# Single-Shot Time-Lapse Target-Oriented Velocity Inversion Using Machine Learning
## 1 Introduction  
Time-lapse seismic is an important tool to unveil reservoir property changes due to oil/gas production [1]. Indeed, during the production life cycle of a reservoir, the displacement of water, oil, and gas in the reservoir changes the impedance properties of the rocks, which are reflected as differences in the seismic record from one survey to another [2]. In this context, the 4D, or time-lapse, seismic has been stated as an important tool to support the decision-making of oil/gas reservoir production. Moreover, in the current context of climate change [3], 4D seismic is also a tool to monitor and manage CO\({}_{2}\) storage in geologic formations [4]. In this study, we explore a straightforward 4D seismic inversion methodology. In our method, we assume acoustic propagation, and we invert seismic data to obtain velocity models. To standardize the notation along the paper, we consider that we have seismic acquisition from a baseline reservoir and a subsequent, during production, monitor acquisition. To be precise, we use the time-lapse difference (monitor minus baseline) ofseismic data to invert the velocity model perturbation (monitor minus baseline)--we call this anomaly the change or perturbation--in the reservoir region. Target-oriented time-lapse inversion is a challenging task due to the complex physics relating the velocity changes in the reservoir to the seismic response [5]. In this context, a statistical inversion approach like the ML methodology seems to be appropriate to deal with uncertainty and lack of information. Some studies have proposed ML inversion techniques to produce velocity models directly from seismic data [6], but the huge amount of data limits the success of this endeavor. Several studies about 4D seismic and ML are focused on the preprocessing of seismic data to diminish non-repeatability noise [7; 8] or to find the water velocity layer [9; 10]. In time-lapse seismic research, some authors use seismic data and ML to estimate reservoir properties like water saturation or change in reservoir pressure [11; 12; 13]. These studies generally use not only seismic data as input but also well-log data, reservoir parameters, or physics rock parameters [14; 15; 16; 17]. The novelty of this paper is the simplicity: we employ ML to perform a target-oriented velocity inversion using only pre-stack data. Moreover, our method is target-oriented, computationally economical, and needs low seismic data. In fact, we invert the reservoir anomalies using seismic data from a single shot. We notice that the usual 4D inversion assumes a well-known baseline acquisition. In particular, the 4D target-oriented problem is focused on the inversion of a restricted reservoir region. Moreover, in the study area of our problem, the Brazilian pre-salt, the overburden issue caused by geomechanical movements above the target area is negligible. Therefore, the 4D target-oriented problem shares information with adjacent areas about the location of major geologic structures like horizontal layers or faults. In this restricted context of the 4D target-oriented problem, the ML inversion approach can be successful because several major issues of the geophysical inversion are minimized [1]. The seismic inversion based on one-shot acquisition is not feasible in standard 2D or 3D inversion problems. The reason for the unfeasibility of the one-shot inversion is due to the ambiguity in the location of the seismic events [18]. In fact, a seismic event caused by, for instance, a reflection in a layer interface does not present a well-defined position but rather can be localized at any point along an isochronous line centered in the seismic source [19]. In order to solve the ambiguity in the location of the seismic event, more shots are necessary. However, the location ambiguity is not a central issue in target-oriented 4D inversion once the overall layer positions are already well defined for the baseline acquisition [2].