geomechanics · elastic properties
Dynamic Elastic Moduli (Young's, Bulk, Shear)
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Inputs
g/cc
ft/s
ft/s
Description
Computes the dynamic Young's, Bulk, and Shear moduli of a formation from compressional and shear sonic velocities and bulk density, using standard isotropic-elasticity identities. These are wellbore-stability, frac-design, and brittleness-screening inputs — genuinely geomechanical quantities, even though they are derived from geophysics-native log data (the same reasoning already applied to Drilling's Eaton sonic pore pressure calc, which also consumes sonic-log inputs but belongs to the geomechanical workflow it serves).
Variables
| Symbol | Unit | Description |
|---|---|---|
| Edyn | GPa | Young's Modulus (dynamic) |
| Kdyn | GPa | Bulk Modulus (dynamic) |
| Gdyn | GPa | Shear Modulus (dynamic) |
| ρ | g/cc | Bulk density of the formation, typically from the density log — same input as Geophysics's Acoustic Impedance and Lambda-Rho/Mu-Rho. |
| Vp | ft/s | True compressional velocity (e.g. checkshot-calibrated sonic, or 1/DT already converted from slowness) — not a raw uninverted slowness curve. |
| Vs | ft/s | True shear velocity from a dipole/multipole sonic or converted-wave data — not inferred from Vp via an assumed Vp/Vs ratio, which would circularly bias the resulting moduli. |
Assumptions
- Vp, Vs, and ρ are measured or reliably estimated at the same depth and represent the same rock volume.
- The rock is treated as an isotropic elastic medium — no anisotropic stiffness tensor is modeled, consistent with Lambda-Rho/Mu-Rho and Vp/Vs.
- Vs is a genuine shear-velocity measurement (dipole/multipole sonic or converted-wave derived), not inferred from Vp via a generic Vp/Vs assumption.
Limitations
- These are DYNAMIC moduli — computed from elastic wave velocities at seismic/sonic (kHz-MHz) strain rates and very small (~10⁻⁶) strain amplitudes. STATIC moduli — measured directly from a triaxial core test at the much larger, slower strain typical of actual wellbore or hydraulic-fracture loading — are usually lower than the dynamic value, sometimes substantially so in unconsolidated or highly fractured rock. Wellbore-stability and frac-design work that requires a static modulus must not substitute this dynamic value directly without an appropriate correction.
- No universal dynamic-to-static correction factor is applied here: the static/dynamic gap is rock-type-, stress-, and strain-dependent, and published correlations (see Zoback, Reservoir Geomechanics, 2007, for a discussion of common approaches) require local core calibration to use responsibly — silently baking in an uncalibrated global factor would be worse than disclosing the gap and leaving the conversion to the user's own core data.
- Like Gassmann and Lambda-Rho/Mu-Rho, this treats the rock as an isotropic, homogeneous elastic medium at the log/core scale — near-wellbore stress concentration, anisotropy, and fracture-network effects on effective stiffness are not modeled.
Use Cases
- → Brittleness screening for frac design: Combine dynamic E and ν with a mineralogy-based brittleness index to identify the most frac-able intervals in a horizontal landing zone before completion design.
- → Wellbore stability model input (with static correction): Provide the dynamic moduli baseline for a wellbore-stability model, applying a locally-calibrated static correction alongside Effective Stress and Mohr-Coulomb Failure Criterion for a full geomechanical earth model.
- → Offset-well elastic property logging: Compute a continuous dynamic-moduli log from an offset well's sonic and density curves to extend a geomechanical model laterally where no core data exists.
Related Calculations
Region Notes
Global
Dynamic-to-static correction ratios vary widely by lithology and consolidation state — always calibrate against core triaxial data from the same formation before using these values directly in a static wellbore-stability or frac-design model.
Permian Basin
Wolfcamp/Bone Spring brittleness screening commonly uses dynamic E and ν from sonic/density logs precisely as computed here, cross-plotted against mineralogy (XRD or spectroscopy logs) to rank landing zones.
References
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