Oil slicks on the sea surface will dampen the small-scale sea waves, and then the sea surface covered by slick is much smoother than clean sea. The damping effect caused by slicks can be described by the Marangoni theory. According to the Marangoni theory (Lombardini et al., 1989), the spectrum of the sea surface covered by oil films is related to the clean sea surface spectrum by

where k is the spatial wavenumber of the water wave; ${\psi _{{\rm{oil}}}} (k) $ denotes the spectrum covered by oil; ${\psi _{{\rm{water}}}} (k) $ denotes the clean sea surface spectrum and the damping ratio y_r (k) caused by slicks is given by

where F is the fractional filling factor; y (k) can be expressed as

where

In Eq. (4), $\eta = 74 \times {10^{ - 3}}\,\,\,{\rm{N}}/{\rm{m}}$, is the surface tension; $\rho = {10^3}\,\,\,{\rm{kg}}/{{\rm{m}}^{\rm{3}}}$, is the water density; $g = 9.8\,\,\,{\rm{m}}/{{\rm{s}}^{\rm{2}}}$, is the acceleration of gravity; $\nu = {10^{ - 6}}\,\,{\rm{m}}/{{\rm{s}}^{\rm{2}}}$, is the kinematic viscosity; ${E_0} = 9\,\,{\rm{mN}}/{\rm{m}}$, is the elasticity modulus; and ${\omega _{\rm D}} = 6\;{\rm{rad}}/{\rm{s}}$ is the characteristic frequency (Pinel et al., 2008). Obviously, the damping ratio ${y_{\rm{r}}} (k) $ is related to the sea wave number.

When microwaves illuminate the sea surface, the scattering fields can be approximately described by two kinds of scattering mechanisms, i.e., Bragg scattering and specular scattering. The backscattered signal intensity of Bragg scattering is much stronger than the specular scattering while the incidence angle ranges from 20° to 70°. The relationship between the Bragg and the electromagnetic wave number is

where k_ra is the radar wavenumber; k_B is the wavenumber of the Bragg waves; and ${\theta _{\rm{i}}}$ denotes the incidence angle. In this work, the damping effect caused by slicks for C-band and L-band Bragg sea waves is simulated by Eq. (2). Figure 1 presents the damping effect caused by slicks for Bragg waves corresponding to C- and L-band microwaves. In Fig. 1, the damping ratio increases with the incidence angle at L-band. While for C-band, the maximum damping ratio is located about 30°. For the incidence angle smaller than 30°, the damping ratio increases with the incidence angle. For the incidence angle larger than 30°, the damping ratio decreases with the incidence angle. Overall, the damping ratio for C-band is larger than L-band. The difference of the damping ratio will influence the capacity of oil spill detection at two bands.

The full polarimetric scattering matrix is given as

and the matrix elements represent the measured complex scattering coefficients. The first and second superscripts refer to the polarizations of the sent and received signals respectively, where h denotes horizontal and v the vertical polarization. From the full polarimetric scattering matrix, the Pauli scattering vector $\vec k = \frac{1}{{\sqrt 2 }}{\left[ {{S_{{\rm{hh}}}} + {S_{{\rm{vv}}}}\;\;\;\;{S_{{\rm{hh}}}} - {S_{{\rm{vv}}}}\;\;\;\;2{S_{{\rm{hv}}}}} \right]^{\rm{T}}}$ can be extracted in which T denotes transpose. Here, the reciprocity condition, i.e., ${S_{{\rm{hv}}}} = {S_{{\rm{vh}}}}$, is used. Then, the 3×3 polarimetric coherency matrix ${\text{T}_3}$ is obtained as

where the subscript * denotes the complex conjugate. The averaged coherency matrix $\left\langle {{\text{T}_3}} \right\rangle $ is defined as (Cloude and Pottier, 1996)

According to the results simulated in Fig. 1, the oil slick seems to have a greater impact on Bragg sea waves at C-band. In order to verify this conclusion, six SIR-C/X-SAR images at C-band and L-band are processed in this part. The SIR-C/X-SAR imaging radar took its first flight on the space shuttle endeavour in April 1994 and flew for a second time in October 1994. This multifrequency radar has fully polarimetric capability at C- and L-band, and a single polarization at X-band (X-SAR). The incidence angle of the radar ranges from 20° to 55° and the SAR swath width on the ground varies between 15 and 90 km. During the missions STS-59 (April 1994) and STS-68 (September and October 1994), C-band and L-band full polarimetic data were acquired at same time. Therefore, we can compare C-band SAR data with L-band in despite of the other environmental factors. More details are summarized in Table 1 (Migliaccio et al., 2009).

All of the images listed in Table 1 were acquired under low to moderate wind speeds. Among the three groups data, the first group data are presented and discussed in detail, similar conclusion can be drawn from the other two groups.

Figure 2 shows the vv polarization images of PR17041 (C-band) and PR17040 (L-band), which are acquired under low to moderate conditions. The incidence angle varies from 35.5°–40.4°. The dark areas related to the slicks are visible both in C- and L-band vv polarization images. The color bars indicate the value of the NRCS (normalized radar cross section).

The value of the NRCS is plotted in Fig. 3 based on the two white lines in Fig. 2, which are related to two different bands. For hh polarized channel (Fig. 3a), the NRCS of sea water is about –23 dB for C-band and L-band. And the NRCS of the slick is about –27 dB at L-band while the value is about –32 dB at C-band. Obviously, C-band (9 dB) has a high contrast than L-band (4 dB) between the slick and the sea water. For vv polarized channel (Fig. 3b), the NRCS values of the sea water at C- and L-band are also similar to each other, and the values are both about –18 dB. The signal value of the slick is –23 dB for L-band, –28 dB for C-band. A higher NRCS contrast between the slick and the sea water can also be observed at C-band. The results in Fig. 3 show that the intensity of the echoes backscattered from sea water at C-band is similar to L-band. However, the intensity of the echoes backscattered from the slicks present an obvious difference between C- and L-band polarized channels. Knowing from Fig. 1, the oil film performs a heavy damping effect for C band Bragg waves and induces a weaker backscattered intensity. As a consequence, the oil spills are more significant in C-band SAR images.

Figures 4a–h show the eight multipolarization features at C-band and L-band. From Fig. 4, the slick is clearly distinguished from the sea background in the eight polarization feature images at C-band. However, the oil slick cannot be easily identified by a visual inspection at L-band polarimetric features images. When the radar wave illuminates on the sea surface, the scatter mechanisms of the slicks and the sea water are differ from each other. Many efforts have been made to explain the scattering processes. Generally speaking, under low to moderate conditions, Bragg scattering dominates for the slick-free surface. Bragg scattering is expected to call for a low depolarization. When a slick is present, non-Bragg scattering is in place. This scattering mechanism is expected to call for a high depolarization. In Fig. 4a, the polarimetric entropy of the oil spill is higher than 0.8 while the value of sea water is lower than 0.4 at C-band. However, both slicks and sea water are characterized as a lower polarimetric entropy property at L-band. This phenomenon means that the polarimetric entropy at L-band cannot accurately indicate that the randomness of scattering mechanisms occurs on the oil spill surface. Figure 4b shows the mean scattering angle (α) which is a descriptor of different scattering mechanisms. If the value of the mean scattering angle is below 30°, the surface Bragg scattering is dominant. If the value of it is between 30° and 50°, a dipole scatter is dominant, and if it is between 50° and 90°, an even-bounce scatter is dominant. In Fig. 4b, for C-band, the value of the mean scattering angle for the oil slick is larger than 40°, which suggests a non-Bragg scattering is dominant. However, for the clean sea surface, the value of the mean scattering angle is smaller than 30°, and this suggests that the scattering field is dominated by the surface Bragg scattering. By comparisons, the value of the mean scattering angle for L-band is smaller than 20° in the oil covered area. And thus, it is impossible to discriminate the slicks from the sea backgrounds by a mean scatter angle in L-band SAR images. Figure 4c shows the pedestal height of the ROIs. As a measurement of depolarized backscattered energy, the pedestal height is expected to be high in the oil-covered areas. In Fig. 4c, it is clear that the value in the oil spill region is higher than the oil-free sea at C-band. However, there is no significant difference between the oil-covered and the oil-free areas in L-band SAR image.

The polarimetric entropy, mean scatter angle and pedestal height extracted by using the C-band full poalrimetric SAR data can better reflect the scattering mechanisms. Similar conclusions can be drawn from other features, e.g., the standard deviation of the copolarized phase difference, the co-polarization correlation coefficient, the degree of polarization. While for the copolarization power ratio, the parameter performs not as well as other features mentioned above at C-band. But compared with L-band, the C-band copolarization power ratio is somewhat better on discriminating oil spills.

In fact, the scattering mechanisms occur on the oil-free and oil-covered surfaces are complex processes. We try to explain the processes in terms of two kinds of scatter mechanisms, i.e., Bragg scattering mechanism and the specular scattering mechanism. For the sea surface, the scatter field is dominated by Bragg scattering under low to moderate wind conditions if the incidence angle ranges from 20° to 70°. When oil is spilled on the sea surface, it will spread to form a thin layer on the water surface. This layer will dampen gravity-capillary waves on the ocean surface. The roughness of sea surface covered with oil is much smaller than the clean sea surface. In this case, the specular scatter accounts for a larger proportion among the whole scatter process. The scatter process occurred on the slick surface become more complex. The parameter P described in Section 2 could measure the proportion of the specular scatter mechanism. Figure 4h presents the parameter P extracted from Fig. 2. For C-band, the parameter values of the oil-covered water are quite small because the specular scattering mechanism accounts for a larger proportion. The oil-free area has a larger parameter value than the oil contaminant area because Bragg scattering mechanism accounts for a major proportion. The parameter P is sensitive to the sea surface scattering mechanisms. It is proven that the parameter P is also a useful feature to observe an oil slick at C-band.

On the basis of the above experiments, one can notice that C-band the full polarimetric SAR performs better than L-band under the same conditions. To further compare the two bands, we conduct a segment method to the eight features. Here, due to space constraints, only the segment results by the parameter P are discussed in detail. A threshold method is used to separate the oil slicks from sea water. First, the PDF (probability distribution function) of the polarimetric features for the oil-free areas (the pixels in rectangles in Fig. 5) is established. We assume that the sea water within a narrow incidence angle has a constant polarimetric feature value and that the distribution is only due to speckle. Then, the minimum values of pixels in the rectangles are regarded as thresholds. In Fig. 6a, the red solid line denotes the PDF of the whole region presented in Fig. 5a, the black solid line denotes the PDF of the pixels in the rectangles. The dashed line denotes the minimum values of pixels in the rectangles which are set as thresholds.

The example histograms in Fig. 6 are evaluated based on the polarimetric parameter P. The black curves represent the values of the clean sea surface, and the red lines include all pixels in the polarimetric parameter P images, i.e., values from both the oil-free area and the oil-covered area. In Fig. 6a, the left-hand tails of the red line distribution are dominated by the values observed over the oil spill in Fig. 2. It’s obvious that the tail is more pronounced at C-band than L-band. Figures 6c and d are the segment results by using the thresholds computed in Figs 6a and b. In the case of C-band, most of the pixels are classified correctly, and the segment result consists of experiment fact. However, in Fig. 6b, the distribution of the polarimetric parameter P value in oil-free area is similar to the oil-covered area. The threshold is set 3.17 at L-band. Moreover, only a few pixels in oil-covered area are recognized as oil spill. Most of the slicks pixels are classified as sea water. By the above experiments, one can see that L-band is inferior to C-band, and the parameter P is useful to distinguish the oil spills at C-band.

Knowing from the above experiment, that the C-band SAR performs much better than L-band. However, in some other papers, such as Minchew et al. (2012), the L-band full polarization SAR can separate the oil spills from the sea background clearly. While the L-band SAR data used in this paper cannot distinguish slicks from clean sea as good as Minchew et al. (2012). The discrimination results may be affected by the kinds of slicks, the thickness of slicks, the noise floor or some other external factors. The data used in this paper and in Minchew et al. (2012) have many different factors. The three images used in this paper are collected under similar sea conditions, we suppose that the physical properties and the chemical properties of films influence the discrimination results. Unfortunately, this assumption cannot be assured because we could not get the details about the oil slicks. Further studies are needed to clarify this question. Nevertheless, we can still come to the conclusion that the C-band polarimetric SAR performs better than L-band because the data at two bands used in this paper are acquired under the same condition.

In this part, we conduct an experiment for further investigation of different features at C-band. The data used in this part include C-band SIR-C/X SAR data listed in Table 1, and three single look complex (SLC) fine quad-pol C-band SAR images acquired by Radarsat-2. Figure 7a shows a vv polarization Radarsat-2 image collected from the Gulf of Mexico at 12:01 UTC on 8 May 2010. The dark areas are the oil spills which are caused by nature seeps. The incidence angle varies from 41.9° to 43.4°. The wind speed U₁₀ is about 6.5 m/s. Figure 7b shows an images acquired during the DWH accidence, at 11:56 UTC on 15 May 2010. The accidence caused larger areas of the oil spills on the sea surface. The oil patches on the right are processed in this experiment. For these data, the incidence angle at near range is 29.2° and the incidence angle at far range is 30.9°. The wind speed U₁₀ is 4–7 m/s during the SAR observation. Figure 7c was acquired during the oil spill experiment conducted by the Norway clean seas Association for Operating Companies (NOFO) in the North Sea. Three dark areas can be observed in this image, which correspond to plant oil, oil emulsion and crude oil. In this paper, only the crude oil (right most) is used to investigate the polarimetric features. The wind speed is about 1.6–3.3 m/s when the data is collected (Li et al., 2015). More information about three Radarsat-2 images can be seen in Table 2.

Using the six C-band full polarimetric SAR images, the eight features mentioned above are investigated for the oil spill discrimination. First, the slicks were identified by the visual inspection in the three images. And then the slick-to-sea water contrast of the slicks and sea water is computed on account of the segment results. The slick-to-sea water contrast (Peli, 1990) of different features can be defined as

where ${F_{{\rm{oi}}}}$ the mean value of oil spill regions, and ${F_{{\rm{wa}}}}$ the mean value of sea water. A large value of ${C_{{\rm{ow}}}}$ indicates that the oil spill may be easily separated from water. Figure 8 presents the contrast between the slick and the clean sea water for the eight features.

In Fig. 8a, the slick-to-sea water contrasts are evaluated based on the three images listed in Table 1, the processing numbers of the three images are PR17041, PR44327, and PR49939, respectively. For data PR17041, the slick-to-sea water contrasts of the pedestal height (0.82), the standard deviation (0.86) of the copolarized phase difference and P (0.79) are larger than other features. For data PR44327, pedestal height (0.68) and the polarimetric parameter P (0.58) have the larger slick-to-sea water contrasts. While for data PR49939, the polarimetric entropy (0.27), the pedestal height (0.46) and the polarimetric parameter P (0.28) have larger slick-to-sea water contrast ${C_{{\rm{ow}}}}$ values. In Fig. 8b, the slick-to-sea water contrasts are evaluated based on the three images listed in Table 2, the three lines correspond to RS-1, RS-2, RS-3, respectively. For data RS-1, the pedestal height (0.68) and the polarimetric parameter P (0.63) have larger slick-to-sea water contrasts than other features. For data RS-2, pedestal height (0.35) and the polarimetric parameter P (0.34) have larger slick-to-water contrasts. For data RS-3, the pedestal height (0.76) and the polarimetric parameter P (0.65) have larger slick-to-sea water contrasts. Overall, pedestal height and the polarimetric parameter P seem to have the best potential for the oil spill versus the sea water discrimination.

From Fig. 8a, one can see that the variation trend of the three lines are similar to each other. Some parameters will exhibit a different slick-to-sea water contrast in different images. Take polarimetric entropy as an example, the value of slick-to-sea water contrast is 0.53 (PR17041), 0.38 (PR44327) and 0.25 (PR49939), respectively. On the other hand, some parameters exhibit similar values in different data. For instance, the slick-to-sea water contrast of d_p in PR17041 (0.1) and PR49939 (0.09) are almost same. It seems that the value of the slick-to-sea water contrast will affected by the thickness of films, the wind speed and some other environmental factors. Unfortunately, we are not sure which factor is most important. Further studies are needed to explain this phenomenon.