Gravity inversion with depth normalization

Actually the most common method of gravity data interpretation is a manual fitting method. In this case, the density model is divided into many polygons with constant density and each polygon is editing manually by interpreter. This approach has two main disadvantages:

- significant amount of time is needed to build a high-quality density model;

- if density isn’t constant within anomalous object or a layer, object must be divided into many blocks, which requires additional time, and editing the model during the interpretation process becomes more complicated.

 To solve these problems, we can use methods of automatic fitting of the density model (inversion). At the same time, it is convenient to divide the model into many identical cells with constant density (grid). In this case, solving the inverse problem of gravity is reduced to solving a system of linear algebraic equations. To solve the system of equations, it is necessary to construct a loss function, which includes terms responsible for the difference between the observed gravitational field and the theoretical field, as well as for the difference between the model and a priori data (regularizer). Further, the problem is solved using iterative gradient optimization methods (gradient descent method, Newton's method and etc.).

However, in this case, the problem arises – final fitted model differs from the initial by contrasting near-surface layer due to the greater influence of the near-surface cells on the loss function, and the deep sources of gravity field anomalies are not included in inversion. Such models can be used in the processing of gravity data (source-based continuation, filtering), but are useless in solving of geological problems.

To take into account the influence of the deep cells of the model, the following solution is proposed: multiplying the gradient of the loss function by a normalization depth function that increases with depth. For example, such a function can be a quadratic function (its choice is conditioned by the fact that the gravity is inversely proportional to the square of the distance).

The use of inversion with a normalizing depth function allows solving the following problems:

- taking into account both surface and deep sources of gravity anomalies;

- solving the problem of taking into account the density gradient within the layers (since the layer is divided into many cells, the densities of which can be differen);

- reliably determine singular points of anomalous objects;

- significantly reduce the time of  the density model fitting.