Hello;

I- In general cases, we can apply many statistical tools and machine learning methods to reconstruct the missing data from other measurements. (Handling missing values in exploratory multivariate data analysis, see for example this link https://husson.github.io/index.html

2- There is a special study branch for data analysis for missing data.

3- It is known that real data may have missing sections due to the acquisition environment or to the lack of measurement. In such cases, rock physicists often proceed to reconstruct the missing data from other measurements.

For this purpose, the Rock physics module provides the following tools:

• Gardner approximation: based on either an exponential or polynomial approximation, you can reconstruct bulk density from compressional slowness and reconstruct compressional slowness from bulk density
• Note: Based on the Mavko et al Rock Physics handbook, the maximum polynomial degree used in the approximation is 5.
• Faust approximation: this method is used to reconstruct compressional slowness from resistivity data.
• The Gardner approximation provides a synthetic bulk density log reconstructed from a P-waves velocity Vp or compressional slowness log. Two alternative approaches have been implemented for this purpose: the exponential and the polynomial method.
• The Gardner approximation for the compressional velocity reconstruction Vp from the bulk density RHOB is used to get synthetic compressional velocity and compressional slowness logs.
• The Faust approximation for the compressional velocity reconstruction Vp from the resistivity Ro is used to get synthetic compressional velocity and compressional slowness logs.
• Han's empirical Vp and Vs: This method computes compressional and shear velocity based on the empirical relations developed by Eberhart-Phillips (1989) on Han’s data.
• Display Han's Vp vs Phi : This method generates a parametric cross plot where compressional velocity is displayed versus porosity for the considered depth points. Parametric Han regression lines linking the compressional velocity to porosity are displayed for different clay contents. These lines are based on the work of Eberhart-Phillips (1989).
• Display Han's Vs vs Phi This method generates a parametric cross plot where shear velocity is displayed versus porosity for the considered depth points. Parametric Han regression lines linking the shear velocity to porosity are displayed for different clay contents. These lines are based on the work of Eberhart-Phillips (1989).
• Smooth with missing values, corresponds to a Gaussian smoothing in which the missing values are taken into account to calculate the weighted average and impact the calculation of the smoothed value. It is a way to smooth point data as they usually contain a lot of missing values.
• For example, the K.mod method performs parameter prediction and log reconstruction using multilayer perceptron technology. Dedicated templates enhance usability. Quantitative estimates of the fit quality obtained are provided. Models are stored and applied to other wells.

I hope I have given you some help and good luck.

Dear Abdelbasset Boulassel ,

Thanks for sharing this information, they're really useful.

Yes, different methods are developed for S-wave velocity prediction from other conventional petrophysical logs, generally using rock physics methods or artificial intelligence algorithms. and these methods have their own challenges for predicting S-wave velocity for complex reservoirs, which affects their prediction accuracy and efficiency accordingly. And I want to use a combination of rock physics and machine learning methods on reservoirs to predict S-wave velocity.

For the least amount of uncertainty, a rock physics or Petro-elastic model may be the way to go. Of course, the approach requires more work but offers the most consistent result. Neural Network or multi-dimensional regression may be the next good thing where a rock physics model does not exist. It is fast and yields result that are close to the rock physics model or even better, in some cases. Good luck.

Dear Sunday Oluleye Amoyedo,

Thanks for sharing this information.

• I have two different approaches:

Dear Erfan Rahimi ,

Your project is a multi-faceted one that we could discuss for days.

I have a suggestion for you in order to estimate shear slowness from measured compressional slowness and density. It is based on a simple Rock Physics model (essentially a mix of Biot of Gassmann theories).

The idea is to locate a measured data-point (sonic slowness, bulk density) on a parameterized 'compressional sonic slowness / bulk density' plot and to read the value of shear sonic slowness on the associated 'shear sonic slowness / bulk density' plot.

This will work for consolidated formations (when both plots use the same parameter for sonic and shear sonic modeling).

The charts are built assuming known fluid properties (bulk density, bulk modulus) and matrix properties (bulk density, bulk modulus, shear modulus).

The common parameter varies from 3 (clean grainstone) to 100 (shale, marl).

It will be obtained from the inversion of measured sonic/density data and applied to estimate the shear sonic/density.

Dear @Erfan Rahimi,

This is common in well log measurements/data.

Therefore, for one to approach this problem of data void in some formation. It is vital to first try to understand why the data is missing in the first place.

It might be as a result of the formation environment with respect to drilling or in some cases the anomalous pressure zone or even structural related issues.

The seismic data and rock physics have a major role to play here. They can be interpolated with other well log of proximity and or data type to reduce uncertainty. The end result will be a model also trained with the known existing formation data using machine learning.

Again, the reason for the absence is vital as a factor to consider when building or reconstructing such data.

Wish you the best.

Olatunbosun Kafisanwo

Dear Olatunbosun Kafisanwo ,

Thank you for your answer.

I know, many problems such as collapses, washes, mud cakes, breakouts, knockouts, etc. Charting tools can not record the graphs correctly or at all.

But for technical and cost reasons, graphs are not usually plotted from the surface to the depths, and usually many companies only run the gamma-ray and Sonic (DTC) in the upper formations. My goal is the predict these data gaps.

You can use Machine learning algorithm to learn the data trends, where it is available and what parameters the data depend on, then use the algorithm to predict the data where they are missing the relationships learn from the training.