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Reverse the Inverse problem to spatial superposition where pressure response 

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p_m(t) = p_i + \sum_k \delta p_{mk}(t) = p_i +   \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) = p_i + \int_0^t p_{umm}(t-\tau) \, dq_k(\tau) + \sum_{k \neq m}  \int_0^t p_{umk}(t-\tau) \, dq_k(\tau)

\{ q_k(t_j) \}_{k=1..N, \, j= 1..T}

flowrate variation history

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Drawdown Transient Response (DTR)

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{ p_

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k(t

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_j) \}_{k=1..N, \, j= 1..T}

pressure variation history

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umk}(\tau)

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