The PPDRC approach is an image processing tool that allows expressing the subtle features in an image out of misrepresentation. The approach is proposed by Kovesi (2012) who used it in the qualitative interpretation of magnetic data. The main idea is that the phase or tilt angle remains constant during the application of a desired high-pass filter. This will keep on the fine features to be visible in the analysis. To apply this approach, firstly, a high-pass filter is applied to the data; this controls the desired scale (small- or large-scale features) of analysis, which is important. Under the high-pass filtering, the relative magnitude of features can vary but not their locations (Kovesi, 2012).
Spatial frequencies in the image with wavelengths greater than the specified value will be suppressed allowing the residual features to be seen more readily. Then, the 2D analytic signal (AS) at each point in the image is computed. The AS is a complex vector function that can be expressed in term of the Analytic Signal Amplitude (ASA) and the local phase (tilt angle, θ), which is an important attribute for human visual system for image interpretation. Perceptually important phase information is preserved and the contrast amplification of anomalies in the signal is purely a function of their amplitude. The relationship between the ASA and θ is explained in Eqs. 1 and 2 (Nabighian, 1972, 1974; Miller and Singh, 1994);
ASA= \(\sqrt{{\left(\frac{\partial f}{\partial x}\right)}^{2}+{\left(\frac{\partial f}{\partial y}\right)}^{2}+{\left(\frac{\partial f}{\partial z}\right)}^{2}}\) (1)
θ= \({tan}^{-1}\frac{\frac{\partial f}{\partial z}}{\sqrt{{\left(\frac{\partial f}{\partial x}\right)}^{2}+{\left(\frac{\partial f}{\partial y}\right)}^{2}}}\) (2)
where (∂f/∂x) and (∂f/∂y) are the first horizontal derivatives in the x and y-directions, respectively, and (∂f/∂z) is the vertical derivative of the magnetic (or gravity) field; f.
When the highpass filter is used, the dynamic range of the image is compressed after that the image is reproduced using the initial phase values and the new amplitudes range. Kovesi (2012) shows that the amplitude is lowered by calculating its logarithm then summing with 1 to avert signal reversal for amplitude values less than 1, the signal is then reproduced using the initial phase values. A MATLAB code provided by Peter Kovesi; MATLAB and Octave Functions for Computer Vision and Image Processing [online]. Website https://www.peterkovesi.com/matlabfns/ [accessed 04, 2021]. The website contains an algorithm runs in the wavenumber domain to make sure that the features accuracy is maintained though keeping on the initial phase information. Utilizing this technique enables to produce a set of dynamic range compression (DRC) images at multi scales. Worthy mentioning, the authors have reproduced a MATLAB code to provide a video file of format *.avi for analyzing images (colored images) at each 10 gu. This is important in interpretation since it facilitates following the magnetic and gravity features from high frequencies, supposed at a shallow depth, to low frequencies, supposed at a great depth.
It is expected that applying the PPDRC technique to the potential data of the SD could enhance the gravity and magnetic anomalies at different wavelengths, particularly, the subtle features (low amplitude) and make them more easily for the qualitative interpretation i.e. the new images can not be used in quantitative interpretation since the anomaly amplitudes may be modified.
The RTP image size is 903 × 685 grid unite (gu) (1 gu = 520 m) (Fig. 1) that has been analyzed into 100 colored scales (ranging from wavelength = 10 gu to wavelength = 1000 gu with a scale interval = 10 gu) (RTP.avi, available at supplementary material) for fast inspection of magnetic data. Among these 100 wavelength scales of the RTP image, three-wavelength scales, which are supposed to represent short-, intermediate-, and long-wavelengths, are chosen for interpretation and lineaments detection. Figure (5) demonstrates the results of RTP image analysis into three different scales; a short-wavelength scale of 100 gu (frequency (f) = 1/100 Hz), an intermediate wavelength scale of 500 gu (f = 1/500 Hz), and a long-wavelength scale of 1000 gu (f = 1/1000 Hz).
The analyzed images of scales 500 gu and 1000 gu (Figs. 5b, and 5c, respectively) reveal the possibility of dividing the Proterozoic basement rocks of the SD into three distinctive blocks separated by basement magnetic lows mostly grabens (Al-Rahim and Lima, 2016); the northwestern block (NWB), and the central block (CB) and the southeastern block (SEB) (the solid thick red lines in Figs. 5b and 5c). The grabens are inferred from depth to basement maps, particularly, those deduced from SPI method (Al-Bahadily et al., 2022b; Al-Bahadily and Al-Rahim, 2022; Abdulrahim and Al-Rahim, 2019). Moreover, each block may be subdivided into, at least, two sub-blocks by nearly NS trending lineaments (Figs. 5b and 5c, the dashed red lines). The blocks are separated by magnetic lows, which are either structural lows, or low susceptibility zones and the sub-blocks are characterized by different anomaly patterns or anomaly types and each block may display horst and graben structural configuration.
Conversely, the blocks cannot be ascertained in the short wavelength scales (100 gu) (Fig. 5a) since this scale reveals only the magnetic features of relatively shallow depth. Nevertheless, the anomalies at this scale appear to have mostly NE–SW-oriented lineaments (Fig. 5a). The blocks boundaries coincide well with the regional transversal weak zones within the basement. However, the NS trending lineaments, which divide each block into sub-blocks, agree well with the basement-inherited Neoproterozoic Nabitah Fault System dominated the Arabia.
However, the gravity map, image size 312 × 243 grid unite (gu) (1 gu = 1500 m) (Fig. 2), has been analyzed, into 40 wavelength colored scales starts with wavelength 10 gu and ends with wavelength 400 gu with 10 gu scale interval. The scales are presented in a video file format Grav.avi (available at supplementary material) for fast inspection of gravity data Three different wavelength scales; 50 gu, 100 gu, and 150 gu, of the PPDRC-analyzed gravity images, are demonstrated in Figs. (6a-c), respectively. The gravity features of interest can be followed up from small scale, which reflects shallow depth, to large scales, which reflects great depth. A good example of these features is the two adjacent gravity highs that appear in the extreme northern part of Fig. (6a) are completely disappeared in Fig. (6c, area A). In contrast, the gravity low that appears in the same area in Fig. (6c) is hidden in Fig. (6a). Additionally, lineament interpretation is carried out on the analyses and laid over the pertinent images (green-color lines in Fig. 6). The image of small-scale wavelength; 50 gu, at the shallow depth display more lineaments than large-scale ones i.e. 100 gu and 150 gu, at the great depths indicating increasing density heterogeneity near the ground surface. The heterogeneity is mostly related to nearsurface karst forms as mentioned in the introduction. Most lineaments at wavelength scales of 100 gu and 150 gu are oriented NW–SE and nearly EW directions, however, lineaments at wavelength scale of 50 gu have NW–SE, NS, NE–SW and nearly EW directions. These lineaments are often occurred in the sedimentary cover at shallow-, intermediate- and deep levels. Large-scale and small-scale gravity depressions are more evident in the image of the long-wavelength scale which are respectively assigned as capital and small letters in Fig. (6c).