Giulio Vignoli

An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data

We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host. We present an overview of a mature and general algorithm for inversion of most electromagnetic and geoelectrical data, ground-based and airborne. The implementation uses a 1D formulation for electromagnetics and MRS responses, geoelectric responses are 1D and 2D, and the 3D sheet’s response implements an overburden of varying thickness and resistivity.

Shear wave profiles from surface wave inversion: the impact of uncertainty on seismic site response analysis

Inversion is a critical step in all geophysical techniques, and is generally fraught with ill-posedness. In the case of seismic surface wave studies, the inverse problem can lead to different equivalent subsoil models and consequently to different local seismic response analyses. This can have a large impact on an earthquake engineering design. In this paper, we discuss the consequences of non-uniqueness of surface wave inversion on seismic responses, with both numerical and experimental data. Our goal is to evaluate the consequences on common seismic response analysis in the case of different impedance contrast conditions. We verify the implications of inversion uncertainty, and consequently of data information content, on realistic local site responses. A stochastic process is used to generate a set of 1D shear wave velocity profiles from several specific subsurface models. All these profiles are characterized as being equivalent, i.e. their responses, in terms of a dispersion curve, are compatible with the uncertainty in the same surface wave data. The generated 1D shear velocity models are then subjected to a conventional one-dimensional seismic ground response analysis using a realistic input motion. While recent analyses claim that the consequences of surface wave inversion uncertainties are very limited, our test points out that a relationship exists between inversion confidence and seismic responses in different subsoils. In the case of regular and relatively smooth increase of shear wave velocities with depth, as is usual in sedimentary plains, our results show that the choice of a specific model among equivalent solutions strongly influences the seismic response. On the other hand, when the shallow subsoil is characterized by a strong impedance contrast (thus revealing a characteristic soil resonance period), as is common in the presence of a shallow bedrock, equivalent solutions provide practically the same seismic amplification, especially in the frequency range of engineering interest.

Statistical multioffset phase analysis for surface-wave processing in laterally varying media

Standard procedures for dispersion analysis of surface waves use multichannel wavefield transforms. By using several receivers, such procedures integrate the information along the entire acquisition array. That approach improves data quality and robustness significantly, but its side effects are spatial averaging and loss of lateral resolution. Recently, a new approach was developed to address that issue and maximize lateral resolution. The new method uses multioffset phase analysis to detect and locate sharp lateral variations in velocity. By using the phase analysis approach, the number of usable channels can be maximized, thereby gaining data quality without compromising lateral resolution. In fact, such preliminary data analysis also allows selection of the appropriate traces on which to perform multichannel processing. Such multioffset phase analysis can be enhanced by f-k filtering, which assures the selection of only one wave-propagation mode, and by a statistical analysis that takes advantage of d...

Sharp spatially constrained inversion with applications to transient electromagnetic data

Time-domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam-type regularization constraints, which are meant to address the ill-posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non-vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large-scale time-domain electromagnetic data inversions.

Airborne electromagnetic modelling options and their consequences in target definition

Given the range of geological conditions under which airborne EM surveys are conducted, there is an expectation that the 2D and 3D methods used to extract models that are geologically meaningful would be favoured over 1D inversion and transforms. We do after all deal with an Earth that constantly undergoes, faulting, intrusions, and erosive processes that yield a subsurface morphology, which is, for most parts, dissimilar to a horizontal layered earth. We analyse data from a survey collected in the Musgrave province, South Australia. It is of particular interest since it has been used for mineral prospecting and for a regional hydro-geological assessment. The survey comprises abrupt lateral variations, more-subtle lateral continuous sedimentary sequences and filled palaeovalleys. As consequence, we deal with several geophysical targets of contrasting conductivities, varying geometries and at different depths. We invert the observations by using several algorithms characterised by the different dimensionality of the forward operator. Inversion of airborne EM data is known to be an ill-posed problem. We can generate a variety of models that numerically adequately fit the measured data, which makes the solution non-unique. The application of different deterministic inversion codes or transforms to the same dataset can give dissimilar results, as shown in this paper. This ambiguity suggests the choice of processes and algorithms used to interpret AEM data cannot be resolved as a matter of personal choice and preference. The degree to which models generated by a 1D algorithm replicate/or not measured data, can be an indicator of the data’s dimensionality, which perse does not imply that data that can be fitted with a 1D model cannot be multidimensional. On the other hand, it is crucial that codes that can generate 2D and 3D models do reproduce the measured data in order for them to be considered as a plausible solution. In the absence of ancillary information, it could be argued that the simplest model with the simplest physics might be preferred. Given the range of geological conditions under which airborne EM surveys are conducted, there is an expectation that 2D and 3D methods used to extract models of geological significance would be favoured over 1D inversion and transforms. We analyse data from the Musgrave province, South Australia, used for mineral and for hydro-geological prospecting.

The Influence of Subsoil Structure and Acquisition Parameters in MASW Mode Mis-identification

ABSTRACT Inversion of surface wave dispersion properties is commonly used to derive shear wave velocity depth profiles. However, one of the critical and yet rarely considered issues in this ill-posed inversion process is mode contamination. Rayleigh dispersion modes are the theoretically possible solutions of motion. Experimentally, we define Rayleigh dispersion properties from spectra energy maxima in some domain (as f–k), thus possibly producing only apparent experimental dispersion curves, where energy spreads onto several modes. If this phenomenon is not recognized, the inversion of an apparent dispersion curve can produce results unrelated to the actual subsurface structure. In this work, we present the results of synthetic tests that highlight the most common subsoil conditions and acquisition pitfalls that can give rise to surface wave mode contamination. In particular, we consider three typical subsoil structures that can produce this phenomenon: 1) a simple two-layer system with a strong impedanc...

Frequency-dependent multi-offset phase analysis of surface waves: an example of high-resolution characterization of a riparian aquifer

Multi-offset phase analysis of seismic surface waves is an established technique for the extraction of dispersion curves with high spatial resolution and, consequently, for the investigation of the subsurface in terms of shear wave velocity distribution. However, field applications are rarely documented in the published literature. In this paper, we discuss an implementation of the multi-offset phase analysis consisting of the estimation of the Rayleigh wave velocity by means of a moving window with a frequency-dependent length. This allows maximizing the lateral resolution at high frequencies while warranting stability at the lower frequencies. In this way, we can retrieve the shallow lateral variability with high accuracy and, at the same time, obtain a robust surface-wave velocity measurement at depth. In this paper, we apply this methodology to a dataset collected for hydrogeophysical purposes and compare the inversion results with those obtained by using refraction seismics and electrical resistivity tomography. The surface-wave results are in good agreement with those provided by the other methods and demonstrate a superior capability in retrieving both lateral and vertical velocity variations, including inversions. Our results are further corroborated by the lithological information from a borehole drilled on the acquisition line. The availability of multi-offset phase analysis data also allows disentangling a fairly complex interpretation of the other geophysical results.

An efficient hybrid scheme for fast and accurate inversion of airborne transient electromagnetic data

Airborne transient electromagnetic (TEM) methods target a range of applications that all rely on analysis of extremely large datasets, but with widely varying requirements with regard to accuracy and computing time. Certain applications have larger intrinsic tolerances with regard to modelling inaccuracy, and there can be varying degrees of tolerance throughout different phases of interpretation. It is thus desirable to be able to tune a custom balance between accuracy and compute time when modelling of airborne datasets. This balance, however, is not necessarily easy to obtain in practice. Typically, a significant reduction in computational time can only be obtained by moving to a much simpler physical description of the system, e.g. by employing a simpler forward model. This will often lead to a significant loss of accuracy, without an indication of computational precision. We demonstrate a tuneable method for significantly speeding up inversion of airborne TEM data with little to no loss of modelling accuracy. Our approach introduces an approximation only in the calculation of the partial derivatives used for minimising the objective function, rather than in the evaluation of the objective function itself. This methodological difference is important, as it introduces no further approximation in the physical description of the system, but only in the process of iteratively guiding the inversion algorithm towards the solution. By means of a synthetic study, we demonstrate how our new hybrid approach provides inversion speed-up factors ranging from ~3 to 7, depending on the degree of approximation. We conclude that the results are near identical in both model and data space. A field case confirms the conclusions from the synthetic examples: that there is very little difference between the full nonlinear solution and the hybrid versions, whereas an inversion with approximate derivatives and an approximate forward mapping differs significantly from the other results. We present a hybrid inversion scheme for airborne TEM data that introduces approximation only in the calculation of partial derivatives. The objective function is evaluated with a full nonlinear one-dimensional (1D) forward model.

Sharp Spatially Constrained Inversion

We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes this by allowing a reconstruction with a large number of layers, while preserving abrupt changes in the conductivity distribution. Instead of minimizing the norm of the vertical spatial variation of the model, in the focusing approach, it is the number of layers where the variations occur that is minimized. Thus, the results are compatible with the data and, at the same time, favor sharp transitions. The focusing strategy can also be used to constrain the 1D solutions laterally, guaranteeing that lateral sharp transitions are retrieved without losing resolution. By means of real and synthetic datasets, sharp inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user.

Reply to comment on Shear wave profile from surface wave inversion: the impact of uncertainty on seismic site response analysis

Socco et al (2012 J. Geophys. Eng. 9 241) comment on our study about the effect of non-uniqueness of surface wave solutions on seismic site response analysis. In particular, they refer to the approach we adopted for the selection of equivalent shear wave velocity profiles and argue that it leads to overestimation of the uncertainty due to the inherent ill-posedness of the problem. Moreover, for one of the synthetic cases of our original paper, they calculate a different set of equivalent velocity profiles, retrieving the corresponding amplification spectra. From these results, Socco et al claim that their general conclusion that the impact of solution non-uniqueness on seismic response simulations is negligible. In this reply we demonstrate that (a) the uncertainty bounds used by Socco et al in their prediction analysis, as a consequence of their surface wave inversion procedure, are unreasonably narrow; (b) consequently, their shaking predictions appear to suffer no impact from their underestimated uncertainty; and (c) their presented case shows an amplification spectrum that is only the result of assuming the existence of a bedrock at 150 m that causes resonance of the overlying layer—practically independent of the details of the S-wave velocity distribution.