# Single-Shot Time-Lapse Target-Oriented Velocity Inversion Using Machine Learning
## 2 Methodology
### Machine Learning Training and Testing  
As mentioned in Section 2.1, we simulated a database of 5000 synthetic anomalies in total. These data were randomly split into disjoint 80% train 20% test so that 4000 anomalies could be used for training the network and 1000 for testing. In this work, we train a machine learning algorithm to invert the time-lapse difference of P-wave velocity in the reservoir region from the time-lapse difference of pre-stack seismic data. The proposed ML inversion methodology is illustrated in Figure 3. First, we calculated the differences of all monitor pre-stack seismograms relative to the baseline seismogram. Then, we extracted (crop) from each time-lapse seismic difference the subset of data within the time interval that contains most of the energy reflected from the reservoir. To avoid biasing the algorithm by the specific amplitude range of seismic data--which depends on factors unrelated to the reservoir such as source wavelet amplitude and distances between source and receivers--we normalize each cropped difference by its maximum magnitude, resulting in the normalized time-cropped seismic data \(\Delta S\). Regarding the velocity model, the preprocessing steps are used to calculate the time-lapse velocity differences and extract the subset within the 220 m high and 2020 m wide reservoir region, resulting in the velocity anomaly \(\Delta v\) in the target region. Finally, \(\Delta S\) and \(\Delta v\) are, respectively, passed as inputs and desired outputs (targets) for the supervised training of a neural network. Figure 2: Illumination map produced by a single seismic source. This color map should be interpreted as areas where the energy of the seismic wave pass by and is captured by the receptors: (**a**) traces of sequence numbers from 11 to 20 (inclusive), (**b**) the 5 smallest offset traces, (**c**) traces from 21 to 30, and (**d**) traces from 31 to 40. The yellow rectangle indicates the target reservoir region as in Figure 1. The illumination map reveals that this simple acquisition geometry provides reasonable information to invert the target region. The core of the inversion methodology is formed by the neural network shown in Figure 4. The network has a novel architecture, inspired by the temporal convolutional network (TCN) [24]. The first step is to disregard from \(\Delta S\) the large-offset traces 1 to 7 and 42 to 49, because the illumination study (Section 2.3) revealed that those traces carry little reflection information from the reservoir region; keeping them could induce the network to learn spurious input-output associations. The remaining traces pass through a sequence of five convolutional layers arranged in a novel way. Recall that the standard convolutional layer applies a sliding 2D kernel to inputs that are neighboring to each other (unit dilation) in both dimensions. The layers we use apply the sliding 2D kernel to neighboring inputs in the horizontal axis, and further apart from each other in the vertical axis across layers. In other words, the convolutional layers use unit dilation in the space dimension, and exponentially increasing dilations in the time dimension. This way, we capture longer duration time relationships between seismic samples and spatially localized relationships across traces. The values of kernel size and dilation increasing rate were chosen such that each element at the output of the fifth layer is a function of all input elements (full  
Figure 3: Block diagram of the proposed ML inversion methodology. The input set consists of the seismic time-lapse (TL) difference and the output consists of the inverted reservoir anomaly. The red dashed rectangles indicate the subsets of time-lapse differences considered to calculate input and target data: we extract from seismic differences the time window concentrating most of the reflection energy coming from the reservoir, and from the velocity differences we consider the spatial region of the reservoir. history coverage).