# Geophysical integration

Geophysical integration relates to techniques used in geophysical imaging and inversion to account for diverse sources of information, and to enable the simultaneous or cooperative use of different geophysical datasets, in order to better constrain the geophysical problem and to decrease uncertainty.

## Introduction

The integration of two or more geophysical datasets in geophysical inversion was introduced in the 70’s as a means of reducing the uncertainty on inversion results (Vozoff and Jupp, 1975). The integration of multiple datasets in a single inversion scheme, called joint inversion (as opposed to single domain inversions where a single geophysical dataset is considered), has been proven to be an efficient tool to reduce uncertainty and to decrease the effect of inversion’s inherent non-uniqueness (Moorkamp, 2016). Other strategies to improve inversion results involve the integration of non-geophysical data such as stratigraphic and/or structural geological information (Fullagar et al., 2009, Balidemaj and Remis, 2010, McMillan et al., 2015, Zhang and Revil, 2015), petrophysical information and statistics (Sun and Li, 2015, 2016, Grana et al., 2010), etc., into the geophysical inversion process. Applications range from greenfield exploration in the mining sector to freshwater table and reservoir monitoring.

## Joint inversion strategies

Over the years, various approaches to joint inversion have been developed, based on different hypotheses pertaining to the type of relationships, sensitivity and possible coupling between the different geophysical datasets.

To date, most published papers use approaches exploiting structural similarities (as introduced by Gallardo and Meju, 2003) between the models generating the corresponding geophysical datasets (Moorkamp et al., 2016). Alternatively, petrophysical relationships and rock-physics laws can be used to link the different geophysical datasets at a more fundamental level (Gao et al., 2012, Dell’Aversana et al., 2011, Hoversten et al., 2006, Miotti and Giraud 2015). Others developed approach relying on statistical correlations between the physical properties being inverted for jointly (Lelièvre et al., 2012, Sun et al. 2017).

In general, the type of inversion chosen by practitioners depends on the amount of data, geological knowledge and available computational power.

### Structural approaches

Structural joint inversion approaches rely on structural relationships between the models being inverted jointly (Gallardo and Meju, 2003, Haber and Oldenburg, 1997, and Molodstov et al., 2013), and can be performed simultaneously or cooperatively. Simultaneous joint inversions permit to retrieve a model honoring geophysical datasets and the above-mentioned structural constraints by solving a single inverse problem (de Stefano et al., 2011). Meanwhile, in the cooperative approach, inversions consist in a sequential process where one model is used to constrain the other iteratively, thus solving two inverse problems in a cooperative manner (Lines et al., 1988).

### Petrophysical approaches

Petrophysical approaches to joint inversion require knowledge of the petrophysical laws linking the properties inverted for or of the statistics of relevant petrophysical attributes. Such petrophysical laws can either be empirical laws calibrated using well-log data or derived from rock physics. As for structural approaches, joint petrophysical inversions can be divided into two categories. The first one treats and inverts geophysical data directly, coupling the inverted geophysical dataset through petrophysical transforms (Hoversten et al., 2006, Gao et al., 2012) relying on constitutive equations (Carcione et al., 2007) or using the statistics of petrophysical data (Sun and Li, 2015, 2016). The second category inverts for petrophysical properties utilizing the results of geophysical inversion as input data using static models for reservoir characterization (Dell’Aversana et al., 2011, Medina et al., 2016, Miotti and Giraud, 2015) and monitoring (see Liang et al., 2016, who also include production data in the inversion scheme); in such cases, inversions are referred to as petrophysical joint inversions because the problem is posed in petrophysical domain.

## Integration of non-geophysical data in geophysical inversion

### Constraints for geophysical imaging

Non-geophysical data is widely used to improve imaging and to constrain geophysical inversion. In such cases, constraining geophysical imaging consists in using non-geophysical data in the form of prior information to impose structural features in inverted models (via structural and stratigraphic framework integration), model value range, trends, rock physics relationships, etc. to derive, for example, reservoir attributes (Mavko et al. 2005). Sources of information include, but are not limited to, results or measurements from: borehole, well-log and petrophysical data, geostatistical analysis, geological data and observation, remote sensing data, geochemical measurements, regional geological knowledge (see example of integrated basing modelling, Al Kawai and Mukerji 2016).

### Towards unified inversions

Although prior information is often used to derive hard constraints, recent developments allow quantitative integration of geological and geostatistical geological modelling in integration geophysical inversion. Inversion schemes integrating geological measurements in geophysical data in a quantitative fashion permit to honour geological and geophysical data simultaneously (Lelièvre and Oldenburg, 2009, and Scholl et al., 2016,). Current research in this topic involves the integration of petrophysical data with geological measurements in geophysical inversion (Zhou et al., 2016, Zhang and Revil, 2015, Bijani et al., 2017), allowing interaction between the different disciplines throughout the optimization process, with the aim to honour geological modelling, petrophysical and geophysical data simultaneously to reduce the effect of non-uniqueness and uncertainty (Giraud et al., 2017).

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