Missing Log Estimator

Estimate missing well logs using empirical correlations from other available logs. Common problem in old wells where certain logs were not run or failed during acquisition. Choose the appropriate relationship based on lithology and available data.

Petrophysics Well Logging Empirical Correlation Gardner Equation

Input Parameters

What to Estimate

Target Log Choose which log you want to estimate

Estimation Method

Method Select estimation method

Lithology

Formation Type Lithology affects correlation coefficients

Input Log Value

Input Value

Value from available log

Custom Coefficients

Coefficient a First coefficient

Coefficient b Second coefficient

Matrix Properties

Matrix Density (ρ_ma)

g/cm³

Grain density (2.65 sandstone, 2.71 limestone, 2.87 dolomite)

Fluid Density (ρ_fl)

g/cm³

Pore fluid density (1.0 water, 0.85 oil, 0.25 gas)

Quick Presets

Results

Theory & References

Gardner's Equation (Density from Sonic)

ρ = a × Vp^b

Standard Forms:

SI units: ρ = 0.31 × Vp^0.25 (ρ in g/cm³, Vp in m/s)
US units: ρ = 0.23 × Vp^0.25 (ρ in g/cm³, Vp in ft/s)
From sonic slowness: ρ = 0.23 × (10⁶/DT)^0.25 (DT in μs/ft)

Application:

Most widely used empirical velocity-density relationship
Derived from extensive borehole measurements worldwide
Works well for consolidated sedimentary rocks
Typical uncertainty: ±5-10% in density
Less accurate for shales, gas zones, and unconsolidated sands

Reference: Gardner, G.H.F., Gardner, L.W., and Gregory, A.R., 1974, Formation velocity and density—The diagnostic basics for stratigraphic traps: Geophysics, v. 39, p. 770-780.

Sonic from Density (Inverse Gardner)

Vp = (ρ / a)^1/b

Standard Form (SI):

Vp = (ρ / 0.31)⁴ (Vp in m/s, ρ in g/cm³)
Less accurate than forward Gardner equation
Uncertainty amplified due to inverse calculation: ±10-15%

Limitations:

Less reliable than forward calculation (density from sonic)
Small density errors lead to large velocity errors
Should only be used when no other option available
Always validate against offset wells

When to Use: Only when sonic log is missing but density log is available. Prefer using regional velocity-depth trends if available.

Vs from Vp (Multiple Relationships)

Mudrock Line (Castagna et al., 1985):

Vs = 0.8621 × Vp - 1.1724 (km/s)

For shales and shaly formations
Most widely used relationship
Typical uncertainty: ±5-8%

Greenberg-Castagna (Sandstone):

Vs = 0.8042 × Vp - 0.8559 (km/s)

For clean sandstones
Better accuracy than mudrock line for sands

Carbonate Relationship:

Vs = Vp / 1.9

Simplified for limestones and dolomites
Fixed Vp/Vs ratio

References:

Castagna et al., 1985, Geophysics, v. 50, p. 571-581
Greenberg & Castagna, 1992, Geophysical Prospecting, v. 40, p. 195-209

Neutron from Density

φ_N ≈ (ρ_ma - ρ_b) / (ρ_ma - ρ_fl)

Physical Basis:

Both neutron and density respond to porosity
Assumes water-saturated or oil-saturated conditions
Uses density-porosity equation as proxy for neutron

Limitations:

Gas effect: Density and neutron separate in gas zones
Lithology effect: Different neutron responses per mineral
Clay-bound water: Neutron sees more porosity than density
Typical uncertainty: ±3-5 p.u. in good conditions

Best Use: Quick QC in water zones with known lithology. Not recommended for gas zones or clay-rich formations.

Gamma Ray from Density/Neutron

GR ≈ k × (ρ_ma - ρ_b) × 10

Empirical Basis:

Higher porosity (lower density) often correlates with shale
Low density + high neutron → high GR (shale indicator)
Very rough correlation, highly variable by basin
Coefficient k varies widely (typical 30-100)

Major Limitations:

Highly uncertain: GR depends on clay type, not just amount
Non-unique: Clean high-porosity sand ≠ shale on GR
Regional variation: Must calibrate to local wells
Not recommended: Use only for very rough QC

Alternative: Better to use regional shale indicator trends or calibrate from nearby wells with full log suites.

When Empirical Correlations Work

Best Conditions:

Uniform lithology: Single clean lithology (sandstone, limestone)
Normal pore fluids: Brine or oil-saturated (not gas)
Consolidated rocks: Reasonable cementation
Regional calibration: Coefficients tuned to local data
Offset wells: Validation data available nearby

Poor Conditions (Use with Extreme Caution):

Mixed lithology: Interbedded sand/shale, dolomitic limestone
Gas zones: Low gas density breaks density-sonic-neutron relationships
Unconsolidated: Young sediments, shallow depths
Heavy minerals: Pyrite, siderite, glauconite alter density
Overpressure: Abnormal compaction trends

Uncertainty Quantification

Typical Uncertainties (1σ):

Density from Sonic (Gardner): ±0.05-0.10 g/cm³ (5-10%)
Sonic from Density: ±200-400 m/s (10-15%)
Vs from Vp (Castagna): ±100-200 m/s (5-8%)
Neutron from Density: ±3-5 p.u.
GR from Density: ±20-40 API (very poor)

Factors Affecting Uncertainty:

Lithology homogeneity
Pore fluid type (gas increases error)
Depth and compaction state
Quality of regional calibration
Availability of offset well control

Best Practice: Always quote uncertainty range and validate against offset wells or core data when available.

Usage Guidelines & Best Practices

Before Using Empirical Estimates:

Check alternatives: Can you use a regional trend? Nearby well?
Understand lithology: Uniform or mixed? Clean or shaly?
Know the fluid: Water, oil, or gas-saturated?
Calibrate if possible: Use offset wells to tune coefficients
Document uncertainty: Quote typical error range

Quality Control:

Compare with offset wells at same depth/formation
Check crossplots of estimated vs. measured logs where available
Look for outliers that suggest data quality issues
Validate with core calibration if available

When Estimates Fail:

Gas zones: density-sonic-neutron separations invalidate correlations
Mixed lithology: no single coefficient set works
Consider weighted combinations for interbedded sequences
Use caution flags in your interpretation

Documentation: Always document which relationship was used, coefficients, assumptions, and estimated uncertainty in your reports.