Torgeir Wiik

TIV Contrast Source Inversion of mCSEM data

We present a 3D contrast source inversion scheme for electromagnetic data in conductive media. We consider only contrasts in electric conductivity but allow the medium to be transversely isotropic in the vertical direction. This has applications in, for instance, inversion of marine controlled-source electromagnetic data. The contrast source inversion (CSI) method is based on the integral equation formulation of electromagnetic field propagation and solves the inverse problem of determining the conductivity structure of the subsurface. The method minimizes a cost functional that enforces both data fidelity and that the solution satisfy the Lippmann-Schwinger equation. Further regularization is introduced linearly into the cost functional to incorporate prior model information. Although the problem is nonlinear, the chosen strategy splits the minimization problem into two linear problems, which are solved alternatingly. To this end, contrast sources are introduced, which may be interpreted as sources emitting the scattered field from a scattering object. Two synthetic and two real field examples are inverted, which demonstrates the method and how the transversely isotropic in the vertical direction (TIV) inversion performs compared with isotropic inversion. The CSI method is found to be applicable to real field examples, and the results show that a TIV inversion is preferred over isotropic to identify weak anomalies in these examples. The reason for this is that both the horizontal and vertical conductivity affects the signal propagation in the overburden.

Inversion of inline and broadside marine controlled‐source electromagnetic data with constraints derived from seismic data

We present a structural smoothing regularization scheme in the context of inversion of marine controlled-source electromagnetic data. The regularizing hypothesis is that the electrical parameters have a structure similar to that of the elastic parameters observed from seismic data. The regularization is split into three steps. First, we ensure that our inversion grid conforms with the geometry derived from seismic. Second, we use a seismic stratigraphic attribute to define a spatially varying regularization strength. Third, we use an indexing strategy on the inversion grid to define smoothing along the seismic geometry. Enforcing such regularization in the inversion will encourage an inversion result that is more intuitive for the interpreter to deal with. However, the interpreter should also be aware of the bias introduced by using seismic data for regularization. We illustrate the method using one synthetic example and one field data example. The results show how the regularization works and that it clearly enforces the structure derived from seismic data. From the field data example we find that the inversion result improves when the structural smoothing regularization is employed. Including the broadside data improves the inversion results even more, due to a better balancing between the sensitivities for the horizontal and vertical resistivities.

Detecting Skrugard by CSEM — Prewell prediction and postwell evaluation

AbstractThe discovery of Skrugard in 2011 was a significant milestone for hydrocarbon exploration in the Barents Sea. The result was a positive confirmation of the play model, prospect evaluation, and the seismic hydrocarbon indicators in the area. In addition, the well result was encouraging for the CSEM interpretation and analysis that had been performed. Prior to drilling the 7220/8-1 well, EM resistivity images of the subsurface across the prospect had been obtained along with estimates of hydrocarbon saturation at the well position. The resistivity distribution was derived from extensive analysis of the multiclient CSEM data from 2008. The analysis was based on joint interpretation of seismic structures and optimal resistivity models from the CSEM data. The seismic structure was furthermore used to constrain the resistivity anomaly to the Skrugard reservoir. Scenario testing was then done to assess potential alternative models that could explain the CSEM data in addition to extract the most likely re...

Directional interpolation of multicomponent data

ABSTRACT A method for interpolation of multicomponent streamer data based on using the local directionality structure is presented. The derivative components are used to estimate a vector field that locally describes the direction with the least variability. Given this vector field, the interpolation can be phrased in terms of the solution of a partial differential equation that describes how energy is transported between regions of missing data. The approach can be efficiently implemented using readily available routines for computer graphics. The method is robust to noise in the measurements and particularly towards high levels of low‐frequent noise that is present in the derivative components of the multicomponent streamer data.

Deblending Seismic Data by Directionality Penalties

In conventional seismic surveys, there is a waiting time between sequentially fired shots. This time is determined such that the deepest reflection of interest is recorded before the following source is fired. In a survey with simultaneous or blended sources, the waiting time between the firing of shots is not dependent on the deepest reflection of interest, it is usually much shorter and/or can have random time delays. Thus, the wavefields due to independent sources are overlapped in the records. The blended data exhibit strong discontinuities in the source direction, in contrast to the coherency expected from seismic measurements. A strategy for deblending could then be to suppress these discontinuities. In this paper, we propose to do this by designing an energy functional that uses a combination of individual functionals that penalize deviations from local plane waves in the reconstructed (deblended) data, as well as a least squares term that penalizes discrepancies between the deblended and the measured data. In this way, we derive a set of coupled nonlinear partial differential equations that we use for the deblending procedure.

Data-driven Interpolation of Multicomponent Data by Directionality Tensors

We focus on the problem of interpolating towed streamer data where multicomponent measurements exist and where the crossline direction is sparsely measured. We propose to use an assumption of few crossing events as a regularization constraint for the interpolation, which is formulated using structure tensors. Under this condition, we can obtain slowly varying directions along which the pressure data can be treated as constant. This condition is used to derive a partial differential equation for performing pressure data interpolation. The proposed method is entirely data-driven (it does not use any assumptions about the sea surface, the water velocity, or earth model).

2.5D EM modelling in TIV conductive media and the effect of anisotropy in normalized amplitude responses

We present an integral equation framework for 2.5D frequency domain EM modelling in conductive media, i.e. in media which are assumed invariant in one direction. Furthermore, we consider media which are transversely isotropic in the vertical direction (TIV), thus allowing the horizontal and vertical conductivities to differ. The integral equation framework allows for discretization of only a very limited area of the model, given a proper background model, thus leading to a small system of equations to be solved. The 2.5D integral equation method is suitable for studying the effect of localized resistivity anomalies efficiently and makes the generalization to real-world examples easier than for 1D modelling codes. We model three experiments to analyse and better understand the uncertainties of normalized amplitude and phase difference plots. Anisotropy has a significant effect on marine controlled source electromagnetic (mCSEM) data, and normalized amplitude graphs change both magnitude and position when changing the model to which one normalizes. It suggests that interpreters should be cautious when applying this to real data, where the model that caused the response at the reference receiver is unknown and may change along the line of receivers. Finally, we investigate whether mCSEM data are likely to be able to detect conductive inclusions in the stem of a salt diapir. When the models are exactly known, normalized amplitude plots can be used to check the sensitivity to perturbations.

2.5D Frequency Domain EM Modeling in Conductive TIV Media

We present a framework for 2.5D EM modeling in conductive TIV media based on integral equations. The method is developed for mCSEM purposes, thus assuming inline polarization of the source and crossline invariant media. The framework is tested numerically