Australia is well known for its relative tectonic stability and is a stable continent located in an intraplate position. The paleovalley networks are coherent, dominantly dendritic, and largely concordant with modern topographic expression (Magee, 2009). Although paleovalleys in the arid zone are partly covered by Quaternary eolian deposits, the topographic expression of the paleovalley pattern is still evident in high-resolution digital elevation model (DEM) data (Magee, 2009). In the APY lands, crustal architecture has been preserved since the Cenozoic, and it is considered to have been unaffected by later tectonic events (Drexel and Preiss, 1995). Previous studies in the study area have considered that the paleovalleys are coincident with topographic lows that characterize the contemporary landscape, with AEM images being particularly useful for locating the position of the deeper portions of the older valley system (Munday et al., 2013). It is thus assumed that the present-day valley pattern indicated by topographic lows in the study area is comparable to the paleovalley pattern according to the principle of uniformitarianism (Simpson, 1970), but shifts in valley width, orientation and connectivity between present-day valley and paleovalley are allowed. Following this principle, we generate a synthetic paleovalley image based on a digital elevation model (DEM).

First, a DEM of the study area with a resolution of 30 m ×30 m (https://earthexplorer.usgs.gov/, last access: 23 December 2018) is used to generate 15 sets of paleovalley images, mimicking paleovalleys of various spatial densities and width over an area of 80 km ×80 km based on the hydrological analysis in ArcGIS (Fig. 2a) (details in Maidment and Morehouse, 2002). For convenience in the subsequent neural network operation, each resulting valley image is downscaled by the bicubic interpolation method to contain 800×800 pixels with spatial resolution of 100 m. Valley widths range from 1 to 10 pixels (i.e., 100 to 1000 m). The 15 images generated from the DEM were rotated between zero and 360∘ and randomly cropped into 20 000 small training images with a size of 50×50 pixels (Fig. 2b). Thus, the potential differences in the width and orientation of present-day valley and paleovalley induced by several uncertain factors, e.g., variation in the river discharge and geomorphology, can be addressed in the training images. The recombination of small training images allows recreation of valley patterns beyond those 15 full-size images generated from DEM data. A broad range of likely paleovalley patterns at varying principle orientations, widths and connectivity are available in the SRCNN training image pool.

The properties in the porous paleovalley sediments are then converted to EC values using Archie's law (Archie, 1942): 1R=R0θ-m, where R is the electrical resistivity of the water-bearing formation (Ωm), R0 is the electrical resistivity of the pore water relating to water salinity (Ωm), θ is the porosity and m is a constant relating to the lithology (with value ranging from 1.8 to 2.0) (Worthington, 1993). Electrical conductivity values are calculated as the inverse of resistivity values (i.e., EC =1/R). In the present study area, R0 is considered to range from 1.4 to 1.7 Ωm, corresponding to water salinities of 3000 to 6000 mg L-1 (Varma, 2012), while θ is considered to range from 10 % to 30 % (Taylor et al., 2015; Varma, 2012). As a result, paleovalley EC values are estimated to be within the range of 6 to 80 mS m-1, which is in the range of AEM-derived EC values in Fig. 1.

In contrast, the non-paleovalley zone is predominantly fractured rock with solid-phase EC values <1 mS m-1, characteristic porosity of <1 % and fluid salinity values of <150 mS m-1 EC (1000 mg L-1) (Olhoeft, 1981; Parkhomenko, 2012). The bulk EC values in the non-paleovalley zones were estimated as the volume-weighted average of EC in fractured rock and fluid, following 2EC=ECs⋅1-φ+ECf⋅φ, where EC is the bulk electrical conductivity, ECs is the EC value of rocks, ECf is the EC of fluid and φ is the ratio of fracture void volume to total volume. The resulting bulk EC values are lower than 2.5 mS m-1. Again, these synthetic EC values are similar to the AEM-derived values for the presumed fractured bedrock areas (Fig. 1).

Furthermore, to represent the effects from data smoothing and inherent noise associated with the AEM survey, inversion and data interpolation, artificial noise is generated by randomly sampling EC values in the non-paleovalley zones (following a uniform distribution ranging from 1 to 10 mS m-1) and in the paleovalley zones (following a uniform distribution ranging from 6 and 80 mS m-1). It is also noted that the upper-limit EC values in fractured bedrock areas are enlarged artificially from 2.5 to 10 mS m-1, to assure that in the training images paleovalley and non-paleovalley zones overlap in EC by 4 mS m-1 (5 % of the total range of EC values between 1 and 80 mS m-1) (Fig. 2c). The SRCNN can then learn to identify this overlap in EC between paleovalley and non-valley zones. However, Appendix A1 shows that setting the overlapping size in EC too large results in the trained SRCNN overestimating the extent of the non-valley zones, which make the predicted paleovalleys disconnected.

The overlap in EC near the boundary between paleovalley and non-valley is further enhanced by data smoothing: the resultant EC images of 50×50 pixels is first downscaled into images with a smaller number of pixels, i.e., 40×40 (20 000 images), 30×30 (20 000 images), 20×20 (20 000 images) and 10×10 (20 000 images) pixels, respectively, by nearest-neighbor interpolation. These resulting 80 000 images are then upscaled by bicubic interpolation to yield blurred images with the original resolution of 50×50 pixels (Fig. 2d). In this manner, the EC values in the paleovalley and non-paleovalley zones are smoothed and the boundary between paleovalley and non-paleovalley becomes blurred.

We then randomly selected 70 000 EC images from a total of 100 000 images, composed of 20 000 pre-interpolation EC images (Fig. 2c) and 80 000 reconstructed blurred EC images (Fig. 2d) with a size of 50×50 pixels, as input to the neural network (see further), with the original synthetic paleovalley images (pixel code 1) and non-paleovalley (pixel code 0) pixels (Fig. 2b) as output. From the random set of 70 000 images, 60 000 pairs of EC (Fig. 2c and d, as input) and paleovalley images (Fig. 2b, as output) are used as a “training dataset” for training the SRCNN. A total of 6000 pairs are used as “validation dataset” for validation and another 4000 are used as “testing dataset” to demonstrate the performance of the trained SRCNN in removing the noise in EC images and lithofacies (paleovalley and non-paleovalley) classification.

To quantify the relationship between EC images and paleovalley images, the super-resolution convolutional neural network (SRCNN) algorithm is employed. Neural networks are regression models that provide a general way of identifying nonlinear relationships between two sets of variables (Bishop, 1996; Moysey et al., 2003), where one set of variables is considered to be the input (herein electrical conductivity) and another is a network output (binary paleovalley). The SRCNN algorithm can directly train the relationship between a low-resolution (input) and a high-resolution image (output) (Dong et al., 2016). A typical SRCNN is composed of three convolution layers (Fig. 3), representing patch extraction and representation, nonlinear mapping, and reconstruction.

In the patch extraction and representation layer, the input is a normalized 50×50 pixel EC image, which is operated by a convolution process: 3H1X=max0,XW1+b1, where H represents the output images, <> is the convolution operator, X represents the input EC image, and W and b represent the weight filter and bias, respectively. W1 corresponds to n1 filters with a size of f1×f1 and b1 is an n1-dimensional vector. After convolution, H1 contains n1 generated 50×50 pixel images that are input into the nonlinear mapping layer. It is then convoluted by 4H2H1=max0,H1W2+b2 to generate H2 composed by n2 50×50 pixel images, where W2 contains n2 filters with a size of n1×f2×f2 and b2 is a n1×n2 matrix.

Finally, an output paleovalley index (with values approaching zero indicating a non-valley pixel and values approaching unity indicating a paleovalley pixel) can be reconstructed from H2 by 5H3H2=GH2W3+b3. H3 contains one 50×50 pixel paleovalley index image, and W3 contains one filter with a size of n2×f3×f3 and b2 is a n2×1 matrix. G(⋅) is a sigmoid function to assist the paleovalley classification and accelerate the training processes, which is written as 6G⋅=exp(⋅)/[1+exp(⋅)]. In this study, f1, f2 and f3 are referred to as filter size with values of 9, 1 and 5, respectively, and n1 and n2 are the layer width (the number of images contained in each layer) with values of 64 and 32, respectively, following the classical structure of SRCNN used in Dong et al. (2016). The influence of the filter size and width on the quality of the output images was investigated in Appendix A3. The filter size in the SRCNN controls the spatial correlation length of EC values that can be considered in the neural network operator. As illustrated in Fig. 3d, in each calculation, the EC values in the filter are convoluted to form a value at a single pixel in the output image. An EC image convoluted by the filter with the size of 2 and stride of 1 (i.e., filter moving 1 pixel at the time) and one hidden layer, leads to a paleovalley index at 1 pixel of the output image that relates to EC values from 3×3 pixels in the input image. In this example, the spatial correlation scale able to be addressed is equal to 3 pixels multiplied by the size of each pixel (meter). In addition, the width of each layer determines the degree of the nonlinear relationship between input and output, while the depth of the network affects both the spatial correlation length and the nonlinearity (see further in Appendix A3).

The initial weight values are randomly generated, following a standard normal distribution, while initial bias values are given as 0.1. Both weight and bias values for each of the three convolutional neural network layers are optimized simultaneously using the adaptive moment estimation algorithm (Kingma and Ba, 2014) to minimize the loss function, L, which is defined as the mean sum of squared residuals: 7LW1,W2,W3,b1,b2,b3=1N∑i=1NH3-Y2, where Y is the known binary paleovalley pattern (0 represents non-paleovalley, 1 corresponds to the paleovalley) in the training data, and N is the number of image pixels in each training.

To verify the performance of the SRCNN, the following image quality indices are calculated.

Peak signal-to-noise ratio (PSNR) (Wang and Bovik, 2002):8PSNR=-10log⁡101N∑i=1N(Ỹi-Yi)2,where Y represents the synthetic binary paleovalley index generated from the DEM (0 for non-paleovalley and 1 for paleovalley) (Fig. 2b) and Ỹ is the calculated paleovalley index (Eq. 5) from SRCNN using EC images as input, and the term between brackets is the mean square error. PSNR is a traditional approach to image quality assessment. A high PSNR represents a high-quality paleovalley generation; e.g., a PSNR =20 value is equivalent to a mean-square error of 0.01.

The training dataset composed of 60 000 pairs of EC and valley images in Fig. 2 is divided into 1200 batches (inner number of iterations) with each batch containing 50 images. The epoch (outer number of iterations) is set to 5, and the 60 000 training image pairs are resorted at the beginning of each epoch. In this scenario, weights and biases in the SRCNN are updated by 6000 iterations (5×1200), according to the loss function calculated based on 50 pairs of images in each batch.

After each iteration, the PSNR (Eq. 8) and SSIM (Eq. 9) for 50 training images in each batch are calculated (Fig. 4a and b). Moreover, the PSNR and SSIM for 6000 validation images are calculated for every 50 iterations. It is illustrated that PSNR for each training batch fluctuates near 18 (which corresponds to a mean-square error of 0.015 based on Eq. 8), while the SSIM stabilizes at 0.96. The PSNR and SSIM values for the validation images agree well with those of the training images. This suggests that the SRCNN is sufficiently trained to recreate the paleovalley with a high accuracy without overfitting problems, and importantly preserving structural similarity.

The trained SRCNN is then applied to generate paleovalley images based on 4000 testing EC images; we here randomly selected four images to demonstrate the ability of SRCNN. The synthetic paleovalley images from DEM and their corresponding blurred EC images are illustrated in Fig. 5a and b, respectively. The histogram of EC values for all 4000 images (each containing 50×50 pixels) in the testing dataset follows a unimodal, right-skewed distribution (Fig. 5c). It is not trivial to define an EC threshold value from such unimodal distribution that can be used to distinguish the paleovalley and non-paleovalley cells from Fig. 5b. After calibration of the SRCNN, a paleovalley index map is obtained (Fig. 5d). However, the histogram of the resultant paleovalley index displays a bimodal behavior, with peaks centered at 0 and 1 (Fig. 5e). By selecting a threshold paleovalley index value of 0.5, the paleovalley and the non-paleovalley data can be differentiated and converted to a binary paleovalley map (Fig. 5f). The resultant paleovalleys compare well with the reference (i.e., synthetic) paleovalleys in Fig. 5a. The selection of a threshold paleovalley index in the range of 0.2 to 0.8 does not have a significant influence on the resultant binary paleovalley pattern.

Moreover, the resultant paleovalley index is less noisy in both paleovalley and non-paleovalley parts (Fig. 5d). The SRCNN is able to create connected paleovalley networks from the poorly connected EC values generated by bicubic interpolation (Fig. 5b), which is one of the most challenging features in geostatistics. Figure 5 demonstrates three advantages of applying SRCNN: (1) it removes the noise in EC values, (2) it recreates the connectivity of the paleovalleys, and (3) it classifies the paleovalley and non-paleovalley components, which allows the selection of a threshold index to define paleovalley and non-paleovalley zones.

The next synthetic example considers 400 m wide synthetic paleovalleys generated in ArcGIS from the DEM in the zone about 60 km southwest of the study area in Fig. 1a. The total extent of each synthetic paleovalley image is 80 km by 80 km, with the resolutions ranging from 200×200 to 2000×2000 pixels. The paleovalley image (Fig. 6e) with 200×200 pixels is converted to EC values based on Archie's law (Fig. 6a), with EC values overlapping by 2.5 % between paleovalley and non-paleovalley zones. This low-resolution EC image is upscaled to a high-resolution EC image by bicubic interpolation (Fig. 6b), which is then cropped to images of 50×50 pixels and used as an input image for the SRCNN. Subsequently, the paleovalley index and histogram at different resolutions are obtained (Fig. 6c). Following the histogram of the paleovalley index, it is easy to select an arbitrary threshold in the range 0.25–0.8 to convert the paleovalley index (Fig. 6c) to a binary paleovalley (Fig. 6d). The choice of threshold in this range does not affect the resultant binary paleovalley pattern, as after SRCNN processing, the paleovalley index is already well grouped. The calculation of the paleovalley index at the resolution of 2000×2000 pixels takes 52 s.

It is worth noting that as the resolution of the resultant paleovalley increases, the PSNR and SSIM goodness-of-fit metrics and connectivity do not change significantly (Fig. 7). Both PSNR and SSIM increase with the resolution from 200×200 to 800×800 pixels because the bicubic interpolation smoothes the EC values and reduces the noise in EC values. When the image resolution further increases from 800 to 2000, PSNR degrades weakly from 18.48 to 17.09 (corresponding to an increase in mean-square error from 0.014 to 0.019) and, similarly, SSIM decreases from 0.8919 to 0.8522.

Because each image has a fixed extent of 80 m ×80 km, as the resolution increases, the distance between pixels and the real geological scale of 50×50 pixel images decreases. When the resolution increases from 200×200 to 2000×2000 pixels, the distance between pixels decreases from 400 to 40 m and the real scale of each training image decreases from 20 km ×20 km to 2 km ×2 km. When training the SRCNN, the distance between pixels was not accounted for. The training images in the training dataset include images without any paleovalley and images being fully occupied by the paleovalleys, with the narrowest paleovalley occupying merely 1 pixel. These paleovalley patterns are unrelated to the real scale of the training image, i.e., across the range from 20 km ×20 km to 2 km ×2 km. Thus, the trained SRCNN works well to infer paleovalleys across different resolutions and scales.

Following the training and testing of the SRCNN method based on synthetic DEM-derived paleovalley networks, we now apply the trained network to an area in the APY lands to convert EC values at a spatial resolution of 400 m ×400 m to identify paleovalleys at a resolution of 40 m ×40 m in an area of 80 km ×80 km. The methodology was first applied to a single depth AEM image (i.e., 100 m) to illustrate the procedure and discuss the main findings. In a second step we will apply the methodology to the AEM images from all 10 depths to extract specific information on the depth structure of the paleovalley network.

Figure 8 summarizes how the previously trained SRCNN successfully converts the low-resolution EC values resulting from an AEM survey to a binary map composed of paleovalleys and non-paleovalley areas (Fig. 8a). First, the bicubic interpolation generates a high-resolution EC image characterized by a right-skewed distribution of normalized EC values (Fig. 8b). This map does not yet allow a clear differentiation of the paleovalley from the surrounding fractured rocks. However, once we apply the SRCNN, a paleovalley index map with the paleovalley index following a binomial distribution is produced (Fig. 8c). Selecting an appropriate index (0.5 here) separates paleovalley from non-paleovalley pixels (Fig. 8d).

Inversion of AEM-derived EC maps at 10 depths within the first 100 m below the land surface (at 10 m intervals) is shown in Fig. 9a. EC values available at 10 layers are converted to binary paleovalley images by SRCNN, based on the premise that both the paleovalley pattern and bulk electrical conductivity from the 100 m depth interval can be represented in training images. As shown in Fig. 9a, normalized EC values derived from the AEM survey are characterized by a right-skewed distribution. However, once we apply the SRCNN, the resulting paleovalley index map (Fig. 9b) displays a binomial distribution of paleovalley indices. Selecting an appropriate index (0.5 here) generates a regional-scale 3-D binary paleovalley image with a horizontal resolution of 40 m and vertical resolution of 10 m (Fig. 9c).

In the subsequent discussion we first test the derived paleovalley map with independent, yet limited, borehole data and auxiliary land surface maps. Next we extract further information from Fig. 9c about the depth structure of the paleovalleys to better constrain the areas for groundwater prospection.

To compare the paleovalley map (Fig. 9c) with borehole logs and an alternative indictor of the location of valley in the land surface (i.e., the multiple resolution valley bottom flatness index; Gallant and Dowling, 2003), we aggregated the 10 depth slices of Fig. 9c into a 2-D paleovalley index map, with values ranging from zero (i.e., no paleovalley within the 10 depth layers) to 10 (i.e., paleovalley detected across all depth layers) (Fig. 10a).

The resulting paleovalley index map in Fig. 10a is first compared to the Multiple Resolution Valley Bottom Flatness (MRVBF) index in Fig. 10b, which was originally calculated by Gallant and Dowling (2003) based on a digital elevation model with a spatial resolution of 100 m. High MRVBF values indicate a high probability of deposition of alluvium sediments. It was used by Munday et al. (2013), together with field observations of regolith, to obtain a hydrofacies map (black line in Fig. 10a). A comparison of the contours of the SRCNN paleovalley index 10 and 6 with the MRVBF index shows the emergence of similar patterns (Fig. 10a and b). While this confirms that the SRCNN paleovalley index map is not inconsistent with the MRVBF index, the latter contains insufficient information for testing the paleovalley map.

The degree to which the MRVBF index can be used to identify the main three hydrofacies (bedrock, alluvium and transition material) is discussed on the basis of Fig. 10d. High MRVBF values correspond to bores with both alluvial lithology and transition material lithology, while a large number of bedrock boreholes also show high MRVBF values. In other words, the alluvial (i.e., paleovalley) and bedrock/transition material (non-paleovalley) lithology classes could not be fully identified by the MRVBF index.

In contrast, the AEM survey and the paleovalley classification based on automatic neural networks in this study have improved our capability of identifying the position of paleovalleys. The boxplot of Fig. 10c shows that the boreholes classified as “alluvium” correspond to a higher median SRCNN paleovalley index of 4, compared to the two other lithology classes of median paleovalley index of 0 and 2, respectively. For 128 boreholes identified in the study area, (i) those drilled in bedrock (66 boreholes) had the smallest SRCNN paleovalley index (median of 0), (ii) those drilled in alluvium (57 boreholes) had the largest SRCNN index (median of 4) and (iii) those drilled in transition zones (five boreholes) had the next largest SRCNN index (median of 2). Despite the relatively small dataset of borehole logs (three per 100 km2), there is a clear trend that bores in alluvial sediments correspond to the areas with the highest SRCNN index. It is reasonable to assume that these alluvial sediments represent paleovalleys, although the lithological classification did not provide this level of detail. However, for 11 alluvial boreholes, only a low corresponding paleovalley index of <2 was identified. This may be due to the limited lithological and sedimentary information captured by the downhole logs, which were mainly recorded in the 1970s with limited description of the subsurface environment. The same is true for the boreholes in bedrock and transition zones, which may have been misclassified due to insufficient data.

The paleovalley network shown in Fig. 10a is based on an analysis of 10 depth layers and hence gives greater confidence about the location of deep paleovalleys than the analysis of a single-depth paleovalley map (Fig. 8). A significant proportion of the image has a maximum index of 10, meaning that a paleovalley has been detected throughout the full investigation depth. This is thus an area with a high certainty (i.e., all pixels with index 10 have 10 layers identified as paleovalley) that at least a 100 m deep paleovalley is present. For the subsequent indices, e.g., 8, 6 and 4, at least eight, six and four depth layers with a paleovalley were identified, respectively.

Moreover, the burial depth of the paleovalley (defined by the vertical distance between the uppermost parts of the paleovalley to the land surface) is calculated based on the 3-D binary paleovalley. It is shown in Fig. 11a that a wide range of the paleovalleys are buried up to a depth of 10 to 20 m, which cannot be observed directly from the land surface, but can be revealed by the methodology proposed in this work based on geophysical prospecting (here 3-D AEM data).

We finally calculate the thickness of paleovalley layers (potentially representing the thickness of an alluvium aquifer) from the 10 depth layers with paleovalley indices. As a result, the thickness of the paleovalley calculated by the distance between bottom (lowest part) and top (uppermost part) of the paleovalley (Fig. 11b) is identical to the paleovalley index (Fig. 10b) multiplied by the layer thickness of 10 m. This indicates that except for those pixels that were shown to have a 10 to 20 m cover of non-paleovalley sediments (see burial depth in Fig. 11a), all other pixels had uninterrupted paleovalley layers starting from the land surface. In those paleovalley zones without surface sediment cover, the SRCNN paleovalley indices 8, 6 and 4 of Fig. 10a are representative for uninterrupted paleovalley sediments in the depth intervals 0–80, 0–60 and 0–40 m, respectively.

Note that in Fig. 10a at any pixel with given paleovalley index n (from 0 to 10), the probability of finding n consecutive paleovalley layers can be inferred; in our test case area this was 100 % everywhere – except for the buried pixels with 10 to 20 m cover of non-paleovalley sediments – as no interruption was detected in the sequence of paleovalley layers identified. This demonstrates that despite expected vertical lithological heterogeneities within paleovalleys (Knight et al., 2018), AEM images combined with our SRCNN methodology are able to identify and differentiate a broad series of sediments that make up a paleovalley from the surrounding bedrock. The SRCNN paleovalley index map thus provides an improved tool for groundwater prospectivity.