Asia Conference of Remote Sensing 2013

Geological Structure Detection Digitally Using Synthetic Aperture Radar (SAR) Data

Atriyon Julzarika

Remote Sensing Application Center

Indonesian National Institute of Aerospace (LAPAN)

Jl. Kalisari No. 8 Pekayon, Pasar Rebo, Jakarta 13710

Geodesy and Geomatics Engineering

Faculty of Engineering

Gadjah Mada University

Jl. Grafika No. 2 Yogyakarta

E-Mail: verbhakov@yahoo.com

ABSTRACT

Geological structures detection can be performed using the height model data. This data is Synthetic Aperture Radar (SAR), Shuttle Radar Topographic Mission (SRTM) and XSAR. Geological structure consists of joint, faults, folds. Geological structures can be used for various applications such as geological mapping and mining. Height model is made using the integration method, namely the incorporation of at least two height models with the same reference plane, and be weighted at each height models. SRTM is made of interferometry C band. XSAR made of interferometry X band. SRTM and XSAR still in the form of Digital Surface Model (DSM). Then do the terrain correction, which transform DSM into the Digital Elevation Model (DEM) or by changing the DSM to be Digital Terrain Model (DTM). Bull Eye’s correction needs to be done if the terrain correction has completed. Bull Eye’s correction done in order to eliminate the high anomaly of value happens to be eight pixels around the pits and spire or fill and sink. It cultivated near zero error value or a minimum of 3σ. After that, do the Geoid undulation correction using Earth Gravitational Model (EGM) 2008. EGM 2008 is made from Grace satellite data. SRTM and XSAR has had the same reference plane, then later be weighted in order to obtain new height models with high accuracy and precision. Then carried out by the geological structures detection using dip and strike methods. This detection is done digitally. This dip and strike method can be done with three-point approach, contact plane, strike from the map, retrace, and parallel contact. The geological structure can be used for energy and mineral mining detection, such as coal, copper, tin, petroleum, geothermal, iron ore, and others. This digital geological structure method could be used to geological preliminary survey so that it will minimize the cost and time and improve efficiency of geological mapping.

Keywords: geological structure, SRTM and XSAR, Dip and Strike, cost, time

I.     Introduction

Geological structure is formed by the pattern structure formed naturally by geological processes in the long term. Therefore, the detection of the geological structure does not require the data to the latest acquisition, but can use old data. The detection of geological structures can be done with the data of optical and Synthetic Aperture Radar (SAR). It also can use the data model 3D/height models to improve accuracy and precision of a geological structure.

Geological structure referred to in the study include Stump, Fault, and folds. Stump (Joint) is a fracture / fault in the rock layers that occur due to the influence of both endogenous forces of pressure and traction, without any displacement. Stump has several types, namely Stump Grind and Pull. Stump Grind (Joint Shear) is Stump the rock caused by pressure. Pull Stump (Tension Joint) is Stump the rocks that occur due to the pull. Faults (Faults) is a fracture / fault in the rock layer caused by the influence of the forces of pressure and pull of both endogenous and experienced displacement / dislocation / shift. Fault has several types, namely Fault Normal / Down (Normal / Gravity Fault), Fault Up (Reverse / Thrust Fault), Fault Horizontal / Scroll (Horizontal / Strike-Slip Fault), pop (Horst), Terban (Graben). Folds (Folds) is a layer of sedimentary rock structure shaped crease / wave / style arch formed by endogenous form of pressure. Folds have several types, namely Folds Upright / symmetric (Upright Fold / Fold Symmetrical), folds are symmetric (Asymmetrical Fold), Folds Tilt / Dangling (Inclined Fold / Fold overturned), Folds Damping (Recumbent Fold), Anticline (Anticline), syncline (Syncline). Geological structure can be determined if it has to know the type of deformation that occurred in the study area. This deformation concept can be approached scientifically through leveling or geo-mathematic count.

Geology is the study of the structure of the three-dimensional distribution of rock bodies and the surface is flat or folded, and their internal structure (Davis and Reynolds, 1996). Geological structure includes the shape of the surface are also discussed in the study of geomorphology, metamorphism and geological engineering. Natural forms on rocks (frozen, sedimentary and metamorphic) are caused by the forces of plate tectonics in the geological structure of the rock is determined by: rock physical properties (hardness, specific gravity, density), compression forces, the forces of stress and strain.
And orogenik tectonic forces that formed the geological structure in the form of stress (voltage). Based on the uniformity of strength, stress can be divided into 2, namely:

a.         Uniform stress (confining stress) that suppress voltage or pull with equal strength in all directions.

b.        Differential Stress is tension or push or pull from a single direction and could also be from or to any direction, but one way is more dominant force. Introduction to geological structures can be done indirectly through the following ways:

- Geological mapping by measuring the strike and dip.

- Interpretation of topographic maps, namely the appearance of symptoms of the river search, search and morphological contour lines and contour line pattern.

- Aerial photo

- Drilling.

- Geophysics, which is based on the properties owned by the rocks.

Geometric forms contained in the earth's crust formed by the influence of endogenous forces, either pressure or traction. Geologists call Geological Structure, and known as Stump, Fault, and folds (Ragan, 2009). There are several factors that affect the process of the formation of the geological structure of the rock: rock elastic properties, resistivity, plasticity and viscosity. Other factors such as: The pores of rocks and rock textures. A structure can be formed by a geological forces that occur, namely: tension (pull), compression (compression force), coupling (multiple styles), torque (turning force). A compression force can produce a multiplicity of structures, pensesaran, and subduction. Whereas a tension force produces a structural fault. This study aimed to the detection plate and geological structures using satellite data (optical and SAR) is an efficient and low cost.

Interferometry

Interferometric Synthetic Aperture Radar (InSAR) is a Remote sensing technology which uses the image of the radar sensors of the aircraft / satellite (Julzarika, 2007). Radar sensors on aircraft and satellites constantly emit radar waves, radar waves are then recorded as received by the sensor is reflected by the target due to the earth's surface. Radar images obtained from aircraft and satellite contains two vital information. That information is in the form of the transmit beam power phase and amplitude are affected by a number of waves emitted and reflected back. Figure 1-1 is a graph of the amplitude of the phase of the radar image recording.

At the time of the emitted wave phase measurements. In the image obtained from each image element (pixel) will have two such information. The intensity of the signal can be used to determine the characteristics of the wave-reflecting objects, while the phase of the wave is used to determine whether there has been a movement (deformation) on the surface of the reflecting wave. InSAR is a technique used to extract the information of three-dimensional (3D) observations of the Earth's surface with radar wave phase (Julzarika, 2007). Was originally used for radar interferometry observations of the surface of the moon and the planet Venus. In 1974 this technique was first applied in the field of mapping. To obtain the topography of the image must meet two requirements, namely the object imaged on the surface of the earth which must be clearly visible or has a high-resolution image so that it can be done and the identification of the appropriate interpretation.

Figure 1. Grafik Fase

Besides the image must have a three-dimensional position enough so that the area to be mapped to known topography. Both of these can only be met by the InSAR technique. This is why a growing number of field studies that apply InSAR. Interferometry technique imaging an object at the Earth's surface by observing the phase difference of two waves of phosphorescence from a single object. In this study, the data used InSAR using airplane rides. The purpose of this study is to make a 3D modeling DEM and DTM results derived InSAR DSM.

Height model/3D Model

The 3D model is a display of a 3D model of the coordinate system (polar, geodetic, raster and kartesi) reference plane defined by the projection and datum specified. 3D models can be created from optical and radar data. There are several types of 3D models, the DSM, DEM, DTM, DTED, DHM, DGM, and EGM. According to the International Association of Geodesy (IAG) and (Li, Zhu, Gold, 2004) and (Miller and Laflamme, 1958), (Petrie and Kennie, 1987), (Helmert, 1880/1884), (Vanicek, 1976), (Vanicek and Krakiwsky, 1986) has been agreed upon understanding of the various types of 3D models, namely:

1. Digital Surface Model (DSM)

A DSM is an elevation model that includes the tops of buildings, trees, powerlines, and any other objects. Commonly this is seen as a canopy model and only 'sees' ground where there is nothing else overtop of it. Essentially the full point cloud, with ground, structures, and vegetation (cheapest). Digital surface model (DSM ) – a first-reflective-surface model that contains elevations of natural terrain features in addition to vegetation and cultural features such as buildings and roads.

2. Digital Elevation Model (DEM)

A DEM is a 'bare earth' elevation model, unmodified from its original data source (such as lidar, ifsar, or an auto correlated photogrammetric surface) which is supposedly free of vegetation, buildings, and other 'non ground' objects. Incidentally, a DEM is far cheaper to produce an a DTM. Bare Earth with structures and vegetation removed.  Digital Elevation Model (DEM ) – a bare-earth model that contains elevations of natural terrain features such as barren ridge tops and river valleys. Elevations of vegetation and cultural features, such as buildings and roads, are digitally removed. Elevation: “height above a given level, especially that of sea”; “height above the horizon”; etc. the terms elevation emphasize the “measurement from a datum to the top” of an object. elevation do not necessarily refer to the altitude of the terrain surface, but in practice, this is the aspect that is emphasized in the use of these terms. DEM was widely used in America

3. Digital Terrain Model (DTM)

A DTM is effectively a DEM that has been augmented by elements such as breaklines and observations other than the original data to correct for artifacts produced by using only the original data. This is often done by using photogrammetrically derived linework introduced into a DEM surface. An example is hydro-flattening commonly seen in elevation models done to FEMA specifications. DEM with thinned ground points (mass points) and breaklines. (most expensive). the DTM was defined as a digital (numerical) representation of the terrain. Terrain: “tract of country considered with regarded to its natural features, etc.”; “an extent of ground, region, territory”; etc. The meaning of “terrain” is more complex and embracing. It may contain the concept of “height” (or “elevation”), but also attempts to include other geographical elements and natural features. Therefore, the term DTM tends to have a wider meaning than DHM or DEM and will attempt to incorporate specific terrain features such as rivers, ridge lines, breaklines, etc. into the model. Generally, a DTM could contain the following four groups of (topographic and non topographic) information as follows:

Ø  Landforms, such as elevation, slope, slope form, and the other more complicated geomorphological features that are used to depict the relief of the terrain.

Ø   Terrain features, such as hydrographic features (i.e., rivers, lakes, coast lines), transportation networks (i.e., roads, railways, paths), settlements, boundaries, etc.

Ø  Natural resources and environments, such as soil, vegetation, geology, climate, etc.

Ø  Socioeconomic data, such as the population distribution in an area, industry and agriculture and capital income, etc.

A DTM is an ordered set of sampled data points that represent the spatial distribution of various types of information on the terrain. The mathematical expression could be something like: KP = f (uP , vP ), K = 1, 2, 3, . . . ,m, P = 1, 2, 3, . . . , n (1.1) where KP is one attribute value of the kth type of terrain feature at the location of point P (which can be a single point, but is usually a small area centered by P); uP , vP is the 2-D coordinate pair of point P; m (m ≥ 1) is the total number of terrain information types; and n is the total number of sampled points. For example, suppose soil type is categorized as ith type of terrain information, then the DTM of this component is expressed as IP = fi(uP , vP ), P = 1, 2, 3, . . . , n. (1.2)

A DTM is a digital representation of the spatial distribution of one or more types of terrain information and is represented by 2-D locations plus a mathematical representation of terrain information. It is commonly regarded as a 2.5-D representation of the terrain information in 3-D geographical space.

4. Geoid

The term Geoid is used to portray the shape of the Earth's surface, and it identifies that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction and the centrifugal force of the Earth's rotation. Among the Earth’s equipotential surfaces, the Geoid coincides with the mean sea level of the oceans through a process of Least Squares Approximation. The Geoid extends under the continents and differs from an ellipsoid of revolution by vertical distances that are within the order of one hundred metres. Ignoring for the moment that soundings on charts are referred to a low water chart datum, the Geoid is the reference surface for heights (orthometric or dynamic, defined below) used in mapping. As such it is often called a "vertical datum" and the heights referred to it are commonly known as "heights above mean sea level". The practical realization of the vertical datum is normally achieved by accepting a mean sea level at the locations of tide gauges along the seashore. This realization carries with it some inherent errors that may reach well over one metre. The local mean sea level is determined indirectly, by studying the tide-gauge record for a certain time period and is thus tacitly valid for that time period.

DEM1 X SAR

            DEM1 X SAR is a 3D model that generated by interferometry from SRTM X Band, it has spatial resolution 25 m. DEM1 X SAR belongs to German Aerospace Center DLR. its horizontal accuracy is ± 20 m (abs.)/± 15 m (rel.), CE 90%. Vertical accuracy ± 16 m (abs.) / ± 6 m (rel.), LE 90%. If we generate new DEM 1 X SAR using CoKriging, it has vertical accuracy 1-5 m (rel.), LE 90% (DLR, 2010).

Figure 2. Interferometry SRTM with ERS Tandem (Knopfle, W., Strunz, G., Roth, A., 1998)

3D model is the key data used for the manufacture of DAS from remote sensing data. 3D models with high accuracy and good precision watershed boundary will produce a much more thorough. 3D Model of DEM1 X SAR has a vertical accuracy of 3-4 meters (results CoKriging) has been able to produce a more thorough watershed boundaries for areas of Indonesia. Accuracy can be increased further if the correction Bull Eye's that aims to eliminate sinks contained in the 3D model. One method to detect the sink is by making height error maps of the 3D model data itself. Height error maps that contain spatial information is the degree of error in such data in accordance with the standard value at a certain tolerance deviation (3 sigma).

Height error sources there are three types, namely phase accuracy, imaging geometry, atmospheric distortions. One way to eliminate is to use some of the interferogram for DEM creation. It also can use a variety of other atmospheric correction methods. Height error from itself data are computed by two process, they are coordinate transformation and least square adjustment computation. The result is standard deviation map in all raster map or it calls height error maps.

Shuttle Radar Topographic Mission (SRTM)

SRTM mission is a mission to map the Earth's surface elevation using the space shuttle that contains instrument SAR. SRTM mission carried out in February 2000, the space shuttle orbiting the Earth for 11 days. Topographic mapping conducted on the Earth's surface using SAR instruments. This mission successfully mapped 80% of the land area of ​​the earth's surface at a latitude of 600 N to 560 S.

Figure 3. Recording X-band coverage for the region of western Indonesia

Figure 4. Recording X-band coverage for the region of eastern Indonesia

SRTM C-XSAR data consists of 3 spatial resolution, namely: spatial resolution of 1 km (30 arc second), 90 m (3 arc second) and 30 m (1 arc second). Examples of differences in appearance and accuracy of third SRTM data are shown in Figure 2-10. SRTM data accuracy X band with a spatial resolution of 30 m is in the range 3-5 m (D. Gesch, 2005), the accuracy of the data C band with a spatial resolution of 90 m is in the range: ± 16 m (Standard product), while the accuracy of the SRTM XC band (Data combined X-and C-band) with a spatial resolution of 30m is around 5-9 m (Yastikh et.al, 2006). The third type of dataSRTM with resolution.

Kriging interpolation

Kriging interpolation method is a method based geostatistics (Widjajanti and Sutanta, 2006). This method is derived from the theory of the limiting variable (variable region) which assumes that the variation of geographic data can be referred to as variable delimiter. Kriging lower weighting for its interpolation of the semivariogram. Each measurement has an error measure, both random errors and uncertainty error. Equity in the geodetic control network affects the accuracy of geodetic control and precision of data (Julzarika, 2007).

Semivariogram calculation and depiction is the core of the Kriging interpolation method. Semivariogram determine the level of spatial relationships (spatial correlation) between the measured data in a region, or the relationship of spatial data is a variable delimiter (Widjajanti and Sutanta, 2006). Semivariogram regulates the process of weighting interpolation method Kriging, and also regulates the quality of the results of interpolation. Before doing the Kriging interpolation method should be determined in advance of semivariogram.

Semivariogram which is the level of spatial relationships is actually a picture of semivarian having intervals between data that is not the same for a retrieval of data within a data group (Widjajanti and Sutanta, 2006). If there is a group of data by the number n, and the interval between the same data or Δ, then the equation can be expressed semivariance relationship between a pair of data into the data-I and-h, which is denoted by "γ" in the equation 1

                                              ...................................  equation 1

In this equation, Xi is the data to-i and Xi-h is another measurement data with the interval h. If the interval between data points are not equal or h has different values​​, then the result of calculation is described semivariance become a form of semivariogram (Soetaat, 1996).

Mathematically, the method CoKriging an interpolation point, need a map point as input data and produces raster maps to estimate and map faults/errors. CoKriging is a multivariate variant with the basic operation of Kriging. CoKriging calculate an estimate or prediction with a minimum sample with better variable (covariable). Variable must be a high correlation (positive or negative). CoKriging good to get precise results. CoKriging using semivariograms covariance taking into account the weight of S wi = 1 and S hj = 0 and the Kriging method (Ilwis, 2009). Variogram value with semivariogram model g A, g B and cross-variogram models for observation and predictand Ai n Bj covariable observations of in accordance with the equation CoKriging.

s² = S w_i g_A(h_i) + S h_j g _AB(h_j) + m₁ ……….……….  equation 2

Research Methodology

 

Figure 5. research methodology

Structural geology detection using Dip and Strike methods

Strike and dip refer to the orientation or attitude of a geologic feature. The strike line of a bed, fault, or other planar feature is a line representing the intersection of that feature with a horizontal plane. On a geologic map, this is represented with a short straight line segment oriented parallel to the strike line. Strike (or strike angle) can be given as either a quadrant compass bearing of the strike line (N25°E for example) or in terms of east or west of true north or south, a single three digit number representing the azimuth, where the lower number is usually given (where the example of N25°E would simply be 025), or the azimuth number followed by the degree sign (example of N25°E would be 025°).

The dip gives the steepest angle of descent of a tilted bed or feature relative to a horizontal plane, and is given by the number (0°-90°) as well as a letter (N,S,E,W) with rough direction in which the bed is dipping. One technique is to always take the strike so the dip is 90° to the right of the strike, in which case the redundant letter following the dip angle is omitted. The map symbol is a short line attached and at right angles to the strike symbol pointing in the direction which the planar surface is dipping down. The angle of dip is generally included on a geologic map without the degree sign. Beds that are dipping vertically are shown with the dip symbol on both sides of the strike, and beds that are flat are shown like the vertical beds, but with a circle around them. Both vertical and flat beds do not have a number written with them.

Figure 6. Strike and dip of the beds. 1-Strike, 2-Dip, 3-Apparent dip 4-Angle of dip

This study aims to make the detection of geological structures using a digital height model of the result of merging the data radar interferometry.

Result and Discussion

The geological structure making use of SAR data. The data used is combined with SRTM C XSAR. 3D models can be created from optical and radar data. Radar and optical data can be obtained from satellite, airborne mapping, and terrestrial survey.

SRTM C and XSAR height can produce models with interferometry. Height models are still in the form of DSM, which is still showing the condition of the earth surface objects. DSM data is necessary terrain corrections, which turn it into a DTM. Prior to the terrain correction, a correction needs to be done Bull Eye’s, it aims to eliminate the high value of the anomaly approximately eight stairs. This Bull Eye’s correction done by making the height error maps (HEM). HEM is made with arithmetic averaging approach.

Calculate the least squares smoothing is intended to get a price estimate of a parameter that is closest to the actual price by determining the amount of the unknown (parameters) of the size of the data set has more observations (Widjajanti, 1997). The principle of least squares completion count is the sum of squares of the residuals is minimal (Hadiman, 1999).

ΣVi2 = minimal

Count smoothing effect on the accuracy and precision factors (Wolf, 1981). Accuracy is the degree of closeness or consistency of measurements to the true value (true value), while precision is the degree of closeness or proximity measurement of the mean value. (Soetaa't, 1996). There are various methods of least squares smoothing count, such as the method parameter, constraint and minimum constraint that considers more than fixed point of the study (Spiegel, 1975) and (Uotila, 1985). Another method is the method of weighted parameters and free nets and inner constraint that takes into account the error of the point of the study (Widjajanti, 1997).

Bull Eye’s is a random error that occurs due to a blunder anomalous high values ​​of the nearest neighbors. Bull Eye’s contour interpolation can be caused by incorrect due to a high point spread unevenly or it could be due to the higher point value that does not correspond to the truth. Bull Eye’s is a point, line, or area that has a height value, but that value does not represent the real situation on the ground.

Bull Eye’s correction needs to be done to 3D models from a variety of input data. Bull Eye’s Correction aims to eliminate anomalous high values ​​that differ from surrounding neighbors and is a blunder and cause a false contour conditions. Figure 7 is a checking Bull Eye’s pits and spires.

 

Figure 7. Pengecekan Bull Eye’s berupa spires dan pits

There are three methods for correction Bull Eye’s, which FillSink, Cut Terrain and Height Error Maps. Height error is made on the value of the standard deviation or vertical error on the 3D model data. Height error can be made from the data itself. Fill sink is anomalously high removal method to areas Cut basin while the Terrain is a high anomaly removal method for convex areas / steep.

Bull Eye’s Correction (Fig. 6) performed with three existing methods, namely FillSink (Figure 8), Cut Terrain (Figure 8), and Height Error Maps (Figure 9). Height Error Maps method produces output data with accuracy and precision better than FillSink and Cut Terrain. FillSink method has advantages in charging anomalous high values ​​in the valley area, but could not correct the data area of ​​a convex / steep, whereas the opposite applies methods Cut Terrain and methods FillSink.

Figure 8. Bull Eye’s coorection using FillSink method

Figure 9. Bull Eye’s correction using Cut Terrain method

Figure 10. Bull Eye’s correction using Height Error Maps method

After correction Bull Eye’s will require checking the accuracy of a Bull Eye;s is still present in the 3D model data. Figure 11 is the result of checking the Bull Eye’s.

Figure 11. Bull Eye’s checking

In addition to checking each pixel value too high to be checked against the value of a geostatistical study area elevation histogram pattern (Figure 12), elevation distribution graph (Figure 13), and the proportion of area (Figure 14). If the pattern is on the condition of minimum standard deviation (3 sigma), the 3D model is already in the free state or a Bull Eye’s there was no blunder again.

Figure 12. Elevation histogram pattern

     

Figure 13. elevation distribution graphic

Figure 14. area proportion

After that needs to be corrected geoid undulations using EGM 2008. It is intended to equate the two fields geoid height models. After two height models have the same reference plane height, then the merger of these two models with the height integration method. This method uses weighting in both height models so that the maximum correlation occurs in both the height model. If the merger had done so then conducted terrain correction.

Method detection of geologic structures

1. Models with height data preparation methods of integration
2. The detection of geological structures (joints, faults, folds) by the method of dip and strike

Figure 15. integration of height model

 Perform error checking Bull Eye’s on the model height. Bull Eye’s is the high value of the error that occurred on 8 pixels around in the form of pits and spires or fill and sink. Keep the error value close to 0 or a minimum of 3σ. Set limits on the pits checking radius and spires, eg within 100 m. Then will appear the results of checking the pits and spires. The detection of geological structures by the method of dip and strike can be done with a three-point approach, the contact plane, strike from the map, retrace, parallel contact.

In the determination of the three-point, can be done by determining the presence of the three point locations of geological structures. Then be obtained by the condition of the geological structure of the three points.

    

Figure 16. structural geology using three points (left) and contact plane (right) method

        

Figure 17. structural geology using strike from maps (left), retrace (mid), and contact plane (right) method

Conclusion

This study has five conclusions, namely:

1. SAR remote sensing data can be used to manufacture height models with high accuracy and precision integration method.
2. The detection of geological structure of the height model of integration can be carried out by the method of dip and strike digitally.
3. Scale and accuracy of the geological structure of the resulting height depends on the type of model used.
4. Height XSAR models of integration and SRTM C is an alternative height model can be used for detection of digital geological structure with a time-efficient and low cost.
5. Correction bull's eye is very important to do on the model height in order to minimize the occurrence of pits and spires.

Reference

Anam, S., 2005, Menggunakan ArcInfo untuk Proyeksi Peta, Cetakan ke-1, Informatika, Bandung

Arsana, I.M.A. and Julzarika, A., 2006. Liscad: Surveying & Engineering Software. Leica GeoSystem. Jakarta. Indonesia.

DLR, 2010. SRTM-DLR. German Aerospace Center. Germany.

Helmert, F.R. , 1880/1884. Die matematischen und physikalischen Theorien der höheren Geodäsie. Teubner, Leipzig.

Julzarika, A., 2007, Analysis of Coordinates Changing Caused by the Changing of Map File Types in Developing Internet Based Geographic Information System, Geodesy and Geomatics Engineering, Faculty of Engineering, Gadjah Mada University, Yogyakarta. Indonesia.

Julzarika, A. and Sudarsono, B., 2009. Penurunan Model Permukaan Dijital (DSM) menjadi Model Elevasi Dijital (DEM) dari Citra Satelit ALOS Palsar. Jurnal Teknik UNDIP. Semarang.

Knopfle, W., Strunz, G., Roth, A., 1998. Mosaiking of Digital Elevation Models Derived by SAR Interferometry. IAPRS, Vol. 32 part 4. Stuttgart, Germany.

Konecny dan Lehmann, 1984, Photogrammetrie, Walter de Gruyter & Co., Berlin, Jerman.

Li, Z., Zhu, Q., and Gold, C., 2005. Digital Terrain Modeling Principles and Methodology. CRC Press. Florida. USA.

Miller, C. and Laflamme, R., 1958. The digital terrain model — theory and applications Photogrammetric Engineering.

Moffitt, F. H. And Mikhail, E. M., 1980, Photogrammetry. Edisi Kedua, Harper and Row Publisher, Newyork, USA.

Petrie, G. and Kennie T., 1987. An introduction to terrain modeling: applications and terminology. University of Glasgow.

Soeta’at., 1996, Hitung kuadrat terkecil lanjut, Geodesy and Geomatics Engineering, Gadjah Mada University, Yogyakarta.

Soeta’at., 2001, Sistem dan Transformasi Koordinat, Geodesy and Geomatics Engineering, Gadjah Mada University,  Yogyakarta.

Spiegel, M.R., 1975, Theory and Problems of Probability and Statistics, Mc Grow-Hill book company, USA.

Uotila, U.A., 1985, Adjustment Computations Notes, Department of Geodetic Science and Surveying The Ohio State University, Ohio.

Vanicek, P. & Krakiwsky, E., 1986. Geodesy, the concepts. North-Holland, Amsterdam, NY, Oxford, Tokyo.

Widjajanti, N., 1997, Hitung Perataan, Geodesy and Geomatics Engineering, Gadjah Mada University,  Yogyakarta.

Widjajanti, N.,dan Sutanta, H. 2006: Model Permukaan Digital, Geodesy and Geomatics Engineering, Gadjah Mada University,  Yogyakarta.

Wolf, P.R., 1981, Adjustment Computations: (practical least square for surveyors), edisi ke-2, Institut Teknologi Bandung, Bandung.