penalty operator
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2018 ◽  
Vol 14 (6) ◽  
pp. 709-724 ◽  
Author(s):  
Mauro Guglielmin ◽  
Marco Donatelli ◽  
Matteo Semplice ◽  
Stefano Serra Capizzano

Abstract. Here we present the results of the inversion of a multi-annual temperature profile (2013, 2014, 2015) of the deepest borehole (235 m) in the mountain permafrost of the world located close to Stelvio Pass in the Central Italian Alps. The SHARE STELVIO Borehole (SSB) has been monitored since 2010 with 13 thermistors placed at different depths between 20 and 235 m. The negligible porosity of the rock (dolostone,  <  5 %) allows us to assume the latent heat effects are also negligible. The inversion model proposed here is based on the Tikhonov regularization applied to a discretized heat equation, accompanied by a novel regularizing penalty operator. The general pattern of ground surface temperatures (GSTs) reconstructed from SSB for the last 500 years is similar to the mean annual air temperature (MAAT) reconstructions for the European Alps. The main difference with respect to MAAT reconstructions relates to post Little Ice Age (LIA) events. Between 1940 and 1989, SSB data indicate a cooling of ca. 1 °C. Subsequently, a rapid and abrupt GST warming (more than 0.8 °C per decade) was recorded between 1990 and 2011. This warming is of the same magnitude as the increase in MAAT between 1990 and 2000 recorded in central Europe and roughly doubling the increase in MAAT in the Alps.


Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. U65-U76 ◽  
Author(s):  
Tongning Yang ◽  
Jeffrey Shragge ◽  
Paul Sava

Image-domain wavefield tomography is a velocity model building technique using seismic images as the input and seismic wavefields as the information carrier. However, the method suffers from the uneven illumination problem when it applies a penalty operator to highlighting image inaccuracies due to the velocity model error. The uneven illumination caused by complex geology such as salt or by incomplete data creates defocusing in common-image gathers even when the migration velocity model is correct. This additional defocusing violates the wavefield tomography assumption stating that the migrated images are perfectly focused in the case of the correct model. Therefore, defocusing rising from illumination mixes with defocusing rising from the model errors and degrades the model reconstruction. We addressed this problem by incorporating the illumination effects into the penalty operator such that only the defocusing by model errors was used for model construction. This was done by first characterizing the illumination defocusing in gathers by illumination analysis. Then an illumination-based penalty was constructed that does not penalize the illumination defocusing. This method improved the robustness and effectiveness of image-domain wavefield tomography applied in areas characterized by poor illumination. Our tests on synthetic examples demonstrated that velocity models were more accurately reconstructed by our method using the illumination compensation, leading to a more accurate model and better subsurface images than those in the conventional approach without illumination compensation.


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