# Removing Regional Trends in Microgravity in Complex Environments: Testing on 3D Model and Field Investigations in the Eastern Dead Sea Coast (Jordan)

Authors: A. Al-Zoubi; L. Eppelbaum; A. Abueladas; M. Ezersky; E. Akkawi
Journal: International Journal of Geophysics
 (2013)

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## Abstract

Microgravity investigations are now recognized as a powerful tool for subsurface imaging and especially for the localization of underground karsts. However numerous natural (geological), technical, and environmental factors interfere with microgravity survey processing and interpretation. One of natural factors that causes the most disturbance in complex geological environments is the influence of regional trends. In the Dead Sea coastal areas the influence of regional trends can exceed residual gravity effects by some tenfold. Many widely applied methods are unable to remove regional trends with sufficient accuracy. We tested number of transformation methods (including computing gravity field derivatives, self-adjusting and adaptive filtering, Fourier series, wavelet, and other procedures) on a 3D model (complicated by randomly distributed noise), and field investigations were carried out in Ghor Al-Haditha (the eastern side of the Dead Sea in Jordan). We show that the most effective methods for regional trend removal (at least for the theoretical and field cases here) are the bilinear saddle and local polynomial regressions. Application of these methods made it possible to detect the anomalous gravity effect from buried targets in the theoretical model and to extract the local gravity anomaly at the Ghor Al-Haditha site. The local anomaly was utilized for 3D gravity modeling to construct a physical-geological model (PGM).


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## Body

## 1. Introduction

The development of new modern gravimetric and variometric (gradientometric) equipment, which makes it possible to record small previously inaccessible anomalies, has enhanced observational methodology as well as new gravity data processing methods and interpretation. These advances have triggered the rapid rise in the number of microgravity methodology applications in environmental and economic minerals geophysics.Microgravity is now recognized as an effective tool for the analysis of a whole range of geological subsurface inhomogeneities, the monitoring of volcanic activity, and prospecting for useful minerals (e.g., [3–36]).At the same time different kinds of noise of different origin complicate analysis of microgravity data. For removing (elimination) the noise components numerous procedures and methodologies were developed. We will analyze in this paper a problem of regional trend removing under complex geological-geophysical environments. Such a problem is highly essential by delineation of weak anomalies from buried karst terranes in the Dead Sea Basin where regional horizontal gravity gradients may exceed values of 10 mGal/km.


## 2. A Brief Review of Microgravity Investigations in Subsurface Studies

Colley [4] apparently was the first to apply the gravity method for cave delineation. Despite the fact that the accuracy of gravity observations at that time was not sufficiently precise, he presented some examples of typical negative gravity anomalies in large caverns in Iraq.Fajklewicz [6] examined the vertical gravity gradient (Wzz) over underground galleries. He was probably the first to note a significant difference between the physically measured Wzz and this value obtained by transformation. Interesting examples of microgravity anomalies from archaeological targets are presented in Blížkovský [7]. Butler [9] showed that microgravity measurements could be used to detect and delineate the main components of complex underground cavity systems. He computed the second and third derivatives of the gravity potential and polynomial surface to develop the initial physical-geological models (PGMs).  Butler [10] surveyed gravity and gravity-gradient determination concepts and their corresponding interpretative microgravity procedures.A nonconventional attempt to use microgravity observations for weight determination of stockpiled ore was reported by Sjostrom and Butler [37] who estimated the mass of many chromite and other ore bodies noninvasively.Crawford [14] employed microgravity to detect sinkhole collapses under highways in the USA. Elawadi et al. [38] showed that the application of well-known neural network procedures could increase the assessment effectiveness of the depth and radius of subsurface cavities revealed by microgravity data.  Rybakov et al.’s [17] work triggered the use of microgravity to find sinkholes in the complex geological conditions of the Dead Sea coastal plain.Types of noise (disturbances) arising in microgravity investigations were studied in detail in Debeglia and Dupont [39]. Styles et al. [20] discussed the key problems related to the removal of noise components in microgravity in complex environments.The need for additional computation of the surrounding terrain relief by 3D gravity modeling in ore deposits occurring in the very complex topography of the Greater Caucasus was discussed in Eppelbaum and Khesin [19].Abad et al. [25] carried out an assessment of a buried rainwater cistern in a Carthusian monastery (Valencia, Spain) by 2D microgravity modeling. Microgravity monitoring is one of the most widely used geophysical techniques for predicting volcanic activity; for instance,  Carbone and Greco [40]  described in detail their microgravity monitoring of Mt. Etna.Advanced methods in magnetic prospecting can be adapted to quantitative analysis of microgravity anomalies in complex environments [27]. Eppelbaum et al. [3] described various transformation methods to identify buried sinkholes including 3D gravity modeling to develop a PGM of Nahal Never South in the western Dead Sea coast.Deroussi et al. [29] applied precise gravity investigations for delineating cavities and large fractured zones by planning road construction in lava flow after recent volcano eruption in Réunion island. Microgravity combined with absolute gravity measurements has also been used to study water storage variations in a karst aquifer on the Larzac Plateau (France) [41]. Castiello et al. [42] reported a microgravity studying an ancient underground cavity in the complex urban environment of Naples.Types of noise associated with microgravity studies of shallow karst cavities in areas of developed infrastructure are presented in detail in Leucci and Georgi [32]. Porzucek [43] discusses the advantages and disadvantages of using the Euler deconvolution in microgravity studies. A new method for the simultaneous, nonlinear inversion of gravity changes and surface deformation using bodies with a free geometry was proposed by Camacho et al. [33].The importance of gravity field observations at different levels as well as the precise calculation of topographic effects in intermediate and distant zones was analyzed in Eppelbaum [34]. Dolgal and Sharkhimullin [44] suggested using a “localization function” to enhance the quality of PGMs and reduce the ambiguity of the results in high-precise gravity.Kaufmann et al. [45] successfully employed microgravity to identify subsurface voids in the Unicorn cave in the Harz Mountains (Germany). Hajian et al. [35] applied locally linear neurofuzzy microgravity modeling to the three most common shapes of subsurface cavities: sphere, vertical cylinder, and horizontal cylinder. The authors showed that their method can estimate cavity parameters more accurately than least-squares minimization or multilayer perceptron methods.Panisova et al. [46] fruitfully applied a new modification of close range photogrammetry for calculation of building corrections in the microgravity survey for karst delineation in the area of historical edifice (Slovakia).


## 3. Different Kinds of Noise in Microgravity Surveys

A microgravity survey is the geophysical method most affected by corrections and reductions caused by different kinds of noise (disturbances). A chart showing the different types of noise typical to microgravity studies is presented in Figure1.Figure 1
Noise affecting microgravity investigations (adapted from [1]).These types of noise are described in more detail below.


### 3.1. Artificial (Man-Made) Noise

Theindustrial component of noise mainly comes from surface and underground constructions, garbage dumps, transportation and communications lines, and so forth. The instrumental component is associated with the technical properties of gravimeters (e.g., shift zero) and gradientometers. Human error, obviously, can accompany geophysical observations at any time. Finally, undocumented (poorly documented) results of previous surveys can distort preliminary PAM development.


### 3.2. Natural Disturbances

Nonstationary noise includes, for instance, known tidal effects. Meteorological conditions (rain, lightning, snow, hurricanes, etc.) can also affect gravimeter readings. Corrections for the atmosphere deserve special attention in microgravity investigations, since the air layer attraction is different at various levels over and below the m.s.l. Soil-vegetation factors associated with certain soil types (e.g., swampy soil or loose ground in deserts) and dense vegetation, which sometimes hampers movement along the profile, also need to be taken into account.


### 3.3. Geological-Geophysical and Environmental Factors

These constitute the most important physical-geological disturbances. The application of any geophysical method depends primarily on the existence of physical properties contrast between the objects under study and the surrounding medium. Thephysical limitation of method application assesses the measurable density contrast properties between the anomalous targets and the host media.


### 3.4. Spatial Coordinates and Normal Gravity Field Determination

Spatial coordinates and normal gravity field determination are also crucial to precise gravity studies and any inaccuracies here may lead to significant errors in subsequent analyses.


### 3.5. Uneven Terrain Relief

Uneven terrain relief can hamper the movement of equipment and restrict gravity data acquisition. Physically, the gravity field is affected by the form and density of the topographic features composing the relief, as well as variations in the distance from the point of measurement to the hidden target [34]. Calculations for the surrounding terrain relief  (sometimes for radii up to 200 km) are also of great importance [47, 48].


### 3.6. Earthquake Damage

Earthquake damagezones are widely spread over the Eastern Mediterranean, especially in the regions near the Dead Sea Transform (DST) Zone [49]. These zones may significantly complicate microgravity data analysis.


### 3.7. The Variety of Anomalous Sources

The variety of anomalous sources is composed of two factors: the variable surrounding medium and the variety of anomalous targets. Both these factors are crucial and greatly complicate the interpretation of magnetic data.


### 3.8. Variable Subsurface

Variable subsurfacecan make it difficult to determine the correct densities of bodies occurring close to the earth’s surface.


### 3.9. Local and Regional Trends

Local and regional trends (linear, parabolic, or other types) often mask the target gravity effects considerably (e.g., [2, 47, 48, 50]). Sometimes regional gravity trend effects may exceed local desired anomalies by some tenfold.Let us consider the last disturbing factor in detail. The correct removal (elimination) of regional trends is not a trivial task (e.g., [47]). Below we present two examples showing disturbing trend effects in detailed gravity investigations. Figure 2 shows two cases of nonhorizontal gravity observations with the presence of an anomalous body. The distorting effect of a nonhorizontal observation line occurs when the target object differs from the host medium by a contrast density and produces an anomalous vertical gradient. Comparing the ΔgB anomalies from the local body observed on the inclined and horizontal relief indicates that the gravity effects in these situations are different (Figure 2). Despite the fact that all the necessary corrections were applied to the observations on the inclined relief, the computed Bouguer anomaly is characterized by small negative values (minimum) in the downward direction of the relief, whereas the anomaly on the horizontal profile has no negative values (this kind of noise is described in Section 3.5). Thus, applying all conventional corrections does not eliminate this trend because the observation point for the anomalous object was different [2]. Hence a special methodology is required for gravimetric quantitative anomaly interpretation in conditions of inclined relief [34].Negative effect of gravitational anomalies from a local anomalous body observed on inclined and horizontal profiles (after [2], with modifications). (a) Smooth slope, (b) complicated slope. (1) Inclined profile; (2) horizontal profile; (3) anomalous body with a positive contrast density Δσ=1500 kg/m3; anomaly ΔgB from the same body after topographic mass attraction correction: (4) on an inclined profile, (5) on a horizontal profile.
(a)
(b)Sometimes even simple computing of the first and second derivatives of the gravity fieldΔgx and Δgxx (second and third derivatives of the gravity potential, resp.) is enough to locate local bodies against a disturbing field background. One such example is presented in Figure 3 where the Bouguer gravity ΔgB is practically impossible to interpret, whereas the calculation of ΔgBx was informative regarding the geometry of two closely occurring sinkholes. Finally, the behavior of the graph ΔgBxx clearly reflects the location of the vertical boundaries of two closely occurring objects with a small negative interval (surrounding medium) between them.Figure 3
Computation of the horizontal derivatives of the gravity field for two proximal sinkhole models. (a) Computed gravity curve (level of computation: 0.3 m), (b) first horizontal derivative of gravity fieldΔgx, (c) second horizontal derivative Δgxx, and (d) physical-geological model (after [3]).The area under study—Ghor Al-Haditha—is situated in the eastern coastal plain of the Dead Sea (Jordan) in conditions of very complex regional gravity pattern (Figure4). The satellite gravity data shown in this figure were obtained from the World Gravity DB as retracked from Geosat and ERS-1 altimetry [51]. These observations were made with regular global 1-minute grids that can differentiate these data from previous odd surface and airborne gravity measurements. This complex gravity field distribution in the vicinity of the area under study is caused mainly by the strong negative effect of the low density sedimentary associations and salt layers accumulated in the DST and also several other factors.Figure 4
Areal map of the investigated site.


## 3.1. Artificial (Man-Made) Noise

Theindustrial component of noise mainly comes from surface and underground constructions, garbage dumps, transportation and communications lines, and so forth. The instrumental component is associated with the technical properties of gravimeters (e.g., shift zero) and gradientometers. Human error, obviously, can accompany geophysical observations at any time. Finally, undocumented (poorly documented) results of previous surveys can distort preliminary PAM development.


## 3.2. Natural Disturbances

Nonstationary noise includes, for instance, known tidal effects. Meteorological conditions (rain, lightning, snow, hurricanes, etc.) can also affect gravimeter readings. Corrections for the atmosphere deserve special attention in microgravity investigations, since the air layer attraction is different at various levels over and below the m.s.l. Soil-vegetation factors associated with certain soil types (e.g., swampy soil or loose ground in deserts) and dense vegetation, which sometimes hampers movement along the profile, also need to be taken into account.


## 3.3. Geological-Geophysical and Environmental Factors

These constitute the most important physical-geological disturbances. The application of any geophysical method depends primarily on the existence of physical properties contrast between the objects under study and the surrounding medium. Thephysical limitation of method application assesses the measurable density contrast properties between the anomalous targets and the host media.


## 3.4. Spatial Coordinates and Normal Gravity Field Determination

Spatial coordinates and normal gravity field determination are also crucial to precise gravity studies and any inaccuracies here may lead to significant errors in subsequent analyses.


## 3.5. Uneven Terrain Relief

Uneven terrain relief can hamper the movement of equipment and restrict gravity data acquisition. Physically, the gravity field is affected by the form and density of the topographic features composing the relief, as well as variations in the distance from the point of measurement to the hidden target [34]. Calculations for the surrounding terrain relief  (sometimes for radii up to 200 km) are also of great importance [47, 48].


## 3.6. Earthquake Damage

Earthquake damagezones are widely spread over the Eastern Mediterranean, especially in the regions near the Dead Sea Transform (DST) Zone [49]. These zones may significantly complicate microgravity data analysis.


## 3.7. The Variety of Anomalous Sources

The variety of anomalous sources is composed of two factors: the variable surrounding medium and the variety of anomalous targets. Both these factors are crucial and greatly complicate the interpretation of magnetic data.


## 3.8. Variable Subsurface

Variable subsurfacecan make it difficult to determine the correct densities of bodies occurring close to the earth’s surface.


## 3.9. Local and Regional Trends

Local and regional trends (linear, parabolic, or other types) often mask the target gravity effects considerably (e.g., [2, 47, 48, 50]). Sometimes regional gravity trend effects may exceed local desired anomalies by some tenfold.Let us consider the last disturbing factor in detail. The correct removal (elimination) of regional trends is not a trivial task (e.g., [47]). Below we present two examples showing disturbing trend effects in detailed gravity investigations. Figure 2 shows two cases of nonhorizontal gravity observations with the presence of an anomalous body. The distorting effect of a nonhorizontal observation line occurs when the target object differs from the host medium by a contrast density and produces an anomalous vertical gradient. Comparing the ΔgB anomalies from the local body observed on the inclined and horizontal relief indicates that the gravity effects in these situations are different (Figure 2). Despite the fact that all the necessary corrections were applied to the observations on the inclined relief, the computed Bouguer anomaly is characterized by small negative values (minimum) in the downward direction of the relief, whereas the anomaly on the horizontal profile has no negative values (this kind of noise is described in Section 3.5). Thus, applying all conventional corrections does not eliminate this trend because the observation point for the anomalous object was different [2]. Hence a special methodology is required for gravimetric quantitative anomaly interpretation in conditions of inclined relief [34].Negative effect of gravitational anomalies from a local anomalous body observed on inclined and horizontal profiles (after [2], with modifications). (a) Smooth slope, (b) complicated slope. (1) Inclined profile; (2) horizontal profile; (3) anomalous body with a positive contrast density Δσ=1500 kg/m3; anomaly ΔgB from the same body after topographic mass attraction correction: (4) on an inclined profile, (5) on a horizontal profile.
(a)
(b)Sometimes even simple computing of the first and second derivatives of the gravity fieldΔgx and Δgxx (second and third derivatives of the gravity potential, resp.) is enough to locate local bodies against a disturbing field background. One such example is presented in Figure 3 where the Bouguer gravity ΔgB is practically impossible to interpret, whereas the calculation of ΔgBx was informative regarding the geometry of two closely occurring sinkholes. Finally, the behavior of the graph ΔgBxx clearly reflects the location of the vertical boundaries of two closely occurring objects with a small negative interval (surrounding medium) between them.Figure 3
Computation of the horizontal derivatives of the gravity field for two proximal sinkhole models. (a) Computed gravity curve (level of computation: 0.3 m), (b) first horizontal derivative of gravity fieldΔgx, (c) second horizontal derivative Δgxx, and (d) physical-geological model (after [3]).The area under study—Ghor Al-Haditha—is situated in the eastern coastal plain of the Dead Sea (Jordan) in conditions of very complex regional gravity pattern (Figure4). The satellite gravity data shown in this figure were obtained from the World Gravity DB as retracked from Geosat and ERS-1 altimetry [51]. These observations were made with regular global 1-minute grids that can differentiate these data from previous odd surface and airborne gravity measurements. This complex gravity field distribution in the vicinity of the area under study is caused mainly by the strong negative effect of the low density sedimentary associations and salt layers accumulated in the DST and also several other factors.Figure 4
Areal map of the investigated site.


## 4. Computation of the 3D Gravity Effect from Models of Sinkholes and the Dead Sea Transform

To test methods of regional trend elimination, two theoreticalPGMs—sinkhole PGM and DST PGM—were developed. The computed gravity effects from these PGMs were also artificially complicated by randomly distributed noise.


### 4.1. Computation of the 3D Gravity Effect from the SinkholePGM

To calculate the 3D gravity field, 12 parallel profiles with a distance between them of 5 m were applied (Figure5). For the PGM a two layer (σ1=2000 kg/m3 and σ2=2100 kg/m3, resp.) PGM with two types of ellipsoidal sinkholes was constructed (Figure 6). The center of the first large sinkhole was located at a depth of −60 m below the earth’s surface in the second layer, with a contrast density of  −900 kg/m3. The center of the second small sinkhole was located at a depth of −20 m below the earth’s surface in the first layer, with a contrast density of  −2000 kg/m3. Profile 6 was selected as the central one, and the left and right ends of sinkhole 1 were defined as −30 and +30 m, and for sinkhole 2 as −12 and +12 m, respectively. For the 3D gravity field modeling of this and the following examples, mainly the GSFC program [19] software was employed. The number of computation points along the sinkholes PGM was chosen to be 200, that is, every 2.5 m.Figure 5
Scheme of gravity field 3D computation for the model example.Figure 6
Gravity field anomalies along profile 6 from models of sinkholes.The compiled gravity map for the 12 profiles for the sinkholePGM is shown in Figure 7. As can be seen from this map, the anomaly from sinkhole 2 is narrower than sinkhole 1 but is characterized by comparatively high amplitude.Figure 7
Compiled gravity map for 12 profiles.


### 4.2. Computation of the 3D Gravity Effect from the DST

The simplifiedPGM of the DST for its deepest part (Figure 8) was constructed from data presented in Ginzburg and Ben-Avraham [52], Weber et al. [53], and the authors’ computations. The location of the sinkhole 500 m profile in the upper right section of the model is shown. The PGM of the DST was computed as the same for all 12 profiles. The computed gravity effect from the DST was added to the gravity field to account for the sinkhole PGM (Figure 9). As can be seen from this figure, the anomaly from sinkhole 2 can be visually detected, but the anomaly from sinkhole 1 is practically undetectable against the regional trend produced by the DST.Figure 8
Simplified density-geological model of the Dead Sea Transform.Figure 9
Combined  gravity field along profile 6 from models of sinkholes and effect of the DST.


### 4.3. Noise Added by Random Number Generation

Given that the geological medium is usually more complex than presented in the models in Figures6 and 8 we used a random number generator to introduce a noise factor into the calculations. Algorithms developed by Bichara et al. [8] and Wichura [54] were applied. The parameters of this randomly distributed noise—the mean values and the standard deviations along 12 profiles—are listed in Table 1. In other words, the randomly distributed nonrecurrent noise was added to 200 computation points for each of 12 profiles.Table 1
Inserted randomly distributed noise.
Profile number
Mean value
Standard deviation
1
0.150
0.040
2
0.160
0.030
3
0.140
0.035
4
0.130
0.038
5
0.170
0.029
6
0.120
0.033
7
0.150
0.038
8
0.140
0.032
9
0.110
0.024
10
0.160
0.031
11
0.125
0.025
12
0.15
0.028Figure10 shows a gravity map compiled on the basis of randomly distributed noise (from Table 1). The combined gravity effects from (1) the sinkhole PGM, (2) the DST PGM, and (3) randomly distributed noise were used to compute the integrated gravity map that sums the effects of these three factors (Figure 11). It should be noted that in the map (Figure 11) there are no visual signatures of the negative anomalies from sinkholes 1 and 2.Figure 10
Compiled gravity map of the random noise for 12 profiles.Figure 11
Compiled  gravity map for 12 profiles with combined effect from: (1) the DST, (2) sinkholes, and (3) random noise.


### 4.4. Results of the Different Algorithms to Eliminate Regional Trends

To remove the regional trends, different algorithms and methods were applied: the first and second derivatives, self-adjusting and adaptive filtering, Fourier series, wavelet decomposition, principal component analysis, inverse probability, and other methods were applied (altogether more than 30 different procedures).Examples of applications of (1) the entropy parameter using a moving window with self-adapting size, (2) gradient sounding, and (3) power estimation by the Morlet transformation are presented in Figures12(a), 12(b), and 12(c), respectively. Computing the entropy with the moving window (Figure 12(a)) revealed a clear ring anomaly from sinkhole 2; the anomaly from sinkhole 1 was difficult to locate. At the same time the boundary effect at the map edges (Figure 12(a)) complicated image reading. The results of gradient sounding (Figure 12(b)) suggested the presence of an anomaly from sinkhole 2. A power estimation based on a Morlet transformation (Figure 12(c)) very clearly indicates the location of sinkhole 2. However, a superposition of computed gravity anomalies and noise effects gives a false weak anomaly (located at 105–108 m) of sinkhole 1.Results of three different methodologies: (a) entropy computation using a moving window with self-adapting size, (b) gradient sounding, and (c) power estimation by Morlet transformation.
(a)
(b)
(c)Regression analysis is now considered one of the most powerful methods for removing trends of different kinds (e.g., [55–57]). Two regression methods were selected. Figure 13 shows the residual gravity map after subtracting a bilinear saddle (F(x,y)=a+bx+cy+dxy) regression. The negative gravity anomaly from sinkhole 1 in the area of 160 m (see Figures 6 and 9) is clearly detected, whereas the negative anomaly from sinkhole 2 in the area of 340 m is small and could not be reliably detected.Figure 13
Residual gravity map after subtracting bilinear saddle regression.The gravity map after subtracting a local polynomial regression(F(x,y)=a+bx+cy+dxy+ex2+fy2) is presented in Figure 14. Here the negative anomaly from sinkhole 1 was weak and was difficult to detect, but the anomaly from sinkhole 2 was unmistakable. These findings suggest that there are advantages to using a combination of methods.Figure 14
Residual gravity map after subtracting local polynomial.


## 4.1. Computation of the 3D Gravity Effect from the SinkholePGM

To calculate the 3D gravity field, 12 parallel profiles with a distance between them of 5 m were applied (Figure5). For the PGM a two layer (σ1=2000 kg/m3 and σ2=2100 kg/m3, resp.) PGM with two types of ellipsoidal sinkholes was constructed (Figure 6). The center of the first large sinkhole was located at a depth of −60 m below the earth’s surface in the second layer, with a contrast density of  −900 kg/m3. The center of the second small sinkhole was located at a depth of −20 m below the earth’s surface in the first layer, with a contrast density of  −2000 kg/m3. Profile 6 was selected as the central one, and the left and right ends of sinkhole 1 were defined as −30 and +30 m, and for sinkhole 2 as −12 and +12 m, respectively. For the 3D gravity field modeling of this and the following examples, mainly the GSFC program [19] software was employed. The number of computation points along the sinkholes PGM was chosen to be 200, that is, every 2.5 m.Figure 5
Scheme of gravity field 3D computation for the model example.Figure 6
Gravity field anomalies along profile 6 from models of sinkholes.The compiled gravity map for the 12 profiles for the sinkholePGM is shown in Figure 7. As can be seen from this map, the anomaly from sinkhole 2 is narrower than sinkhole 1 but is characterized by comparatively high amplitude.Figure 7
Compiled gravity map for 12 profiles.


## 4.2. Computation of the 3D Gravity Effect from the DST

The simplifiedPGM of the DST for its deepest part (Figure 8) was constructed from data presented in Ginzburg and Ben-Avraham [52], Weber et al. [53], and the authors’ computations. The location of the sinkhole 500 m profile in the upper right section of the model is shown. The PGM of the DST was computed as the same for all 12 profiles. The computed gravity effect from the DST was added to the gravity field to account for the sinkhole PGM (Figure 9). As can be seen from this figure, the anomaly from sinkhole 2 can be visually detected, but the anomaly from sinkhole 1 is practically undetectable against the regional trend produced by the DST.Figure 8
Simplified density-geological model of the Dead Sea Transform.Figure 9
Combined  gravity field along profile 6 from models of sinkholes and effect of the DST.


## 4.3. Noise Added by Random Number Generation

Given that the geological medium is usually more complex than presented in the models in Figures6 and 8 we used a random number generator to introduce a noise factor into the calculations. Algorithms developed by Bichara et al. [8] and Wichura [54] were applied. The parameters of this randomly distributed noise—the mean values and the standard deviations along 12 profiles—are listed in Table 1. In other words, the randomly distributed nonrecurrent noise was added to 200 computation points for each of 12 profiles.Table 1
Inserted randomly distributed noise.
Profile number
Mean value
Standard deviation
1
0.150
0.040
2
0.160
0.030
3
0.140
0.035
4
0.130
0.038
5
0.170
0.029
6
0.120
0.033
7
0.150
0.038
8
0.140
0.032
9
0.110
0.024
10
0.160
0.031
11
0.125
0.025
12
0.15
0.028Figure10 shows a gravity map compiled on the basis of randomly distributed noise (from Table 1). The combined gravity effects from (1) the sinkhole PGM, (2) the DST PGM, and (3) randomly distributed noise were used to compute the integrated gravity map that sums the effects of these three factors (Figure 11). It should be noted that in the map (Figure 11) there are no visual signatures of the negative anomalies from sinkholes 1 and 2.Figure 10
Compiled gravity map of the random noise for 12 profiles.Figure 11
Compiled  gravity map for 12 profiles with combined effect from: (1) the DST, (2) sinkholes, and (3) random noise.


## 4.4. Results of the Different Algorithms to Eliminate Regional Trends

To remove the regional trends, different algorithms and methods were applied: the first and second derivatives, self-adjusting and adaptive filtering, Fourier series, wavelet decomposition, principal component analysis, inverse probability, and other methods were applied (altogether more than 30 different procedures).Examples of applications of (1) the entropy parameter using a moving window with self-adapting size, (2) gradient sounding, and (3) power estimation by the Morlet transformation are presented in Figures12(a), 12(b), and 12(c), respectively. Computing the entropy with the moving window (Figure 12(a)) revealed a clear ring anomaly from sinkhole 2; the anomaly from sinkhole 1 was difficult to locate. At the same time the boundary effect at the map edges (Figure 12(a)) complicated image reading. The results of gradient sounding (Figure 12(b)) suggested the presence of an anomaly from sinkhole 2. A power estimation based on a Morlet transformation (Figure 12(c)) very clearly indicates the location of sinkhole 2. However, a superposition of computed gravity anomalies and noise effects gives a false weak anomaly (located at 105–108 m) of sinkhole 1.Results of three different methodologies: (a) entropy computation using a moving window with self-adapting size, (b) gradient sounding, and (c) power estimation by Morlet transformation.
(a)
(b)
(c)Regression analysis is now considered one of the most powerful methods for removing trends of different kinds (e.g., [55–57]). Two regression methods were selected. Figure 13 shows the residual gravity map after subtracting a bilinear saddle (F(x,y)=a+bx+cy+dxy) regression. The negative gravity anomaly from sinkhole 1 in the area of 160 m (see Figures 6 and 9) is clearly detected, whereas the negative anomaly from sinkhole 2 in the area of 340 m is small and could not be reliably detected.Figure 13
Residual gravity map after subtracting bilinear saddle regression.The gravity map after subtracting a local polynomial regression(F(x,y)=a+bx+cy+dxy+ex2+fy2) is presented in Figure 14. Here the negative anomaly from sinkhole 1 was weak and was difficult to detect, but the anomaly from sinkhole 2 was unmistakable. These findings suggest that there are advantages to using a combination of methods.Figure 14
Residual gravity map after subtracting local polynomial.


## 5. Removing Regional Gravity Trend in the Area of Ghor Al-Haditha, on the Eastern Coastal Plain of the Dead Sea (Jordan)

The Ghor Al-Haditha area is located south-east of the northern Dead Sea basin (see Figure4). Alluvial fan deposits from Wadi Ibn Hammad cover the southern part of this area. Borehole sections indicate that the geological material of the shallow subsurface consists of laminated sand interbedded with layers of calcareous silts and possibly clay or marl. The sinkholes at the eastern coast of the Dead Sea can be dated to the mid-1980s [58].The observed gravity map (Figure15) shows the strong influence of the negative gravity effect due to the DST (and possibly other geological factors). Computing the first and second derivatives, self-adjusting filtering, gradient directional filtering, Fourier series, principal component analysis, and other methods were less successful than the bilinear saddle and local polynomial regressions.Figure 15
Bouguer gravity map of the Ghor Al-Haditha area (Jordan).Figure16 displays results of the gradient sounding. After regional trend removal two local anomalies were found: one complex in the center of the area and the other near the western border. Clearly, however, this type of analysis is only valid for target qualitative delineation.Figure 16
Results of gradient sounding.A visual comparison of the residual maps (Figures17 and 18, resp.) shows the great similarity between the two regression methods. A negative anomaly in the center of the map with amplitude of 0.6-0.7 mGal is very visible. An important advantage of the residual maps is that these maps can be used both for qualitative and quantitative analysis.Figure 17
Residual gravity map of the Ghor Al-Haditha area after subtracting bilinear saddle regression.Figure 18
Residual gravity map of the Ghor Al-Haditha area after subtracting local polynomial.The gravity profiles are constructed along the same line (A–B in Figure17) and (A′–B′ in Figure 18) demonstrate (Figure 19)  that there are some small differences, mainly in the amplitude value from the anomalous object with a negative density contrast.Figure 19
Comparison of gravity curves constructed along profile A–B for Figure17 (after subtracting the bilinear saddle regression) and A′–B′ for Figure 18 (after subtracting the local polynomial).3D modeling indicates that such a gravity anomaly may have been produced by a sinkhole (similar to model 2 in Figure6, but enlarged roughly twice) with its upper edge occurring at a depth of 4 m below the earth’s surface (Figure 20). The location of this sinkhole and its size are consistent with the available geological data [59]. The disparity between the observed and computed ΔgB in the right part of the profile may have been caused by the presence of an additional small underground cavity with an irregular shape.Figure 20
An initial physical-geological model along profile A′–B′ developed on the basis of 3D gravity field modeling.


## 6. Conclusion

The different kinds of noise affecting microgravity investigations amply illustrate the need for careful calculation of each of these disturbing factors. In particular, the influence of regional trends often masks the target local microgravity anomalies. The 3D theoreticalPGM of sinkholes combined with the gravity effect from the DST (producing a strong regional trend) as well as the randomly distributed noise (introducing some geological medium complexity) was constructed. Comparison of different methodologies to remove regional trends revealed that the most effective algorithms are the bilinear saddle and local polynomial regressions. The use of these methods to analyze gravity data observed in the complex geological environments of the Ghor Al-Haditha site (eastern coastline of the Dead Sea, Jordan) successfully removed the regional gradient and localized the negative anomaly possibly produced by a subsurface sinkhole. The 3D gravity field modeling led to identification of the parameters of this PGM.



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*Source: 341797-2013-04-09.xml*