A method for implementing a full waveform inversion (FWI) process using angle gathers includes; receiving observed seismic data associated with a subsurface region and captured by one or more seismic receivers, constructing based on the observed seismic data, a scalar velocity model and one or more vector velocity model partitions, where the one or more vector velocity model partitions correspond to one or more unique seismic angles. The method further includes determining one or more vector gradients using the scalar velocity model and the observed seismic data, and updating the one or more vector velocity model partitions using the one or more vector gradients. Additionally, the method also includes determining residual data by comparing synthetic data produced by the scalar velocity model with the observed seismic data, migrating the residual data backwards through time to determine one or more vector gradients, and determining the one or more unique seismic angles as the residual data is migrated backwards through time.

A method of estimating a velocity of a geological layer includes a. providing a first, initial model including an interval velocity associated with a subsurface location and an uncertainty associated with the interval velocity; b. providing data including an actual or approximated root-mean-square (RMS) velocity associated with a subsurface location and an uncertainty associated with the RMS velocity; and c. estimating a second model including an interval velocity associated with a subsurface location and an uncertainty associated with the interval velocity, based on the interval velocity and the uncertainty of the first model, and the RMS velocity and the uncertainty of the data.

A computer-implemented method of enhancing a computer to estimate an uncertainty of an onset of a signal of interest in time-series noisy data. A first mathematical model of first time series data that contains only noise is calculated. A second mathematical model of second time series data that contains the noise and an onset of a signal of interest in the second time series data is calculated. A difference is evaluated between a first combination, being the first mathematical model and the second mathematical model, and a second combination, being the first time series data and the second time series data, wherein evaluating is performed using a generalized entropy metric. A specific time when an onset of the signal of interest occurs is estimated from the difference. An a posteriori distribution is derived for an uncertainty of the specific time at which the onset occurs.

Uncertainty in microseismic monitoring sensor data can be reduced. A computing device can receive information about at least one sensor that is monitoring a subterranean formation, including a location, after a fracturing fluid is introduced into the formation. The computing device can also receive information about a microseismic event and determine a seismic ray bath between a location of the event and the at least one sensor, and an uncertainty value of the location based on information about the formation and the information about the event. The computing device can determine a total uncertainty value associated with the locations of a plurality of microseismic events, including the microseismic event. The computing device can determine a solution to an objective function based on the total uncertainty value and a number of sensors. The computing device can determine a new location of the at least one sensor based on the solution.

Methods of generating a parameter realization, for a subsurface parameter, as a function of depth within a subsurface region are disclosed herein. The methods include dividing a subsurface parameter profile for the subsurface region into a plurality of adjacent stratigraphic units. The methods also include splitting each stratigraphic unit of the plurality of adjacent stratigraphic units into a plurality of stratigraphic unit layers. The methods further include determining a layer parameter value range for each stratigraphic unit layer of the plurality of stratigraphic unit layers and for each stratigraphic unit. The methods also include, within each stratigraphic unit layer, selecting a corresponding layer parameter value from within the layer parameter value range. The methods further include generating the parameter realization by assigning the corresponding layer parameter value to the parameter realization for a corresponding layer depth range of each stratigraphic unit layer.

A method for estimating sonic slowness comprising: obtaining (700) a plurality of sonic waveforms are received by a plurality of receivers of a logging tool after emission of a source sonic wave by a transmitter, obtaining (710) slowness models of the subterranean formation, a slowness model being defined by a at least one cell of constant slowness for at least one wave energy mode, computing (720), for each slowness model, a set of candidate travel times, a candidate travel time of a set of candidate travel times being computed for a wave energy mode and a position of a receiver of the plurality of receivers, computing (730) a relevance indicator for each set of candidate travel times based on the recorded sonic waveforms; searching (740) a match between the sets of candidate travel times and the recorded sonic waveforms by searching a relevance indicator which is optimum, computing (750) a sonic slowness estimate for the subterranean formation from a set of candidate travel times for which the relevance indicator is optimum.

A method is described for full waveform inversion using a tree-based Bayesian approach which automatically selects the model complexity, thereby reducing the computational cost. The method may be executed by a computer system.

A method of predicting model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ) of a geological formation under investigation, wherein said geological formation is distinguished by reservoir parameters including observable data parameters and the model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ) to be predicted, comprises the steps of calculating at least one model constraint (M.sub.1, M.sub.2, M.sub.3, . . . ) of the model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ) by applying at least one rock physics model (f.sub.1, f.sub.2, f.sub.3, . . . ) on the model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ), said at least one model constraint (M.sub.1, M.sub.2, M.sub.3, . . . ) including modelled data of at least one of the data parameters, and applying an inverse model solver process on observed input data (d.sub.1, d.sub.2, d.sub.3, . . . ) of at least one of the data parameters, including calculating predicted model parameters, which comprise values of the model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ) which give a mutual matching of the input data and the modelled data, wherein the modelled data are provided with probability distribution functions, the inverse model solver process is conducted based on the probability distribution functions, wherein multiple predicted values of the model parameters are obtained comprising values of the model parameters (R.sub.1, R.sub.2, R.sub.3, . . . ) which give the mutual matching of the input data and the modelled data, and model probabilities of the predicted model parameters are calculated in dependency on the probability distribution functions.

Systems, devices and methods for evaluating a volume of interest of an earth formation. The method may include modeling the volume as being in one of two states using a plurality of measurements corresponding to a plurality of measurement types, and may include assigning a relative credence indicator value to each measurement in dependence upon the corresponding measurement value and using the relative credence indicator value for each of the plurality of measurements to estimate the state of the volume by estimating the state of the volume using a state indicator value derived from the relative credence indicator values. The first state of the two states may correspond with presence of a condition associated with the formation, and the second state of the two states may correspond with absence of the condition. The condition may comprise presence of a fluid in the formation having a selected fluid type.

A method can include receiving a node-based mesh that represents a geologic environment and a structural feature in the geologic environment; defining a node-based parameter space for structural uncertainty of nodes that represent the structural feature in the geologic environment; defining a hull with respect to nodes of a portion of the mesh where the hull encompasses at least a portion of nodes that represent the structural feature; for a system of equations, imposing boundary conditions on the nodes of the hull and on the at least a portion of the nodes that represent the structural feature; solving the system of equations for a displacement field; and generating a structural uncertainty realization of the node-based mesh based at least in part on the displacement field.