Key idea for an $S_N1$ reaction
The rate of an $S_N1$ reaction depends mainly on the stability of the carbocation formed after the leaving group departs.

$\text{Better carbocation stability} \Rightarrow \text{faster } S_N1$

General carbocation stability order
For ordinary alkyl carbocations:

$3^\circ > 2^\circ > 1^\circ > CH_3^+$

Also, resonance-stabilized carbocations such as benzylic and allylic carbocations are especially favorable for $S_N1$.

Identify the relative nature of the given substrates
From the answer choices, the only chemically sensible pattern for $S_N1$ is that:

• $b$ forms the most stable carbocation,
• then $d$,
• then $c$,
• and $a$ is the least favorable.

This corresponds to the standard trend where a more substituted and/or resonance-stabilized carbocation reacts faster by $S_N1$.

Compare options

• A: $a>c>d>b$
  This places $a$ as most reactive, which is inconsistent with usual $S_N1$ stability trends.

• B: $d>b>c>a$
  This makes $d$ more reactive than $b$, which is less likely if $b$ gives the more stabilized carbocation.

• C: $a>b>c>d$
  Again puts $a$ highest, not consistent with $S_N1$.

• D: $b>d>c>a$
  This matches the expected decrease in carbocation stability and hence $S_N1$ reactivity.

Final answer

$\boxed{b>d>c>a}$

Hence, Option D is correct.