Relaxation Contrast Depth Scans

Spin Echo Recoverable Loss Alternative Scale Scan

Spin echo visibility grows only when the recoverable bucket grows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Recoverable and irreversible buckets trade off inside one budget

Initial transverse budget is 15 and coherent bucket is fixed at 5.

echo visible=coherent+recoverable\text{echo visible}=\text{coherent}+\text{recoverable}
Echo split rowThe echo adds only the recoverable bucket to the coherent bucket.coherent 5recoverable 4irreversible 6echo 9

Three split rows keep the initial budget closed

The irreversible bucket stays outside the echo-visible result.

recoverablelostechoFecho2877154693564111115\begin{array}{c|c|c|c}\text{recoverable}&\text{lost}&\text{echo}&F_{\text{echo}}\\2&8&7&\frac{7}{15}\\4&6&9&\frac{3}{5}\\6&4&11&\frac{11}{15}\\\end{array}

The middle row makes nine visible

Coherent 5 plus recoverable 4 gives echo-visible signal 9.

5+4=95+4=9
Echo split rowThe echo adds only the recoverable bucket to the coherent bucket.coherent 5recoverable 4irreversible 6echo 9