Processing and Modeling of Time Domain Induced Polarization Data

Nivorlis, Aristeidis; Τσούρλος, Π.; Vargemezis, G.; Τσοκασ, Γ. Ν.; Kim, J.H.; Yi, Myeong‐Jong

doi:10.3997/2214-4609.201702085

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, when inverting the time-gates independently, there is a risk of obtaining non-physical decays. This risk can be mitigated by inverting all time-gates at once as suggested by Yi et al (2012) and Nivorlis et al (2017). They also suggest adding constraints between the gates to avoid irregular shapes of the IP decays.…”

Section: Introductionmentioning

confidence: 99%

3-D time-domain spectral inversion of resistivity and full-decay induced polarization data—full solution of Poisson's equation and modelling of the current waveform

Madsen

Fiandaca

Auken

2020

Geophysical Journal International

View full text Add to dashboard Cite

Summary We present a new algorithm for 3D forward modelling and spectral inversion of resistivity and time-domain full-decay induced polarization (IP) data. To our knowledge, all algorithms available for handling 3D spectral inversion of full-decay IP data use a time-domain approximation to Poisson's equation in the forward response. To avoid this approximation, we compute the response in the frequency domain solving the full version of Poisson's equation for a range of frequencies (${10^{ - 8}}$-${10^4}$ Hz) and then transform the response into the time domain, where we account for the transmitted current waveform. Solving Poisson's equation in 3D is computationally expensive and in order to balance accuracy, time, and memory usage we introduce the following: 1) We use two separate meshes for the forward response and the model update, respectively. The forward mesh is an unstructured tetrahedral mesh allowing for local refinements whereas the model (inversion) mesh is a node-based structured mesh, where roughness constraints are easily implemented. By decoupling the two meshes, they can be tuned for optimizing the forward accuracy and the inversion resolution, independently. 2) A singularity removal method known from resistivity modelling has been adapted to the complex IP case and is applied to minimize the numerical errors caused by the fast changing potential close to the source electrodes. The method includes splitting the potential field into a primary part (response of a homogenous background) and a secondary part (from the anomalies). Two different forward meshes are then used to compute the forward response: a dense mesh for the primary potential field (only computed once for each frequency) and a coarser mesh for the secondary potential field (computed in each iteration step of the inversion). With this method, the singularity is minimized and the memory usages is decreased significantly at the same time. 3) Finally, we are sparsing (down-sampling) the Jacobian matrix based on a threshold value of the normalized sensitivity. The Jacobian computation is performed by time-transforming the frequency-domain Jacobian obtained through the adjoint method. The Jacobian down-sampling is carried out before the time-transform in the frequency domain, thus avoiding the time-transformation of the Jacobian elements with negligible sensitivity. We invert resistivity data and all IP time-gates simultaneously and use the Gauss-Newton model update to minimize the L2 misfit function. We invert the resistivity data and all IP time-gates simultaneously and use the Gauss-Newton model update to minimize the L2 misfit function. We demonstrate the performance of our inversion approach with a synthetic data example with 3D anomalies and a field example, where lithology logs verify the results. The datasets contain 1256 quadrupole measurements with 33 IP time-gates each. The inversions results show good data fits and model retrieval. The inversion takes approximately one hour per iteration using four CPUs. With this speed and accuracy, we believe this modelling and inversion approach will be a strong tool for 3D spectral inversion of resistivity and full-decay IP field data for both surface and borehole applications.

show abstract

Section: Introductionmentioning

confidence: 99%

3-D time-domain spectral inversion of resistivity and full-decay induced polarization data—full solution of Poisson's equation and modelling of the current waveform

Madsen

Fiandaca

Auken

2020

Geophysical Journal International

View full text Add to dashboard Cite

show abstract

“…Such methodology allowed for improving the resolution of the estimated Cole-Cole parameters. Recently, Nivorlis et al (2017) proposed a 3-D computation scheme to retrieve in 3-D the Cole-Cole parameters. The last step of their work is accomplished using a particle swarm optimization algorithm.…”

mentioning

confidence: 99%

3D time-domain induced polarization tomography: a new approach based on a source current density formulation

Ahmed

Revil

2017

Geophysical Journal International

View full text Add to dashboard Cite

Induced polarization (IP) of porous rocks can be associated with a secondary source current density, which is proportional to both the intrinsic chargeability and the primary (applied) current density. This gives the possibility of reformulating the time domain induced polarization (TDIP) problem as a time-dependent self-potential-type problem. This new approach implies a change of strategy regarding data acquisition and inversion, allowing major time savings for both. For inverting TDIP data, we first retrieve the electrical resistivity distribution. Then, we use this electrical resistivity distribution to reconstruct the primary current density during the injection/retrieval of the (primary) current between the current electrodes A and B. The time-lapse secondary source current density distribution is determined given the primary source current density and a distribution of chargeability (forward modelling step). The inverse problem is linear between the secondary voltages (measured at all the electrodes) and the computed secondary source current density. A kernel matrix relating the secondary observed voltages data to the source current density model is computed once (using the electrical conductivity distribution), and then used throughout the inversion process. This recovered source current density model is in turn used to estimate the time-dependent chargeability (normalized voltages) in each cell of the domain of interest. Assuming a Cole-Cole model for simplicity, we can reconstruct the 3-D distributions of the relaxation time τ and the Cole-Cole exponent c by fitting the intrinsic chargeability decay curve to a Cole-Cole relaxation model for each cell. Two simple cases are studied in details to explain this new approach. In the first case, we estimate the Cole-Cole parameters as well as the source current density field from a synthetic TDIP data set. Our approach is successfully able to reveal the presence of the anomaly and to invert its Cole-Cole parameters. In the second case, we perform a laboratory sandbox experiment in which we mix a volume of burning coal and sand. The algorithm is able to localize the burning coal both in terms of electrical conductivity and chargeability.

show abstract

Processing and Modeling of Time Domain Induced Polarization Data

Cited by 2 publications

References 0 publications

3-D time-domain spectral inversion of resistivity and full-decay induced polarization data—full solution of Poisson's equation and modelling of the current waveform

3-D time-domain spectral inversion of resistivity and full-decay induced polarization data—full solution of Poisson's equation and modelling of the current waveform

3D time-domain induced polarization tomography: a new approach based on a source current density formulation

Contact Info

Product

Resources

About