Recovering material properties of the subsurface using ground penetrating radar (GPR) data of finite bandwidth with missing low frequencies, and in the presence of strong attenuation is a challenging problem.We propose three non-linear inverse methods for recovering electrical conductivity and permittivity of the subsurface by joining GPR multi-offset and electrical resistivity (ER) data acquired at the surface.All methods use ER data to constrain the low spatial-frequency of the conductivity solution. The first method uses the envelope of the GPR data to exploit low frequency content in full-waveform inversion and does not assume structural similarities of material properties.The second method uses cross-gradients to manage weak amplitudes in the GPR data by assuming structural similarities between permittivity and conductivity.The third method uses both the envelope of the GPR data and the cross-gradient of the model parameters. By joining ER and GPR data, exploiting low frequency content in the GPR data, and assuming structural similarities between electrical permittivity and conductivity we are able to recover subsurface parameters in regions where the GPR data has a signal-to-noise ratio close to one.
We develop an algorithm for joint inversion of full-waveform ground-penetrating radar (GPR) and electrical resistivity (ER) data. GPR is sensitive to electrical permittivity through reflectivity and velocity, and electrical conductivity through reflectivity and attenuation. ER is directly sensitive to electrical conductivity. The two types of data are inherently linked through Maxwell's equations and we jointly invert them. Results show that the two types of data work cooperatively to effectively regularize each other while honoring the physics of the geophysical methods. We first compute sensitivity updates separately for both the GPR and ER data using the adjoint method, and then we sum these updates to account for both types of sensitivities. The sensitivities are added with the paradigm of letting both data types always contribute to our inversion in proportion to how well their respective objective functions are being resolved in each iteration. Our algorithm makes no assumption of the subsurface geometry nor structural similarities between parameters with the caveat of needing a good initial model. We find that our joint inversion outperforms both GPR and ER separate inversions and determine that GPR effectively supports ER in regions of low conductivity while ER supports GPR in regions with strong attenuation.
Using electrical direct-current (DC) data to monitor the subsurface is an efficient solution for observing changes in the shallow subsurface. Recent advances in instrumentation enable the acquisition of large data sets over 3D domains in a reasonable time. We have developed an inversion approach capable of handling very large amounts of data on a finely discretized domain, which enables the delivery of time-lapse results of dense data acquisitions in a feasible time and with high resolution. To spatially represent 3D DC data, a visualization method is introduced that formally generalizes the focusing point of a common pseudo-section in three dimensions. The method physically describes subsurface properties for simple geologic scenarios. In addition, the focusing points are used to design our 3D measuring protocol. We develop a DC data processing scheme using the full time-domain induced polarization (IP) waveform data by applying two novel physics-based criteria that enforce charge buildup and steady-state. These criteria are tested on DCIP field data and find that 98% of the filtered DC data have less than 1% relative error. The 3D visualization method and inversion algorithm are evaluated on synthetic scenarios of 3D DC dense borehole data. Then, we indicate time-lapse results of DC field data acquired at an uncontaminated site where a remediation agent was injected at depth. The data were acquired with a new DCIP instrument capable of measuring dense data sets at fast acquisition times. Accounting for DCIP data acquisition, signal processing, and 3D inversion of 60k DC measurements, our results locate in 14 h the 3D spread of the remediation agent in a 5 km3 volume.
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