Data processing can be considered to be split into three distinct operations (Figure 2): repicking (or retracking); the application of transmission and tidal corrections and editing; and integrating the two datasets using 'geoid to gravity', which involves the precise application of micro-levelling (Fairhead et al, 2001b). Figure 2 shows the processing sequence. The database is central to all the processing steps to record changes in point values due to editing and application of corrections (wet and dry troposphere, tidal corrections, etc). The importance of recording such changes in the database allows, when necessary, these changes to be reversed or modified in later parts of the processing sequence.
Figure 2. Satellite-derived gravity. Processing Flow Diagram
The three distinct data processing operations are:
1. Waveform Retracking: The methods for repicking the ERS1 data have been developed over seven years and have been designed to handle the noise problems in the data and the under-sampling of the waveform along the leading edge (not such a problem with Geosat data, which had twice the sampling in the region of the leading edge) and the variability between adjacent waveforms. To track the onsets of the waveforms, a synthetic signal (Figure 3) was constructed that uses the slope of the leading edge and its amplitude, so that the midpoint position of the leading edge (MSE at 50%, see Figure 4) can be determined. This synthetic waveform is then used to cross correlate with the observed waveforms to determine their onset times. Using such a synthetic waveform, up to 40 waveforms were inverted together to determine the 42 unknowns of average amplitude, average slope and 40 onset times. This method allowed us to isolate waveforms that did not conform within specified limits and these waveform results can be either removed from subsequent analysis and/or visually inspected. This type of analysis has allowed us to track reliably the waveforms to within 2 to 5 km from the coastline.
Figure 3. Stacked 40 consecutive waveforms representing 2 seconds or 14 km of data along the orbital track. If no noise is present on the leading edge then a perfect stack would be produced. (A) shows stack of poorly picked agency data with large noise scatter; (B) shows the synthetic signal (red) used to match the leading edge and triangular sampling points on the raw waveform data; and (C) same stack after GETECH picking reducing scatter by factor of 5
Figure 4. Schematic representation of the change in shape of the radar return signal due to changes in sea conditions. The mean sea level (MSL) occurs at the 50% level for incident (AB for calm sea) and emergent (CD for rough sea) returning radar signals. The black and red wavy lines represent calm and rough sea surfaces, respectively.
2. Corrections and editing: Several corrections need to be applied to the altimetry range to correct for environmental effects which impact either the travel time of the radar pulse (e. g. tropospheric corrections) or the height measured for the sea surface (e. g. tidal corrections). Data gaps found in both the wet and dry tropospheric corrections could lead to bias in the final gravity solution. These gaps were carefully filled using either alternative sources, such as meteorological models or polynomial interpolation. For altimeter range and tidal corrections see Fairhead et al, (2001b). Prior to the editing stage, a long wavelength spherical harmonic definition of the geoid (EGM96) is subtracted from the sea surface height to give the residual sea surface height (RSSH). The RSSH is useful here as it permits straightforward visualisation during editing and a more stable geoid to gravity conversion. Automatic editing of the largest data spikes was performed using several algorithms that check gradients between points and a least squares algorithm which performs a statistical analysis of the data within a window. This allows the identification of the worst data points that exceed a user defined tolerance. This stage of editing removed approximately 6% of the data, the majority of which were located at high latitudes where sea ice contaminates the data. The iterative manual editing is a very time-consuming process but a necessary stage of editing and is carried out prior to and after both the geoid construction and the gravity conversion to eliminate spurious values. Initially all the satellite tracks are edited using computer visualisation software to simultaneously view swaths of 15 geographically adjacent orbital tracks and remove any data which are clearly inconsistent with adjacent tracks. Once the initial editing is complete the data are leveled, gridded and further evaluated in 2D to identify remaining noise. Once a track with spurious data is identified, the satellite track visualisation software is used to remove the associated spike. This process is repeated until all significant noise and spikes have been removed.
3. Geoid to gravity: Converting the repicked sea-surface heights to their gravity equivalent is a complex process. The sea-surface heights can be considered as geoid heights. We have used the 'geoid to gravity' method rather than the 'along track gradient' method used by Sandwell and Smith (1997). The reasons were our need to generate a reliable geoid model and the fact that geoid grid interpolation is more robust than derivative grid interpolation in the presence of noise and where data coverage is irregular. This method also produces a solution which is more isotropic in equatorial regions. This process required the application of levelling techniques to reduce track orientated noise. Significantly, this reduces the effect of time variant ocean currents, which cannot be corrected due to their spatial and temporal variability.
Figure 5 illustrates the 'geoid to gravity' method for the Black Sea after the removal of the 0.5° EGM96 reference geoid model. The method relies on the removal of orbital errors without filtering the data. This is achieved by initially applying cross-over-error corrections and then applying GETECH proprietary micro-levelling methods.
Figure 5. Black Sea example of the 'geoid to gravity' method of converting sea-surface heights to gravity using micro-levelling to minimize sea-surface height errors. For all figures warm colours (red) are high or positive anomalies and cold colours (blue) are low or negative anomalies.
Micro-levelled sea-surface heights are then converted to gravity by using the gravity coating method and the spherical FFT technique using a series of overlapping bands. This is in essence the potential field vertical derivative operator applied to the geoid surface. The gravity equivalent of the EGM96 reference model is then restored to produce the free air anomaly gravity field.
Resolution examples
To appreciate the improved resolution we focus the examples on a number of difficult data areas.
Offshore mouth of the Amazon River: Since the adjacent orbital tracks are not sequential (they can be recorded any time up to 12 months apart), there can be major problems in mapping sea level heights in places such as the mouth of major river systems where the salinity, temperature and seasonal flow rates vary both seasonally and from year to year. Public domain solutions retain track orientated noise in these areas to such an extent that their data are of little value.
GETECH has overcome these problems by the use of micro-levelling technology which is able to level data in these problematical areas without any loss of high frequency information. Figure 6 shows a sequence of processing stages from A) post cross-over adjustment showing the abundance of residual orbital error, B) post micro-levelling where only short wavelength noise (~5km) is present, C) conversion to gravity and D) the total horizontal derivative which is good at identifying any residual orbital noise (absent in this solution).
Figure 6. Sequence of processing stages to derive the Free air anomaly map (C) and its total horizontal derivative (D).
Oceanic currents offshore South Africa: Oceanic currents manifest themselves as temporally and spatially varying long wavelength sea surface heights. This effect is illustrated in Figure 7A, where a packet of adjacent RSSH tracks are cut by an ocean current. The tracks to the left hand side of the image display the influence of a transient current where adjacent tracks differ markedly at the intermediate to long wavelengths. In contrast the tracks on the right of Figure 7A are less affected by the current and are approximately parallel. When these tracks are simply gridded together this leads to short wavelength high amplitude noise contamination across tracks, due to the comparatively small distance that separates adjacent tracks.
Figure 7B shows the RSSH after cross-over-levelling with the ocean current running below the Cape of Africa causing a band of noise contamination running approximately east/west across the centre of the image. If these discrepancies are not resolved prior to conversion to gravity this short wavelength noise will dominate the final gravity solution because of the effect of applying a vertical derivative. However, by careful application of the GETECH micro-levelling technique we have resolved these ocean current discrepancies without a loss of signal, see Figure 7C
Figure 7. Effective suppression of ocean current signal without loss of short wavelength resolution (2" graticule for scale).
Inshore definition: By re-picking the 20 Hz ERS1 data we have been able to track the variability of the waveforms close to shore so that spurious waveforms can be removed prior to finally defining the waveform parameters and inversion. These data have then been integrated with the carefully edited Geosat 10 Hz data, which has allowed us to track solutions to within 2 to 5 km of the coast compared with up to 50 km for public domain solutions. A good example is shown for N Sulawesi in Figure 8, where the definition of our satellite data, either as the free air gravity or its total horizontal derivative, are clear to see. This allows the marine satellite data to be more easily linked to the onshore gravity data.
|
Из за большого объема этот материал размещен на нескольких страницах:
1 2 3 4 5 |
