Depth-to-Basement Estimates Using Magnetic Data of the Iraqi Southern Desert: A Statistical Approach

Regions characterized by a considerable thickness of sedimentary cover situated on a basement complex are always interesting. These regions require accurate basement data that includes defining the locations of high thicknesses in sedimentary beds (the basins). The Southern Desert of Iraq is one of these regions that is still subject to more detailed studies concerning basement geology. Utilizing the magnetic data, we present five depth-to-basement maps using techniques that hold different theoretical assumptions and model characterizations. Further, we have obtained a sixth map using a statistical approach which is built on the selection of depth-position points that have depths confirmed from the five maps. These points are chosen along depth profiles whenever the depth curves, of the depth-to-basement maps, are met or clustered referring to close depth estimations. The derived map could be more reliable than the other five maps and may be used to suggest drilling boreholes in areas of shallow basement. The minimum estimated depth-to-basement is ~4.5 km. Moreover, the derived map shows the locations and depths of deep sedimentary basins that reach 10 km deep.


Introduction
Interpretation of magnetic data is mainly focused on a specific target such as depth estimation of magnetic sources [1].The depth of a crystalline basement and mapping the basement relief or basement structures has been around since the middle of the last century (e.g.[2]; [3]).However, basement fabric determines the boundaries of the overlain sedimentary basins that are the primary targets during the reconnaissance stage of hydrocarbon and mineral explorations.Historically, Fourier transform and automated techniques of 2D and 3D (moving a window over gridded data) rapidly advance the interpretation of magnetic data giving a wide range of interpretation methods.The methods differ in their accuracy, complexity, and sensitivity to anomaly interference and noise [4] and sometimes give results that are only accurate when the type of magnetization is induced and when the magnetic source is of specific geometry.
The study area is the Southern Desert of Iraq, situated in the stable part of the Arabian Platform known as the Stable Shelf (Figure 1) characterized by a deep basement and thick overburden of sedimentary layers [5] where many oilfields were discovered in the region.Different geological structures were determined in the Precambrian basement of the study area including normal, en-echelon, strike-slip faults, and graben systems that reflect the tectonic evolution of this part of the platform [6].Generalized studies to estimate depths of crustal structures including depth-to-basement and Moho Discontinuity have been carried out by [7; 8] utilizing inversion of receiver functions of teleseismic P-and S-waves, and also Pand Rayleigh-waves [9] velocities and phases.They showed that the estimated depth-tobasement is ~12 km within the Transition Zone in two regions located about 80 and 110 km away from the northern border of the study area.They concluded that such estimations may coincide with the stable part of the platform.1300 (2024) 012004 IOP Publishing doi:10.1088/1755-1315/1300/1/012004 2 Getting an accurate depth-to-basement map from potential data, especially magnetic is therefore an essential aim.In this contribution, we applied the Tilt-depth (Td) [10], analytic signal (AS) [11;12], Werner deconvolution (WD) [13], source parameter imaging (SPI), and reliable Euler devolution (RED) [14; 15] methods to magnetic data of the Southern Desert and obtained five depth-to-basement (DTB) maps.Then, we present a DTB map, which is derived from these maps, and could be more reliable than other maps.The procedure of deriving the introduced map can be applied worldwide especially in stable parts of platforms.

Figure 1.
Tectonic map of Iraq with the boundaries of the Southern Desert in blue (after [16].The top-location map shows the position of the study area as red filled polygon.

Theoretical background
For an inclined magnetic contact, the expressions of the horizontal and vertical gradients (HG and VG) of an anomaly (B) are given by [11] as where S = contrast in magnetic susceptibility, f = magnetic field and c =1-cos 2 i sin 2 α, α = angle between the + h axis and the magnetic north, and i = inclination of f, tan I = tan i/cos α, 3 P = dip measured from +h axis, Zc = depth to the top of contact.The trigonometric expressions in degrees.For a profile; h = 0 is immediately above the edge.[11 and 12] decomposed the 2D magnetic anomaly field (along a profile), in the wavenumber domain using the analytic signal transformation, into real component equal to the HG ( The Td method was suggested by [10], which uses the tilt angle (θ) defined by [17] as: Where gradient in the vertical direction (z).The Td assumes that the magnetic sources have vertical contacts and the magnetization is vertical (this is satisfied by using RTP-transformed data).Eqs. 1 and 2 of dipping contact expression given by [11] are used by [10] to show that when there is a vertical contact and f is at 90°, the HG and VG are written as VG= 2 S f c h h 2 +Z c 2 (6) where h = lateral location to the top of contact (at the contact h = 0).By substituting Eqs. ( 5) and ( 6) in (1) will obtain [10] Eq. ( 7) refers to the value of θ immediately over a contact i.e. the ( h) = 0 is 0° and is 45° or +0.7854 radiant (rad) when h = Zc (is -45° or -0.7854 rad when h = -Zc), which means the zero contours of the θ could define the location(s) of the contact(s), whilst by measuring the distance between either +45° contour (or the -45° contour) and the zero contour, the depth of contact-like structures can identify.The distance should be measured perpendicular to the strike [10].The lateral edges of magnetic source interpreted by [13] through collecting the effects of thin sheets-like bodies (for 2D thin dikes) that extend to infinity in depth (a width < Z (for sheet).The total magnetic field anomaly profile (ΔBT) is expressed as: Where h= distance on the profile, h0 = lateral location of the dike's top, the constants E and R are functions of the dip of the dike, magnetic susceptibility (S), inclination (i) and declination (d) as stated by [13].
Euler Deconvolution (ED), however, is re-written by [14] where (x, y, z) = location of measuring station and xo, yo and zo = the location of source, ɳ = structural index (SI) based on source geometrical (shape) and b is the fied background or the base level.
Eq. ( 9) can mathematically be treated as a linear equation of four variables i.e. xo, yo, zo and ɳ.However, the SI (ɳ) can be chosen tentatively.A standard matrix inversion is used to solve (deconvolution) Eq. ( 9) by the automatic moving-data windows approach.A window size not less than double of the grid spacing and larger than one-half the expected depth of exploration are recommended by [14].The SI (ɳ) is an assumed integral number that ranges between 0 and 3, where 0 for a contact/fault, 1 for a dike, 2 for a vertical intrusion and 3 for a spherical source.
A recent approach is known as Reliable Euler Deconvolution (RED) presented by [15] suggest using the standard deviation of the VG as a criterion to eliminate the reliable solutions of Euler deconvolution.They chose the sliding-windows with the higher standard deviation and plot the related solutions for each SI.The correct SI is selected depending on the tightest cluster of position-source solutions.This approach is noise-sensitive as it utilizes the VG of magnetic field.
In the SPI method [18], the 1 st -order local wavenumber is defined as the HG of the local phase (tilt angle, θ), where x-is perpendicular to the strike of a 2D magnetic structure.The 2 nd -order wavenumber is written as Then, they link the local wavenumbers (k1 and k2) with depth and structural index as in the following Where j = 0, 1, and 2 for fault/contact, thin sheet, and horizontal cylinder, respectively.From Eqs. ( 12) and ( 13), the k1 and k2 are independent of the source inclination, S, i, d and the strength of the f.

Aeromagnetic data of the study area
The aeromagnetic data of the Southern Desert is a part of a national aeromagnetic and aerospectrometric survey carried out during the seventeenth of the past century.All the required corrections were applied and the resultant map has a grid interval of 520 m as shown in Figure (2).This figure displays the final magnetic map after applying the reduction-to-pole (RTP) transformation [19; 20] to the total magnetic field data utilizing the algorithm suggested by [21].The magnetic data used in the current study are principally of high resolution [22].The pp' is a magnetic profile that shows the position of the depth profiles used in Figure 8.

Implement of depth-to-basement methods
The five DTB methods have been applied to magnetic data of the Southern Desert.For depth estimation methods, which use profiles i.e. analytic signal and Werner deconvolution methods, thirty-one profiles covering the study area are selected for depth-position solutions of the magnetic sources.The distances between the profiles are varying from 5200 m to 15600 m depending on the distribution of magnetic anomalies.

Analytic signal approach
The analytic signal (AS) method is a 2D approach for computing the following parameters; depth-position, dip and magnetic susceptibility solutions for magnetic sources along a magnetic profile.We used the PDEPTH Geosoft eXecutable (GX) included in Geosoft Oasis Montaj v.8.4 (2014).The GX runs the algorithm of [23] in which Eqs. 1 -2 are involved.A total of 289 depth-position solutions have been deduced from the thirty-one profiles (Figure 3, white solid dots) and used to produce the final depth to the Proterozoic basement map for the study area as presented in Figure (3).These depth-position solutions represent locations of contacts and dykes in the study area.
One advantage of using this approach is the determination of these parameters will not be affected by the presence of remanent magnetization.Horizontal locations are usually well determined by this method, but depth determinations are only reliable for polyhedral bodies [11].

Tilt-depth (Td) method
Eq. 3 and 7 are used by [10] to calculate a DTB map utilizing the Td method of the study area which is shown in Figure (4).The distance between the zero contour and ±0.7854 (radiant; rad) contours is measured for only 18 points that agree with the AS contact solutions.The obtained results of the depth estimates for these 18 points are used to produce the final depth of the Proterozoic basement map as shown in Figure (4).Because of the small number of depth solutions, this map does not cover all parts of the SD (black polygon indicates the SD boundaries in this figure) showing regional variation in the basement depth only.

Werner deconvolution approach
Werner deconvolution (WD), similar to the AS approach, is a 2D approach for estimating depth-position of the magnetic source body.As in the case of the AS approach, thirty-one profiles covering the study area are chosen for depth-position solutions of the magnetic sources.The software, utilized for this purpose, calculates the position, depth, geometry, and magnetic susceptibility of the source, and is based on USGS code PDEPTH [23], which is involved in Geosoft package.The spacing intervals between profiles and along each profile and flight high are used as input data (see Eq. 8).The total solutions resulting from the thirtyone profiles are 167 depth-position solutions that have been used to construct a DTB map as shown in Figure (5).The minimum and maximum depth estimates are 4.7 km and ~11.0 km.

Reliable Euler deconvolution method
The reliable Euler deconvolution (RED) approach was applied to magnetic data using Eq. ( 9).Forty anomalies have been used/selected for the estimation depth-to-basement map.A Python program presented by [15] is used for calculating depth solutions of these anomalies with suitable sliding window size and selection filter.The structural index of 0 and 1 for contact/fault and dyke/thin sheet, respectively, are the best representation of the selected anomalies.The final DTB map was constructed after gridding the forty-depth solutions (Figure 6).The DTB map shows three distinctive oval-shaped basement lows (the blue depressions) of estimated depths excess of 10 km.Regions in the Southern Desert that have no depth solutions are not covered by the DTB map (Figure 6) such as the northwestern parts of Al-Ma'aniyah Depression, because there are no distinctive anomalies in these regions.

Source parameters imaging (SPI) or local wavenumber method
The SPI method is presented by [18] for computing source parameters, especially depth and position, from gridded magnetic data.The method assumes a step-type source model i.e. either a 2-D sloping fault/contact or a 2-D dipping dyke/thin-sheet model.The SPI is a GX within Geosoft Software that utilizes Eqs. 10 and 11 to calculate local wavenumbers (k1 and k2) for estimating basement depth using Eqs. 12 and 13.To minimize the low amplitudes of high-frequency signals and noise, the RTP grid was filtered by applying a 520 m upward continuation filter, which equals one grid spacing.A convolution (hanning) filter has been used for smoothing the results and a low-pass filter with a cutoff of 40 km is applied to reduce the short wavelength results (shallow solutions) from the calculated depths.Then, the final depths were calculated by subtracting 520 m from the processed depth values and displayed in as a DTB map shown in Figure (7) and the basement lows of different sizes, shapes and depths are shown, where some of these lows have depths exceeding 10 km, however, uplifted areas or basement highs with depth estimates reaching 5 km are delineated i.e. red color anomalies in (Figure 7).This map shows more details than the other present maps, where 66634 depth points (solutions) distributed throughout the Southern Desert are used for gridding data.

Depth-to-basement map derived from the five depth estimation methods
The statistical approach, we have used to generate a depth-to-basement map, is represented by deriving a sixth map from the five maps presented in this study.For that, we have performed thirty-one depth profiles, covering the study area, on the depth maps.These profiles trend in east-west direction that perfectly matches the flight-line direction.After that, for each depth profile, the five curves are displayed in one plot in order to assign the intersection or meeting points or regions where the depth estimation curves are clustered (these point are called yellow points).These yellow points represent basement depths confirmed by more than one depth method and are more reliable than each particular depth map. Figure ( 8) explains these procedures along profile pp' (its location shown in Figure 2 and also posted on all presented depth maps for comparison), which passes across the thirty-one depth profiles, where the yellow points are assigned (yellow small circles on this figure).Then, the depth and position solutions that are obtained from each profile are utilized to produce the final depth-tobasement map for the study area.Figure (9) demonstrates the obtained map that is gridded based on 150 yellow points derived from the five depth maps.Further, the posted-colored filled circles in this figure indicate the number of depth estimation methods that confirm a certain yellow point (depth point) as referred to in the legend (Figure 9).
The map shown in Figure (9) has greater reliability than each individual depth map.It shows several basement highs and the most confident high is located at Shibicha in the northwest and is less than 5 km deep.We call it Shibicha high which is confirmed by four depth estimation methods (Figure 9, violet solid circle).Another basement high that has an arcuate shape is surrounding Busaiya and is confirmed by three depth estimation methods (Figure 9, black solid circles).In addition, the most prominent lows are Al-Ma'aniyah in the northwest more than 10 km deep [24; 25], Salman in the central part, ~9.5 km, South Najaf at the north, up to 9 km and south and east Busaiya, more than10 km deep.All these lows are mostly confirmed by three depth estimation methods.

Discussion
The RED method uses the first vertical derivative filter of the magnetic map, this necessitates that the method is noise-sensitive.Thus with a low signal-to-noise ratio data, applying the enhancement filters, for example, the upward continuation filter, is recommended before applying the RED [26].
Magnetic sources of complex geometry could introduce uncertainty in depth estimates, therefore, depth estimated using methods that use the structural index in their algorithms such as WD and RED, would be uncertain.In addition, some parts of the study area, such as the Al-Ma'aniyah Depression at the extreme northwest, are not covered by depth solutions since they do not exhibit magnetic anomalies in this region (Figure 1).The solutions of RED demonstrate that the basement principally consists of contacts with dikes that coincide with AS solutions (Figure 3).Moreover, the depth estimates of the RED appear, in general, shallower than the depth estimates of the WD (Figure 5) and the AS solutions (Figure 3).This may be interpreted as the RED approach is more affected by depths of shallower sources than deeper ones since it uses the vertical derivative that enhances shallow sources.
The SPI and Td methods are easier, in application and give fast depth estimates for determining sedimentary basins than other techniques that give multiple solutions for depthposition locations i.e.RED, WD, and AS methods.Both are useful in the reconnaissance stage of exploration in areas that lack deep boreholes.However, techniques that give multiple solutions are of interest in detailed magnetic studies for specific anomalies.
The WD and AS depth maps are produced by 2D approach in which the profiles oriented EW that results in the depth to basement map will lack contact and dike solutions of magnetic bodies whose strikes trending EW i.e. parallel to the magnetic profiles or flight-line direction.The depth-to-basement map produced by the SPI technique (Figure 7) is gridded based on 66634 depth points (solutions) distributed throughout the Southern Desert.The SPI method uses first-and second-order derivatives in depth estimates, which implies enhancing of highfrequency content of the data.The data as a whole has good quality as stated before and the sedimentary cover is, in general, non-magnetic i.e. it does not add local field components.The technique works better for isolated 2D sources such as contacts, thin sheet, edges, or horizontal cylinders [28] and is independent of the magnetization direction of the magnetic sources.Furthermore, the SPI is convenient in a geological setting of slopping contact or dipping thin sheet model [19;29].However, various resolution powers, i.e. horizontal position (spatial resolution) and vertical position (depth), are observed due to the difference in the algorithms of these methods and the assumed models used and the geological complexity of the study area, as it is evident from profile pp' (Figure 8).Each map may give accurate results in certain regions within the study area, whereas it may give inaccurate results in other regions.The estimated depth near the northwest end of the profile (p') of the Td methods is erroneous because the profile is out of the depth map shown in Figure (4).Generally, the basement lows in Figure (3) coincide with those appearing in the depth map of the RED method (Figure 6).Depth estimates of the AS technique are the deepest; in contrast, RED estimates are the shallowest.The differences in resolutions result in agreements, in depth and position, in some parts, and disagreements in other parts.Nevertheless, positions that display harmonic (in-phase) depth estimates for three methods or more could be regarded as possessing a high level of confidence and are highly recommended to be reliable in the DTB estimates.
In regions near the boundaries of the study area such as Al-Ma'aniyah in the northwest, there are a few or sometimes no yellow points (intersection/meeting points) assigned on the derived map shown in Figure (9).Thus, we utilized the depth estimates of the SPI method to cover these regions (Figure 9, blue solid circles).The SPI depth estimates are generally acceptable in the stable part of the platform i.e. the study area [29].In addition, regions that give large differences in depth estimates are usually deep or have low magnetic susceptibility.Thus, the possibility of having remanent magnetization is large, therefore, only the SPI and AS methods can give accurate depth estimates in such regions because these methods are independent of the direction of magnetization.In the derived map, only the depth estimates from the five depth maps, which are coincided have been used, whereas regions that show large differences in depth estimates have been neglected.The agreement in depth points (the yellow points) occurs only in regions of distinctive anomalies that achieve the models' hypothesis.This gives more confidence for the resultant map.

Conclusions
Five depth estimation methods are applied to aeromagnetic data of the Southern Desert of Iraq and accordingly we obtained five depth-to-basement maps.These methods are analytic signal, tilt-depth, Werner deconvolution, reliable Euler deconvolution, and source parameter imaging methods.These maps have different resolutions and may agree in some regions whereas might disagree in others.A sixth depth-to-basement map is derived from the five depth estimation maps that could be more reliable than each individual depth map.The map shows that the minimum and maximum depths are ~4.5 km and ~10.0 km, respectively.The basement highs in Shibicha and northeast Busaiya are suggested for checking by drilling since they most likely represent the shallowest basement depth in Iraq.The map also shows basement lows that are recommended as regions possess the highest sedimentary thickness and should be considered for hydrocarbon explorations in the study area.The basement features are either structural or topographic that need further qualitative and quantitative studies to confirm their origin.

Figure 2 .
Figure 2. RTP map of the Southern Desert used for applying depth-to-basement methods.The pp' is a magnetic profile that shows the position of the depth profiles used in Figure 8.

Figure 3 .
Figure 3. Depth to Proterozoic basement map of the Southern Desert constructed by applying 2D analytic signal approach to the RTP profiles.White solid dots are locations of AS contact and dyke solutions.Profile pp' is as defined in Figure (2).
Three basement lows separated by basement highs are distinctive in Figure (4, blue color anomalies); south of Busaiya in the southeast, Salman in the central part, and south of Najaf, which partially appears in the extreme northeast.

Figure 4 .
Figure 4. Depth to basement map of the Southern Desert obtained from Tilt-depth method.The white dots indicate positions of (18) vertical contacts picked from the analytic signal approach (Figure 3), profile pp' is as defined in Figure (2).

Figure 5 .
Figure 5. Depth-to-basement map of the Southern Desert obtained from Werner deconvolution approach.White solid dots are locations of WD depth solutions.Profile pp' is as defined in Figure (2).

Figure 6 .
Figure 6.Depth-to-basement map of the SD deduced from the RED approach.The white solid dots represent the depth solutions for 40 anomalous areas selected from the magnetic map.Profile pp' is as defined in Figure (2).

Figure7.
Figure7.Depth-to-basement map of the Southern Desert generated using the SPI method.Profile pp' is as defined in Figure (2).

Figure 8 .
Figure 8. Profile pp' in the Southern Desert (see Figure 2 for location and also posted on all depth-to-basement maps) shows depth estimates (the yellow circles) derived from reliable Euler deconvolution, Werner deconvolution, analytic signal, Tilt-depth, and SPI methods.Note more than one depth solution outlined by yellow circles gives more confident depth estimation results.

Figure 9 .
Figure 9. Depth-to-basement map of the Southern Desert derived from the five depth estimations methods used in this study.The small-filled circles refer to the number of depth estimation methods that confirm the depth at that point according to the infill color explained in the legend.Profile pp' is as defined in Figure (2).
. In this figure, the average depth to basement is ~8 km