Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions

Often in geophysical monitoring experiments time-lapse inversion models vary too smoothly with time, owing to the strong imprint of regularization. Several methods have been proposed for focusing the spatiotemporal changes of the model parameters. In this study, we present two generalizations of the minimum support norm, which favour compact time-lapse changes and can be adapted to the specific problem requirements. Inversion results from synthetic direct current resistivity models that mimic developing plumes show that the focusing scheme significantly improves size, shape and magnitude estimates of the time-lapse changes. Inversions of the synthetic data also illustrate that the focused inversion gives robust results and that the focusing settings are easily chosen. Inversions of full-decay time-domain induced polarization (IP) field data from a CO2 monitoring injection experiment show that the focusing scheme performs well for field data and inversions for all four Cole-Cole polarization parameters. Our tests show that the generalized minimum support norms react in an intuitive and predictable way to the norm settings, implying that they can be used in time-lapse experiments for obtaining reliable and robust result

Sequential and joint hydrogeophysical inversion using a field-scale groundwater model with ERT and TDEM data

Increasingly, ground-based and airborne geophysical data sets are used to inform groundwater models. Recent research focuses on establishing coupling relationships between geophysical and groundwater parameters. To fully exploit such information, this paper presents and compares different hydrogeophysical inversion approaches to inform a field-scale groundwater model with time domain electromagnetic (TDEM) and electrical resistivity tomography (ERT) data. In a sequential hydrogeophysical inversion (SHI) a groundwater model is calibrated with geophysical data by coupling groundwater model parameters with the inverted geophysical models. We subsequently compare the SHI with a joint hydrogeophysical inversion (JHI). In the JHI, a geophysical model is simultaneously inverted with a groundwater model by coupling the groundwater and geophysical parameters to explicitly account for an established petrophysical relationship and its accuracy. Simulations for a synthetic groundwater model and TDEM data showed improved estimates for groundwater model parameters that were coupled to relatively well-resolved geophysical parameters when employing a high-quality petrophysical relationship. Compared to a SHI these improvements were insignificant and geophysical parameter estimates became slightly worse. When employing a low-quality petrophysical relationship, groundwater model parameters improved less for both the SHI and JHI, where the SHI performed relatively better. When comparing a SHI and JHI for a real-world groundwater model and ERT data, differences in parameter estimates were small. For both cases investigated in this paper, the SHI seems favorable, taking into account parameter error, data fit and the complexity of implementing a JHI in combination with its larger computational burden

Experience from Two Resistivity Inversion Techniques Applied in Three Cases of Geotechnical Site Investigation

The combination of in situ geotechnical testing and continuously measured geophysical data can be a powerful tool in geotechnical site investigation. In two cases from Sweden and one case from Denmark electric resistivity surveys are used successfully in geotechnical site investigations. The main contribution of resistivity results is the possibility to interpret continuous geological models. An improved methodology combines two-dimensional (2D) smooth inversion and 2D laterally constrained inversion (2D-LCI) to significantly increase interpretability. The 2D smooth inversion has high horizontal resolution and 2D-LCI high vertical resolution. The possibility to add a priori information from, for example, drill log data to constrain the 2D-LCI increases the confidence in the inverted model and limits ambiguity. In a site investigation for a railway trench in southern Sweden a geotechnical data set is used as a priori data to increase the reliability of the inversion of the resistivity data. From this combined survey a complex Quaternary geology is described in detail. A slope stability study from south of Stockholm, Sweden, employed resistivity data together with refraction seismic and geotechnical drill log data. The result gives necessary geometrical information for the important geological units, for example for stability calculations. Both these surveys were performed with a multielectrode system. In the third case a pulled array resistivity survey was used to map the uppermost 15-20 m to estimate the distribution of the geological formations for freeway construction in Denmark. The result enables a more accurate estimate of the total freeway construction costs

Measuring time-domain spectral induced polarization in the on-time: decreasing acquisition time and increasing signal-to-noise ratio

Combined resistivity and time-domain direct current induced polarization (DCIP) measurements are traditionally carried out with a 50\% duty cycle current waveform, taking the resistivity measurements during the on-time and the IP measurements during the off-time. One drawback with this method is that only half of the acquisition time is available for resistivity and IP measurements, respectively. In this paper, this limitation is solved by using a current injection with 100\% duty cycle and also taking the IP measurements in the on-time. With numerical modelling of current waveforms with 50\% and 100\% duty cycles we show that the waveforms have comparable sensitivity for the spectral Cole–Cole parameters and that signal level is increased up to a factor of 2 if the 100\% duty cycle waveform is used. The inversion of field data acquired with both waveforms confirms the modelling results and shows that it is possible to retrieve similar inversion models with either of the waveforms when inverting for the spectral Cole–Cole parameters with the waveform of the injected current included in the forward computations. Consequently, our results show that on-time measurements of IP can reduce the acquisition time by up to 50\% and increase the signal-to-noise ratio by up to 100\% almost without information loss. Our findings can contribute and have a large impact for DCIP surveys in general and especially for surveys where time and reliable data quality are important factors. Specifically, the findings are of value for DCIP surveys conducted in urban areas where anthropogenic noise is an issue and the heterogeneous subsurface demands time-consuming 3D acquisitions

Impact of Time-domain IP Pulse Length on Measured Data and Inverted Models

The duration of time domain (TD) induced polarization (IP) current injections has significant impact on the acquired IP data as well as on the inversion models, if the standard evaluation procedure is followed. However, it is still possible to retrieve similar inversion models if the waveform of the injected current and the IP response waveform are included in the inversion. The on-time also generally affects the signal-to-noise ratio (SNR) where an increased on-time gives higher SNR for the IP data

Geophysical and hydrogeologic investigation of groundwater in the Karoo stratigraphic sequence at Sawmills in northern Matabeleland, Zimbabwe: a case history

Geophysical and hydrogeological investigations have been carried out around Sawmills in Zimbabwe, Africa. The investigations are components of a larger investigation to assess the groundwater potential of the Karoo sedimentary basin with regards to supplying water to Bulawayo City. The Sawmills area was selected due to the availability of borehole logs indicating favourable stratigraphy for groundwater availability and due to the high yields from the aquifers measured from these boreholes. Data collected using two geophysical methods are presented here: transient electromagnetic (TEM) and continuous vertical electrical sounding (CVES) data. The data have also been processed using laterally constrained inversion (LCI). Because the CVES provides greater detail in the shallow subsurface, whereas TEM is more effective at depth, a more accurate image of the entire subsurface profile is provided based on using both methods. The results suggest that LCI of CVES and TEM data, in the subsurface at the required depths at Sawmills, is able to provide a substantially more accurate image of the subsurface than either method alone. The hydrogeological interpretation of the geophysical data is valuable for determining the depth to and thickness of the potential aquifer horizon(s) and for identifying the position of potential recharge zones

Doubling the spectrum of time-domain induced polarization by harmonic de-noising, drift correction, spike removal, tapered gating, and data uncertainty estimation

The extraction of spectral information in the inversion process of time-domain (TD) induced polarization (IP) data is changing the use of the TDIP method. Data interpretation is evolving from a qualitative description of the subsurface, able only to discriminate the presence of contrasts in chargeability parameters, towards a quantitative analysis of the investigated media, which allows for detailed soil- and rock-type characterization. Two major limitations restrict the extraction of the spectral information of TDIP data in the field: i) the difficulty of acquiring reliable early-time measurements, in the millisecond range and ii) the self-potential drift in the measured potentials distorting the shape of the late time IP responses, in the second range. Recent developments in TDIP acquisition equipment have given access to full waveform recordings of measured potentials and transmitted current, opening a breakthrough for data processing. For measuring at early times, we developed a new method for removing the significant noise from powerlines contained in the data through a model-based approach, localizing the fundamental frequency of the powerline signal in the full-waveform IP recordings. By this, we cancel both the fundamental signal and its harmonics. Furthermore, a novel and efficient processing scheme for identifying and removing spikes TDIP data is developed. The noise cancellation and the de-spiking allow the use of earlier and narrower gates, down to a few milliseconds after the current turn-off. Furthermore, tapered windows are used in the final gating of IP data, allowing the use of wider and overlapping gates for higher noise suppression without signal distortion. For measuring at late times, we have developed an algorithm for removal of the self-potential drift. Usually constant or linear drift-removal algorithms are used, but these algorithms fail in removing the background potentials due to the polarization of the electrodes previously used for current injection. We developed a drift-removal scheme that model the polarization effect and efficiently allows for preserving the shape of the IP responses at late times. Uncertainty estimates are essential in the inversion of IP data. Therefore, in the final step of the data processing, we estimate the data standard deviation based on the data variability within the IP gates and the misfit of the background drift removal Overall, the removal of harmonic noise, spikes, self-potential drift, tapered windowing and the uncertainty estimation allows for doubling the usable range of TDIP data to almost four decades in time (corresponding to four responses in frequency), and will significantly advance the science and the applicability of the IP method

Lateral sammenbunden tolkning - LCI-tolkning af geofysiske data

I denne artikel ønsker vi at diskutere brugen af laterale bånd i forbindelse med tolkningen af geoelektriske og elektromagnetiske data. Vi vil indføre læseren i princippet bag LCI-tolkning og redegøre for de bagvedliggende begreber. Vi vil også beskrive de fordele, der kan opnås ved brugen af laterale bånd i datatolkningen, men vil også understrege, hvilke fejl båndene kan introducere, hvis ikke de anvendes rigtigt

Doubling the spectrum of time-domain induced polarization: removal of non-linear self-potential drift, harmonic noise and spikes, tapered gating, and uncertainty estimation

This paper presents an advanced signal processing schemefor time-domain induced polarization full waveform data.The scheme includes several steps with an improvedinduced polarization (IP) response gating design usingconvolution with tapered windows to suppress highfrequency noise, a logarithmic gate width distribution foroptimizing IP data quality and an estimate of gatinguncertainty. Additional steps include modelling andcancelling of non-linear background drift and harmonicnoise and a technique for efficiently identifying andremoving spikes. The cancelling of non-linear backgrounddrift is based on a Cole-Cole model which effectivelyhandles current induced electrode polarization drift. Themodel-based cancelling of harmonic noise reconstructs theharmonic noise as a sum of harmonic signals with acommon fundamental frequency. After segmentation ofthe signal and determining of noise model parameters foreach segment, a full harmonic noise model is subtracted.Furthermore, the uncertainty of the background driftremoval is estimated which together with the gatinguncertainty estimate and a uniform uncertainty gives atotal, data-driven, error estimate for each IP gate. Theprocessing steps is successfully applied on full field profiledata sets. With the model-based cancelling of harmonicnoise, the first usable IP gate is moved one decade closerto time zero. Furthermore, with a Cole-Cole backgrounddrift model the shape of the response at late times isaccurately retrieved. In total, this processing schemeachieves almost four decades in time and thus doubles theavailable spectral information content of the IP responsescompared to the traditional processing