Question

A geophysical forward problem is expressed as \( d = 7m_1^2 m_2 + 6m_2 \), where \( m_1 \) and \( m_2 \) represent the model parameters and \( d \) represents the data. Then, the relationship between data and model parameters is

• A. explicit and linear
• B. implicit and linear
• C. explicit and non-linear
• D. implicit and non-linear

Hint:

Always check if the equation expresses the data directly as a function of model parameters (explicit). Next, examine the powers of parameters: if only first powers appear, it's linear; otherwise, it is non-linear.

Answer 1

The Correct Option is C

Step 1: Explicit vs Implicit.
The equation is given in the form \[ d = f(m_1, m_2) = 7m_1^2 m_2 + 6m_2 \] This shows \(d\) directly as a function of model parameters \(m_1\) and \(m_2\). Therefore, the relation is explicit. Step 2: Linear vs Non-linear.
A linear model means that the data is a linear combination of model parameters (\(a m_1 + b m_2 + c\)). Here, the equation contains a quadratic term in \(m_1\): \[ 7m_1^2 m_2 \] This introduces non-linearity. Therefore, the relation is non-linear. Final Conclusion: The relationship is explicit and non-linear. \[ \boxed{\text{Option (C)}} \]