Algorithm 1: A 3D gravity inversion method based on the attention fusion mechanism

Input: Training data pair ${\left\{\mathit{d}\right\}}_{p=1}^P$, ${\left\{\mathit{m}\right\}}_{p=1}^P$, Batch size $bs$, Learning rate $\eta$

Initialization: weight ${\mathit{W}}^{\left(t\right)}$, offset ${\mathit{b}}^{\left(t\right)}$, $t=0$

Repeat: $fors=1:P//bsorP//bs+1$

$loss=0fori=1:b{s}_s$

(1) Forward propagation

Encoding

$forj=1:4$

${{\mathit{d}}_j^i}^{\prime }\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_{2j-1}^{\left(t\right)}\ast {\mathit{d}}_{j-1}^i+{\mathit{b}}_{2j-1}^{\left(t\right)}\left)\right)$

${\mathit{c}}_j\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_{2j}^{\left(t\right)}\ast {{\mathit{d}}_j^i}^{\prime }+{\mathit{b}}_{2j}^{\left(t\right)}\left)\right)$

${\mathit{d}}_j^i\hspace{1em}\leftarrow Downsampling\left({\mathit{c}}_j\right)withDropout\left(0.2\right)$

${{\mathit{d}}_5^i}^{\prime }\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_9^{\left(t\right)}\ast {\mathit{d}}_4^i+{\mathit{b}}_9^{\left(t\right)}\left)\right)$

${\mathit{d}}_5^i\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_{10}^{\left(t\right)}\ast {{\mathit{d}}_5^i}^{\prime }+{\mathit{b}}_{10}^{\left(t\right)}\left)\right)$

Decoding

$forj=4:-1:1$

${{\mathit{d}}_j^i}^{\prime }\hspace{1em}\leftarrow Upsampling\left({\mathit{d}}_{j+1}^i\right)withDropout\left(0.2\right)$

${\mathit{a}}_j^{\prime }\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_{24-3j}^{\left(t\right)}\ast AFF({{\mathit{d}}_j^i}^{\prime },{\mathit{c}}_j)+{\mathit{b}}_{24-3j}^{\left(t\right)}\left)\right)$

${\mathit{a}}_j\hspace{1em}\leftarrow RELU\left(BN\right({\mathit{W}}_{25-3j}^{\left(t\right)}\ast {\mathit{a}}_j^{\prime }+{\mathit{b}}_{25-3j}^{\left(t\right)}\left)\right)$

${\mathit{d}}_j^i\hspace{1em}\leftarrow Sigmoid(MS-CAM({\mathit{a}}_j\left)\right)$

${\widehat{\mathit{m}}}^i$ $\hspace{1em}\leftarrow RELU\left(AFF\right({\mathit{d}}_1^i,{\mathit{d}}_2^i,{\mathit{d}}_3^i,{\mathit{d}}_4^i,{\mathit{d}}_5^i\left)\right)$

$loss\hspace{1em}\leftarrow loss+L_i({\widehat{\mathit{m}}}^i,{\mathit{m}}^i)$

(2) Back propagation

${\mathit{W}}^{(t+1)}\hspace{1em}\leftarrow {\mathit{W}}^{\left(t\right)}+Adam(\eta ,loss/{bs}_s)$

${\mathit{b}}^{(t+1)}\hspace{1em}\leftarrow {\mathit{b}}^{\left(t\right)}+Adam(\eta ,loss/{bs}_s)$

Until the neural network converges

The gravity anomaly data of the area to be reconstructed are input d, and the reconstructed model $\widehat{\mathit{m}}$ is predicted.