On the Interferometric Coherence: A Multifrequency and Multitemporal Analysis
The illumination of the same area with two antennas with slightly different look angles leads to the assumption that the statistical phase contribution due to the different speckle characteristic in the two received signals is about the same. Their phase difference is therefore deterministic and corresponds to the path difference of both signals. The interferometric coherence is defined as the normalized complex cross-correlation of both complex signals s1 and s2:
where <...> means the expectation value and * is the complex conjugation operator. The absolute value of the interferometric coherence varies between 0 and 1. The coherence is a maximum if both signals are identical, and vanish if the signals do not correlate. Interferometric coherence depends primarily on:
If the two signals are not received simultaneously (one-pass interferometry) but at different times during two repeating passes over the same area (repeat-pass interferometry) the following additional temporal decorrelation effects decrease the coherence:
The amount of temporal decorrelation describes processes occurring on size scales of the signal wavelength with a time resolution defined by the repeat time interval (temporal baseline). The sensitivity of the coherence to changes in the characteristics of the scattering mechanisms in time can be used for the detection of a wide variety of surface processes and the corresponding surface types.
2. Data description and processing
For the presented investigations data aquired during the second SIR-C/X-SAR mission and ERS-1/ERS-2 tandem data of the Mt. Etna Sicily/Italy test site were used. This test site has been choosen because of the availability of good geological and topographic maps as well as an interferometric and photogrammetric DEM. The multifrequent SIR-C/X-SAR data sets were acquired on October 9 and 10, 1994 (data takes 141.1 and 157.1). The C- and L-band image pairs were processed by NASA/JPL in Pasadena, and the X-band image pair was processed by DLR/D-PAF in Oberpfaffenhofen. The multitemporal ERS-1/ERS-2 data sets were aquired on September 5-6 and on November 14-15, 1995 (frame 0747) and processed by DLR/NE-HF in Oberpfaffenhofen .
After spectral filtering in range and azimuth of the SLC images and coregistration we form the interferogram by multiplying the first image with the complex conjugate of the second image. The coherence images are evaluated using an average window with a size of 4 (range) by 5 (azimuth) pixels for the SIR-C/X-SAR data and of 4 by 12 pixels for the ERS-1/ERS-2 data. Because of this big average window the bias in the coherence estimation is small and has been neglected .. To avoid the influence of topography in the coherence estimation, we have extracted the topography related phase-gradient from the interferogram before the coherence estimation.
3. Multifrequency coherence analysis
Figure 3 shows the slant-range coherence maps of the Etna test site in the three frequencies, aquired with a time difference of one day between the pictures. White corresponds to a coherence of 1, and black corresponds to a coherence of 0.
3.1. Interpretation of the coherence maps
Lava flows around the volcano, where no or only pioneer vegetation is present, show a high temporal stability and have high coherence in all three frequencies. Very young lava on the eastern side of the volcano has a higher coherence in X-band than in C- and L-band. The reason for this effect could be the high scattering sensitivity of the short wavelength for the small scale roughness component, characteristic for young lava surfaces . The high backscattered intensity in X-band increases the signal-to-noise ratio of the received signal and the resulting coherence values are therefore higher compared with the corresponding values in the C- and L- band coherence maps.
On the eastern side of the volcano a triangular feature having a very low coherence can be seen in the L-band coherence map below the three craters. This feature corresponds to an area covered with fresh volcanic fallout. The fact of volume scattering alone is not enough to justify such a high decorrelation, so it can be assumed that a change in the volume-scattering properties has occurred during the time between the two passes, e.g. a change in the volume moisture content. Unfortunately, it was not possible to get detailed information about weather conditions during the mission to verify this assumption.
We can also see that the forested areas around the volcano are dark in X- and C-bands and bright in L-band. The reason for this is that short wavelengths like X-band and C-band do not penetrate into the forest volume, and the backscattering from branches and leaves on the top of the trees is dominant. The movement of the tree branches produces a change in the scatterer geometry inside a resolution cell and therefore, a degradation in the coherence between the two interferometric images. In L-band the waves penetrate into the forest volume, and the backscattering is mainly due to double bounce and surface scattering. Therefore, the influence of the scatterer movement in the upper part of the trees is neglectible, and the coherence is high. The same is valid for agricultural areas around settlements. The settlements, however, have a high coherence in all three frequencies as expected.
3.2. Multifrequency classification
Based on the interpretation of the frequency dependent behavior of the interferometric coherence mentioned in the previous section a first-order classification algorithm is addressed. A schematic representation of this algorithm is shown in Figure 1. The starting frequency for the classification is X-band because this frequency shows a higher sensitivity in its interaction with different surface textures. Four different classes of surface, each having different coherence values and characterized by homogeneous geological and/or morphological properties, were detected:
A very good discrimination can be made in X-band between lava surfaces and the other surface types. Also the discrimination between high and low vegetation is very successful. However, the coherence behaviour of surfaces covered with fresh ash or fresh scoria and high vegetation, and the coherence behaviour of the older ash or scoria mantle and lower vegetation are too similar for discrimination with only one frequency. Further ambiguities are present in the differentiation of prehistorical and historical lava covered with ash and/or pioneer vegetation. For the elimination of these ambiguities it is necessary to extract information from the other two frequencies:
The result of classifying the coherence differences in the three frequencies is given in the following seven classes:
3.3. Error analysis
In order to provide a quality assessment of the classification algorithm it is appropriate to measure quantitatively how good the classification results matches the volcanic terrain. A way to accomplish this is to compare the classification results to the available geological maps. This caused some problems due to the different scales and thematic contents in coherence and geological maps.
Class 2 falls within the 5 January 1990 scoria fall deposit typology, and the classification error is about 10% mainly due to the large dark green triangle in Fig. 3 located SW of the summit craters, which, due to the presence of sparse vegetation, coming out from the scoria deposit, belongs to class 1.
With regard to class 4, we note that the expected typologies are the summit and adventive pyroclastics cones and the older lava, depending on the amount of ageing of the different areas. The classification error is about 12%, because in the lower regions this kind of typology is covered by vegetation and frequently falls into classes 1 and 3.
Since classes 5 and 6 corresponds to the same typology of historical lava flows, only a overall performance analysis can be accomplished. The classification error is around 10%. Several historical lava flows, expected in class 5, are classified in the class 4 due to growth of the vegetation (in particular on the lower flanks of the volcano).
For the classes 1 and 3, including the vegetated areas, it was not possible to find accurate and actual botanic maps of the area to check the accuracy of the separation. Analysis based on selected areas show that the classification error between high and dense and sparce vegetation is around 20%. On the other hand the separation between vegetated and unvegetated surfaces is very high (>95%).
4. Multitemporal coherence analysis
In order to reduce the statistical errors in the coherence estimation and the influence of occasionally local effects we have calculated a mean value between the two one-day maps from the September and November data, and also from the ERS-1/ERS-1 and the ERS-2/ERS-2 constellation with 70 days time difference. Figure 5 shows the resulting two slant-range coherence maps.
Due to the very montainous region with terrain heights between 0 and 3400 meters and the very steep sensor look angle of 22 degrees the coherence maps show strong geometrical deformations, especially on the western side of the volcano. Locally very high slopes are causing either layover areas or are distorting the picture so strong that it is not possible to recognize the features of the coherence map. It is very complicated to make any prediction there. In the following we therefore concentrate only on the eastern side of the volcano.
4.1 Interpretation of the coherence maps
In an elliptic region around the top the coherence is very low in the tandem pair from November and also in both 70-days pairs. The snow line on Etna at the november, 15th 1995 was around 2400m, which corresponds very well with the observed low coherent area. The low coherence in this area does not allow a further classification.
The young and uncovered lava flows around the volcano show a very high coherence in the 1-day and also in the 70-days map. As it could be expected, the temporal stability is very high on this rocky ground. All other surfaces show an essentially higher decorrelation in time. Older lava fields, which are already covered with pioneer vegetation or with some sporadic bushes, show a decrease in the coherence, but even after 70 days they are clearly visible in the coherence map. The highly correlated backscattering from the bare lava surfaces between the vegetation causes this high long-time coherence. Also the settlements and other man-made structures show this kind of stability. The denser vegetation of various height which grows on old, earthy ground, is totally uncorrelated after 70 days and appears black in the correspondig map. But in this regions the short-time coherence allows a separation of the different land covers. High and dense vegetation like forests show a very low coherence even in the 1-day map, mostly because of the movements of the leaves and branches. Lower vegetation is more correlated, especially meadows and harvested agricultural fields have a very high coherence which produces ambiguities with lava surfaces if one only looks at the 1-day coherence.
4.2. Multitemporal classification
Based on the interpretation of the time dependent decay of the coherence in only one band as mentioned in the previous section, a first order classification algorithm has been developed. The snow-covered area around the top has been masked out by hand. A schematic representation of this algorithm is shown in Figure 2. We started with the 70-days coherence map with the intention to extract all lava and man-made surfaces. We are able to detect the following homogenous surfaces:
With the long-time coherence a very good discrimination can be made between mostly uncovered areas with rocky ground and surfaces with vegetation. Also the discrimination between fresh lava surfaces and older, slightly vegetated lava is sucessfull. All the completely vegetated surfaces appear decorrelated in the long-time coherence. To classify these areas it is possible to use the short-time coherence. The lava surfaces are already separated so no ambiguities between lava and other high coherent areas can occur. The result of this classification is shown in Figure 6
With this method we were able to detect following six different classes:
4.2. Error analysis
Like in section 3.3 we compared the obtained results with the geological and also with the topographic map. Geometrical errors in the coherence maps and the low information about the vegetation complicated the error analysis in some cases.
Class 1 corresponds very well to the historical lava flows around the volcano. The classification error is about 15%, mainly due to high regions which are partly covered with fresh ash or pyroclastic material. In this case a misclassification into class 2 could happen. Except for this case, the recognition of lava with sporadic vegetation is very successful. The error in the separation of this kind of vegetation from other vegetated surfaces is around 7%. The completely ash covered lava in the higher regions which also appear in class 4 show an error of about 10%, mostly because partly covered lava sometimes shows also a fast decorrelation.
For the classes 3,4 and 5, which include the dense vegetation on earthy ground, it was not possible to find actual and accurate enough botanic maps of the area to check the accuracy of the separation. Analysis based on selected areas show that the classification error between high and dense and lower vegetation is around 15%. The error in the separation of lower vegetation and meadows and bare soil is around 20%. In any case it is not easy to divide some vegetation types into a special class.
As the obtained results show, the INSAR coherence can be used as a potential tool for the classification of different natural surfaces. The advantage of the coherence classification is the high sensitivity in the detection of temporal changes. The main problem is to relate the detected changes with a certain surface type or scattering mechanism. This relation is not in any case unambiguous because the same amount of change can be the result of different change processes. From this point of view a priori information can increase drastically the accuracy of the classification results.
The separation of vegetated areas from non-vegetated areas could be done very accurate with a short wavelength like X- or C- band and a temporal offset of one day. For further information it is very useful to use either several frequencies or multiple temporal offsets.
The multifrequency classification shows a high sensibility on unvegetated surfaces, because the different wavelengths offer the possibility to detect changing processes occuring on different orders of magnitude. Also the different penetration capabilities of the frequencies allow a better localisation and interpretation of the changing mechanisms.
In contrast the multitemporal approach is more successful in the separation
of different vegetated surfaces. It takes advantage of the different time
scales in the change processes of the vegetation, which can be well obsereved
with a short wavelenght. To get more instructive informations it would
be helpful to observe better distributed temporal offsets than the tandem
data could provide.
Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry
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