Constrained Time-lapse Inversion of 3-D Resistivity Surveys Data

Three-dimensional surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artefacts. 3-D data sets collected at different times are inverted simultaneously using a least-squares methodology that uses roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x, y and z directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models. This method can accurately resolve temporal changes in the resistivity even in the presence of noise. The use of the L1 and L2 norm constraints for the temporal roughness filter are examined using a synthetic model. The L1 norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. A test with field data from a landfill site with methane gas accumulation shows near surface resistivity changes that are probably due to surface temperature variations. The temperature variations cause changes in the gas volume and moisture content in the near surface landfill materials.