Fast inversion of array laterolog measurements in an axisymmetric medium

The array laterolog is an important tool for complex formation logging evaluation due to its high resolution and large detection depth.However,its logging responses are seriously affected by leakage events due to the surrounding rock and by mud invasion.These factors must be considered when inverting array lateral logging data,so that the inversion results reflect the true formation conditions as much as possible.The difficulties encountered in the inversion of array lateral logging data are:too many inversion parameters cause the calculation of the Jacobian matrix to be difficult and the time required to select the initial inversion values due to the slow forward-modeling speed.In this paper,we develop a fast processing method for array laterolog data.First,it is important to clearly define the main controlling factors for the array laterolog response,such as thickness,the surrounding rock,and invasion.Second,based on a depth-window technique,processing the array laterolog data for the entire well is transformed into multiple 2 D inversions of the layers using a series of continuous depth windows.For each formation in a depth window,combined with the1 D equivalent fast-forward algorithm,rapid extraction of the radial resistivity profile of the formation is achieved.Finally,the 1 D inversion result is used as the initial state to further eliminate the influence of surrounding rocks and layer thicknesses on the apparent resistivity response.Numerical simulation results show that the factors affecting the response of the array laterolog are the invasion properties,the layer thicknesses,and the surrounding rocks;the windowing technique greatly reduces the number of inversion parameters needed and improves the inversion speed.A real application of the method shows that 2 D inversion can rapidly reconstruct the actual resistivity distribution and improve the accuracy of reservoir saturation calculations.

Concepts in the Direct Waveform Inversion(DWI)Using Explicit Time-Space Causality

The Direct Waveform Inversion(DWI)is a recently proposed waveform inversion idea that has the potential to simultaneously address several existing challenges in many full waveform inversion(FWI)schemes.A key ingredient in DWI is the explicit use of the time-space causality property of the wavefield in the inversion which allows us to convert the global nonlinear optimization problem in FWI,without information loss,into local linear inversions that can be readily solved.DWI is a recursive scheme which sequentially inverts for the subsurface model in a shallow-to-deep fashion.Therefore,there is no need for a global initial velocity model to implement DWI.DWI is unconditionally convergent when the reflection traveltime from the boundary of inverted model is beyond the finite recording time in seismic data.In order for DWI to work,DWI must use the full seismic wavefield including interbed and free surface multiples and it combines seismic migration and velocity model inversion into one process.We illustrate the concepts in DWI using 1D and 2D models.