Deeper Elasticity Closure Scans

Bulk Pressure Volume Inversion Three-Row Scan

Bulk response can be inverted to recover the compression volume change. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Bulk pressure can be inverted to recover compression volume

This book uses positive compression magnitudes. Pressure change 2 Pa over bulk modulus 12 Pa sets the volume-change fraction; with starting volume 6 cubic meters the recovered volume change is 1 cubic meter.

ΔV=ΔPKV=2 Pa12 Pa×6 m3=1 m3\Delta V=\frac{\Delta P}{K}V=\frac{2\ \text{Pa}}{12\ \text{Pa}}\times6\ \text{m}^{3}=1\ \text{m}^{3}
Bulk inversion rowPressure, modulus, volume, and volume change are checked magnitudes.pressurevolume changevolume=6 m^3volumeChange=1 m^3pressureChange=2 Pamodulus=12 Pa

Bulk pressure can be inverted to recover compression volume

This book uses positive compression magnitudes. Pressure change 3 Pa over bulk modulus 18 Pa sets the volume-change fraction; with starting volume 6 cubic meters the recovered volume change is 1 cubic meter.

ΔV=ΔPKV=3 Pa18 Pa×6 m3=1 m3\Delta V=\frac{\Delta P}{K}V=\frac{3\ \text{Pa}}{18\ \text{Pa}}\times6\ \text{m}^{3}=1\ \text{m}^{3}
Bulk inversion rowPressure, modulus, volume, and volume change are checked magnitudes.pressurevolume changevolume=6 m^3volumeChange=1 m^3pressureChange=3 Pamodulus=18 Pa

Bulk pressure can be inverted to recover compression volume

This book uses positive compression magnitudes. Pressure change 6 Pa over bulk modulus 16 Pa sets the volume-change fraction; with starting volume 8 cubic meters the recovered volume change is 3 cubic meters.

ΔV=ΔPKV=6 Pa16 Pa×8 m3=3 m3\Delta V=\frac{\Delta P}{K}V=\frac{6\ \text{Pa}}{16\ \text{Pa}}\times8\ \text{m}^{3}=3\ \text{m}^{3}
Bulk inversion rowPressure, modulus, volume, and volume change are checked magnitudes.pressurevolume changevolume=8 m^3volumeChange=3 m^3pressureChange=6 Pamodulus=16 Pa