Strictly horizontal lateral parameter correlation for 1D inverse modelling of large datasets

Abstract

This paper presents new developments to the lateral parameter correlation method, a method that can be used to invoke lateral smoothness in model sections of one‐dimensional inversion models. The lateral parameter correlation method has three steps. First, all datasets are inverted individually. Next, a laterally smooth version of each model parameter is found by solving a simple constrained inversion problem by postulating identity between the uncorrelated and correlated parameters and solving the equations including a model covariance matrix that ensures lateral smoothness. As a final step, all sounding data are reinverted with the correlated model parameter values as a priori values to produce models that better fit the data. Because the method separates inversion and correlation, it is much faster than methods where the inversion and correlation are solved simultaneously. The new development to the lateral parameter correlation method presented in this paper is an option to perform a strictly horizontal correlation, thereby avoiding the model artefacts sometimes seen when correlating along layers, namely that formations tend to follow the topography. Furthermore, a solution to the intractable computation times arising with large datasets is formulated, employing a tessellation of the plane and an averaging scheme within the subareas that reduces the size of the numerical lateral parameter correlation inversion problem while maintaining correct correlation within a very large area. In a field example, correlation along layers and the new strictly horizontal correlation are compared, and it is demonstrated that the horizontal correlation removes the above mentioned artefacts that can appear when correlating along layers. The lateral parameter correlation method is very flexible and is capable of correlating models from inversion of different data types, including information from boreholes, and it lends itself easily to “embarrassingly parallel” computation.

Focused attributes derived from AEM surveys using the continuous wavelet transform

“…Data were recorded with the SkyTEM312 system and the inversion was implemented with a hybrid approach using both the approximate inversion (Christensen, 2016a) and full accuracy calculations. Laterally correlated models were produced using a strictly horizontal Lateral Parameter Correlation procedure (Christensen, 2016b). As can be seen the simplifications obtained by binning are close to what one would expect from a manual categorization of the model section.…”

Using geophysical survey results in the inference of aquifer vulnerability measures

“…There are mainly two methods that will be brought into play: The Lateral Parameter Correlation method (LPC); and the Continuous Wavelet Transform (CWT) methodology. The LPC was developed as a technique for lateral correlation of one‐dimensional earth models after individual inversions of the data from a survey area (Christensen and Tølbøll, 2009; Christensen, 2016b). In the present context, the LPC is used mainly as an advanced interpolation tool, and it is introduced in Appendix A.…”

Interpretation attributes derived from airborne electromagnetic inversion models using the continuous wavelet transform

“…Data were recorded with the SkyTEM312 system and the inversion was implemented with a hybrid approach using both the approximate inversion (Christensen ) and full accuracy calculations. Laterally correlated models were produced using a strictly horizontal lateral parameter correlation procedure (Christensen ). The MLM profile consists of 3696 soundings inverted with 30‐layer models, which gives in total 110,880 parameter values.…”

“…Figure shows a plot of a MLM with 30 layers from an airborne electromagnetic (AEM) survey. The inversion was carried out using the methodologies outlined in Christensen (, ). Again, as was the case with the log example, a visual inspection would enable the interpreter to define the major layer boundaries, but with large surveys with millions of inversion models a manual procedure is out of the question and there is a need for an automatic algorithm.…”