In this paper, an inversion method based on the Marquardt's algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. According to the interpreted parameters, the best shape that can imagine for the gravity anomaly source is the vertical cylinder with a depth to top of 7.4 m and a radius of 11.7 m.

Abstract. The Greenlandic and Antarctic Ice Sheet are important indicators of climate change and major contributors to sea level rise. Hence, precise, long-term observations of surface elevation change are required to assess changes and their contribution to sea level rise. Satellite radar altimetry has been used by various missions to measure surface elevation change since 1992. It has been shown that, next to the surface slope and complex topography, one of the most challenging issues is the spatial and temporal variability of radar pulse penetration into the snow pack, especially over the vast East Antarctic plateau. This results in an inaccurate measurement of the true surface elevation and consequently affects surface elevation change (SEC) estimates. To increase the accuracy of surface elevations retrieved by retracking the radar return waveform and thus reduce the uncertainty in SEC, we developed a deep convolutional neural network architecture (AWI-ICENet1). The AWI-ICENet1 is trained using a simulated reference data set with 3.8 million waveforms, taking into account different surface slopes, topography, and attenuation. The successfully trained network is finally applied as AWI-ICENet1-retracker to the full time series of CryoSat-2 Low Resolution Mode (LRM) waveforms over both ice sheets. We compare the AWI-ICENet1 retrieved SEC with estimates of conventional retrackers like TFMRA and ESA ICE1 and ESA ICE2 products. Our results show less uncertainty and a greatly diminished effect of time variable radar penetration, reducing the need to apply corrections based on a close relationship with backscatter- and/or leading edge width, as typically done in SEC processing. This technique provides new opportunities to utilize convolutional neural networks in altimetry, waveform retracking, and processing of satellite altimetry data, which can be applied to historical, recent, and future missions.

<p>The Antarctic Ice Sheet is an important indicator of climate change and a major contributor to sea level rise. Hence, precise, long-term observations of surface elevation change are required to assess changes and their contribution to sea level rise. Satellite altimetry has been used by various missions to measure surface elevation change since 1992. It has been shown that, next to the surface slope and complex topography, one of the most challenging issues is the spatial and temporal variability of radar pulse penetration into the snowpack, especially over the vast East Antarctic plateau. This results in an inaccurate measurement of the true surface elevation and consequently affects surface elevation change (SEC) estimates.</p> <p>To increase the accuracy and correct the SEC, we developed a deep convolutional neural network (CNN) architecture. The CNN was trained by a simulated waveform data set containing more than 3.6 million waveforms, considering different surface slopes, topography, and attenuation. The CNN follows standard architectural design choices. The successfully trained network is finally applied as a CNN-retracker to the full time series of CryoSat-2 low resolution mode (LRM) waveforms over the Antarctic ice sheet. We will show the CNN retrieved SEC and compare it to estimates of conventional retrackers like OCOG or ICE2. Our preliminary results show reduced uncertainty and a strongly reduced time variable radar penetration, making backscatter or leading edge corrections typically applied in SEC processing obsolete. This technique provides new opportunities to utilize convolutional neural networks in altimetry, waveform retracking, and processing altimetry data, which can be applied to historical, recent, and future altimetry missions.</p>

In this paper, two modeling method are employed. First, a method based on the Marquardt's algorithm is presented to invert the gravity anomaly due to a finite vertical cylinder source. The inversion outputs are the depth to top and bottom, and radius parameters. Second, Forced Neural Networks (FNN) for interpreting the gravity field as try to fit the computed gravity in accordance with the estimated subsurface density distribution to the observed gravity. To evaluate the ability of the methods, those are employed for analyzing the gravity anomalies from assumed models with different initial parameters as the satisfactory results were achieved. We have also applied these approaches for inverse modeling the gravity anomaly due to a Chromite deposit mass, situated east of Sabzevar, Iran. The interpretation of the real gravity data using both methods yielded almost the same results.