own power spectrum pattern, and consequently, using the same wavenumber ranges for all analyses may not be appropriate. Furthermore, the use of different transformed magnetic datasets in this study necessitated the selection of different wavenumber intervals for calculating the CPD.

Figure 4 illustrates the power spectrum curves for regions 1 and 10 as typical examples to estimate the depths. Tables 1–5 exhibit the estimated depth to the bottom of the magnetic sources (Z _b), as well as GG and HF values for each squared area as applied to different magnetic data. Table 1 shows that the CPD values, which are determined using the TMI magnetic data, ranges from 14.37 km for area 1 to 26.95 km for area 9. Subsequently, the GG and HF were found to vary from 20.41 to 38.28°C/km and from 51 to 95.7 mW/m², respectively. The RTP magnetic data yielded CPD values, ranging from 14.21 km for area 1 to 28.21 km for area 9, with GG and HF varying from 19.49 to 38.69°C/km and from 48.73 to 96.74 mW/m², respectively (Table 2). Table 3 shows the CPD, GG, and HF values using the TMI LP wavelength filtered data. The CPD varies from 14.99 km for region 2 to 24.8 km for region 11. Consequently, the GG and HF vary from 22.17 to 36.7°C/km and from 55.41 to 91.75 mW/m², respectively.

Figure 4

Examples of the two-dimensional radially average power spectrum analysis of the TMI data (a1 and a2), 20 km LP filtered TMI data (b1 and b2), reduced to the pole data (c1 and c2), 40 km LP filtered RTP data (d1 and d2), and 20 km LP filtered RTP data (e1 and e2). Z _t– depth to the top of a magnetic source, and Z _o– depth to the centroid of a magnetic source. Red and blue lines are best fit slopes.

Tables 4 and 5 show the CPD, GG, and HF values, which are derived from applying spectral analysis on the RTP LP wavelength filtered data using wavelengths 40 and 20 km, respectively. The wavelengths used had a significant impact on the estimated CPD as the 40 km LP filter yielded CPDs varying from 24.69 km for region 13 to 39.7 km for region 11. Additionally, the estimated HF values were reduced to a range from 34.63 to 55.69 mW/m². In contrast, the 20 km RTP LP wavelength filter decreased the CPD to a range from 14.71 to 28.65 km, while increasing the HF range from 48 to 93.5 mW/m².

The estimated CPD and HF values obtained using the different transformed magnetic data and plotted at the center of each region were subsequently regridded and contoured to prepare CPD and HF color image maps (Figures 4 and 5, respectively). The centers of the analyzed regions are denoted by solid black circles. Figure 5a shows that the CPD estimated from the TMI data has a minimum depth of 14 km in the southern portion of the Sinai Peninsula, whereas the maximum depth of 27 km is located in northwestern portion of the peninsula. The CPDs in general decrease both toward the east and the south. Likewise, the CPDs estimated from the RTP magnetic data (Figure 5b) agree with the depths, with the depth decreasing trends as those imaged with the TMI data as shown in Figure 5(a). The CPDs derived from 20 km LP wavelength filtered TMI data as shown in Figure 5(c), range from 15 to 25 km and reflect a similar depth pattern in the southern Sinai as in Figure 5(a and b). Also, all three figures show an increase in the CPD toward the East. The 40 km LP wavelength filtered RTP data, as shown in Figure 5d, indicates the CPD values differ from the other estimated depths. The southern Sinai Peninsula has deeper CPD values than the TMI, RTP, and 20 km LP wavelength TMI maps (Figure 5a–c) with maximum value of approximately 40 km. The shallow CPD values (<25 km), which are shown in Figure 5a–c, were not imaged on Figure 5d. Additionally, the decreasing trend of the CPD values differs, as it decreases from the eastern to the western portion of the peninsula. Throughout the Sinai Peninsula, the CPD values are deeper than those determined by the other data. Figure 4e shows the CPD values using the 20 km LP wavelength RTP data, and the depth amplitudes and trends are similar to Figure 5a–c.

Figure 5

CPDs determined using: (a) the TMI data, (b) the RTP data, (c) 20 km LP filtered TMI data, (d) 40 km LP filtered RTP data, and (e) 20 km LP filtered RTP data. Black circles represent the centers of the analyzed regions. All maps are superimposed by the triangle of the exposed basement rocks and other major structural elements.

The HF maps (Figure 6a–e) reveal an inversely proportional relationship with the corresponding CPD maps. The HF values determined from the TMI data range from 50 to 96 mW/m², and increase from the northwest to the eastern and the southern regions (Figure 6a). The HF values derived from the RTP data range from 48 to 97 mW/m², and the distribution pattern is similar to that obtained from the TMI data as demonstrated in Figure 6b. The LP wavelength filtered TMI data yielded HF values varying from 55 to 92 mW/m² as shown in Figure 6c. The middle part of the Sinai Peninsula is characterized by low HF. In contrast, the 40 km LP wavelength filtered RTP data is characterized by a lower HF values (from 35 to 56 mW/m²) for the whole peninsula (Figure 6d). However, there is an obvious increase in the HF from the western and the eastern portions of the peninsula toward the northern and southern portions as shown in Figure 6d. The HF values determined using the 20 km LP filtered RTP data range from 48 to 93 mW/m² as shown in Figure 6e. In general, Figure 6e indicates similar trends as those determined in Figure 5a–c.

Figure 6

Heat flow values determined using: (a) the TMI data, (b) the RTP data, (c) 20 km LP filtered TMI data, (d) 40 km LP filtered RTP data, (e) 20 km LP filtered RTP data, and (f) the available HF data [69,70,71]. Black circles represent the centers of the analyzed regions. All maps are superimposed by the triangle of the exposed basement rocks and other major structural elements.

5 Discussion and conclusion

The effect of applying RTP and LP wavelength filtering on the estimation of CPD and the HF was investigated. LP wavelength filters that passed wavelengths greater than 20 km were applied to TMI and RTP data over the Sinai Peninsula, while the 40 km LP wavelength filter was also applied to the RTP data. The data were divided into a 100 km × 100 km square area overlapped with 50 km, and 2D radially averaged spectral analysis was applied to estimate the bottom of a magnetic source. To be consistent between the different magnetic datasets, different intervals within the intermediate and high wavenumbers (>0.1 rad/m), and low wavenumbers (<0.06 rad/m) were used for estimating both Z _t and Z ₀, respectively.

The resultant CPD maps indicate that similar results were found using either the TMI or RTP data. Additionally, applying a small wavelength LP filter (e.g., 20 km) on both TMI and RTP data slightly modified the estimated depths, to a degree the trend in the depth variations compared to what was found for the TMI or RTP data. The CPDs derived from 20 km LP wavelength filtering applied to TMI and RTP data are of approximately the same range (from 15 to 25 km) and spatial distribution. Conversely, applying a higher LP wavelength filter (e.g., 40 km) had a significant effect, as the depths increased for the entire studied area reaching unreasonable values which sometimes exceeded the Moho discontinuity (32–36 km) [55]. This validates that removing the short-wavelength anomalies may be appropriate if the area is highly affected by volcanic rocks as in the present case. However, excessive filtering using high cut-off wavelengths adversely affects the depth calculation and may lead to spurious and extraneous depths. A statistical analysis was attempted and involved in creating the CCs (Table 6), the RSSs (Table 7), and the RMSE between the various depth results to determine the preferred transformed magnetic data utilized for estimating the CPD and HF. Table 6 displays the CC between the various depths, and indicates that both TMI and RTP data produced similar results, which were well correlated (CC = 0.9616). Moreover, the calculated RSS and RMSE between TMI and RTP depths were 44.7 and 1.78, respectively suggesting comparable results. This result can be related to the fact that the centroid method depends mainly on the wavenumber factor, which undergoes only a slight variation when applying the RTP processing procedure. Additionally, the spatial shift in the CPD due to applying the RTP transform is small when compared with the utilized window size. The CC and RSS between the depths derived from the RTP and 20 km LP wavelength filtered RTP magnetic data were 0.8266 and 116.7 respectively, indicating that the calculated depths are similar with minor differences. On the other hand, the CC between the depths obtained from the 20 km LP filtered TMI and the TMI was 0.6356, indicating that the LP filtering of TMI data using small wavelengths slightly affects the final results. In contrast, the CC values between the depths of 40 km LP wavelength RTP data and those derived from all other magnetic data forms are very low as shown in Table 6. Furthermore, the RSS between the CPD results for the 40 km LP wavelength data with that of the TMI and RTP derived depths are 3330.3 and 2860.9, respectively (Table 7) and the RMSEs are 15.42 and 14.3, respectively. These values indicate that the estimated CPDs from the 40 km LP wavelength RTP magnetic data are unreliable results for the entire study area especially in the southern part, where the basement terrains are located. This result can be interpreted by the effect of a longer LP wavelength filter that eliminates a portion of the deeper magnetic layer. The use of the longer wavelength filter led to an error in the estimation of both Z _b and Z ₀.

A comparison was carried out between the estimated HF from all magnetic datasets except the 40 km LP wavelength RTP, and the available HF data within the western, southern, and the eastern portions of the Sinai Peninsula [69,70,71]). Feinstein et al. [69] and Morgan et al. [70] used the data from the bottom hole temperature and recognized that the topmost part of the Gulf of Suez (Suez city) is characterized by low HF with a value of 40–52 mW/m² that increases southward, reaching 80 mW/m² in the Ras Garra area (Figure 6f). Further to the eastern part of Sinai Peninsula, Girdler and Evans [71] showed that the median value of HF along the Gulf of Aqaba is approximately 92 mW/m². This result indicates that our HF values agree with previous results in the individual values and regional distribution. Previous magnetic-based CPD studies indicate a range of CPDs as El-Qady et al. [59] divided the Sinai Peninsula into 5 blocks, and their estimated CPDs were determined from magnetic data, which ranged from 6 to 20 km. Aboud et al. [72] divided the Sinai Peninsula into 9 regions and analyzed magnetic data to determine the CPDs that ranged from 14 to 24 km. In terms of depth range, our results, particularly the depths derived from 20 km LP TMI and 20 km LP wavelength RTP, are generally consistent with the latter study.

To validate the outcomes of this study, the seismic activity of Sinai Peninsula in the period between 1995 and 2007 [73] was correlated with the HF maps derived from TMI, RTP, 20 km LP wavelength TMI, and 20 km LP wavelength RTP magnetic data (Figure 7a–c, respectively). The depth-based variation classifies the earthquakes into three categories, which are denoted by colored star symbols. According to the seismicity data [73], the majority of earthquakes have depths ranging from 15 to 25 km (red symbols in Figure 7), which is completely consistent with the Curie isotherm surface derived from magnetic data specially 20 km LP wavelength TMI and 20 km LP wavelength RTP. Furthermore, the earthquake depths are mostly shallow along both the Gulfs (Aqaba and Suez) and in the southern part, and can be correlated with the estimated CPDs. In terms of the distribution of earthquakes, significant variations in earthquake activity surrounding the Sinai subplate from west to east can be observed. However, the earthquakes are well clustered along the Gulf of Suez and the Gulf of Aqaba, and confined to the southern part of Sinai Peninsula, primarily south to latitude 29°30′N. These regions exhibit HF values that are typically greater than 80 mW/m². Conversely, the northern part of Sinai Peninsula shows low HF and few numbers of recorded earthquakes during the same time period. The only exception is the northeastern part which displays HF values ranging from 75 to 82 mW/m² and low number of earthquakes. These indicate that the seismic activity may be the primary cause of thermal accumulation.

Figure 7

Correlation and superposition of seismicity data of Sinai Peninsula recorded by Egyptian National Seismic Network (ENSN) in the time period from 1995 to 2007 with the heat flow maps derived from: (a) the TMI data, (b) the RTP data, (c) 20 km LP filtered TMI, and (d) 20 km LP filtered RTP data.

There is a lack of deep seismic studies on the Sinai Peninsula with only four seismic refraction profiles just to the north of the study area [74] and a surface wave dispersion analysis along one profile [41]. The surface wave analysis only found general depths to velocity interfaces with a depth of 2 km of the sedimentary units and a 31 km thickness of the crust. A gravity based analysis to determine the crustal thickness is shown in Figure 8 [55]. In all cases, the CPD values are shallower than the crustal thickness values but there are similarities in the shape of the two maps. The thicker crustal regions in the northwest and eastern parts of the Sinai Peninsula are associated with deeper CPD values, while the thinnest crustal region (south) is associated with shallow CPD depths.

Figure 8

Gravity based Moho depth map of the Sinai Peninsula [55].

Our results demonstrate that either the TMI or RTP data can be used to determine the CPD and subsequent HF. We used land-based magnetic data and the process of LP filtering of the data, which slightly affects the calculation of the CPD, if the wavelength is not too large. We did not test the effect of using airborne magnetic data but since the data is collected at certain heights above the surface, LP filtering may not be needed as short wavelength anomalies are already removed. However, the calculation of the HF from the airborne and satelite-based magnetic data is our forthcoming work.